Curvilinear One-Dimensional Antiferromagnets
- Oleksandr V. PylypovskyiOleksandr V. PylypovskyiHelmholtz-Zentrum Dresden-Rossendorf e.V., Institute of Ion Beam Physics and Materials Research, Dresden 01328, GermanyTaras Shevchenko National University of Kyiv, Kyiv 01601, UkraineMore by Oleksandr V. Pylypovskyi,
- Denys Y. KononenkoDenys Y. KononenkoTaras Shevchenko National University of Kyiv, Kyiv 01601, UkraineInstitute for Theoretical Solid State Physics, IFW Dresden, Dresden 01069, GermanyMore by Denys Y. Kononenko,
- Kostiantyn V. YershovKostiantyn V. YershovInstitute for Theoretical Solid State Physics, IFW Dresden, Dresden 01069, GermanyBogolyubov Institute for Theoretical Physics of National Academy of Sciences of Ukraine, Kyiv 03143, UkraineMore by Kostiantyn V. Yershov,
- Ulrich K. RößlerUlrich K. RößlerInstitute for Theoretical Solid State Physics, IFW Dresden, Dresden 01069, GermanyMore by Ulrich K. Rößler,
- Artem V. TomiloArtem V. TomiloTaras Shevchenko National University of Kyiv, Kyiv 01601, UkraineMore by Artem V. Tomilo,
- Jürgen FassbenderJürgen FassbenderHelmholtz-Zentrum Dresden-Rossendorf e.V., Institute of Ion Beam Physics and Materials Research, Dresden 01328, GermanyMore by Jürgen Fassbender,
- Jeroen van den BrinkJeroen van den BrinkInstitute for Theoretical Solid State Physics, IFW Dresden, Dresden 01069, GermanyInstitute for Theoretical Physics, TU Dresden, Dresden 01069, GermanyMore by Jeroen van den Brink,
- Denys Makarov*Denys Makarov*Email: [email protected];.Helmholtz-Zentrum Dresden-Rossendorf e.V., Institute of Ion Beam Physics and Materials Research, Dresden 01328, GermanyMore by Denys Makarov, and
- Denis D. Sheka*Denis D. Sheka*Email: [email protected]Taras Shevchenko National University of Kyiv, Kyiv 01601, UkraineMore by Denis D. Sheka
Copyright © 2020 American Chemical Society
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Abstract
Antiferromagnets host exotic quasiparticles, support high frequency excitations and are key enablers of the prospective spintronic and spin–orbitronic technologies. Here, we propose a concept of a curvilinear antiferromagnetism where material responses can be tailored by a geometrical curvature without the need to adjust material parameters. We show that an intrinsically achiral one-dimensional (1D) curvilinear antiferromagnet behaves as a chiral helimagnet with geometrically tunable Dzyaloshinskii–Moriya interaction (DMI) and orientation of the Néel vector. The curvature-induced DMI results in the hybridization of spin wave modes and enables a geometrically driven local minimum of the low-frequency branch. This positions curvilinear 1D antiferromagnets as a novel platform for the realization of geometrically tunable chiral antiferromagnets for antiferromagnetic spin–orbitronics and fundamental discoveries in the formation of coherent magnon condensates in the momentum space.
Introduction
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Antiferromagnets (AFMs) have emerged as a versatile material science platform that enabled numerous fundamental discoveries including observation of monopole quasiparticles in frustrated systems (1−3) and collective quantum effects, such as spin superfluidity (4−6) and Bose–Einstein condensation (BEC) of magnetic excitations. (5,7,8) This trend is even further facilitated by the advent of antiferromagnetic spintronics (6,9−11) and related novel physical concepts of staggered spin–orbit torques. (11−13) These effects are specific to AFMs possessing broken inversion symmetry in a local environment, which is also a source of DMI. (14−16) The presence of DMI can cause noncollinear AFM states, characterized by weak ferromagnetism and (or) chiral helimagnetism. (17,18) DMI significantly affects dynamics of solitary excitations in AFMs including much higher domain wall velocities (19) and absence of the gyroforce (Magnus force) for skyrmions. (20,21) The portfolio of material systems available for these studies is very limited due to the stringent requirement on symmetry, as DMI-induced chiral textures in an AFM can exist only in magnetic materials belonging to gyrotropic crystal classes. (15,17) In addition, the efficient manipulation of arbitrary textures of any kind by spin–orbit torques also requires broken inversion symmetry of the crystal lattice or staggered spin current polarization. (22) This requirement renders the progress in AFM-related fundamental and technological research to depend on time-consuming material screening and optimization of intrinsic chiral properties of AFMs.
For ferromagnets (FMs) chiral responses in nanowires and thin films can be tailored by using curvilinear geometries. (23−26) This framework, known as curvilinear magnetism, (27−30) allows induction of magnetochiral effects in otherwise conventional achiral FMs. (25,31,32) In contrast to FMs, no theory of curvilinear antiferromagnetism is available to date. Therefore, the appealing approaches to use geometrical curvatures to enable chiral properties in AFMs have not been explored. If available, it would be possible to decouple the design of chiral responses of AFMs and their intrinsic magnetic properties. We emphasize that the case of curvilinear AFMs is fundamentally different from curvilinear FMs primarily due to the necessity to self-consistently account for the mutual interplay of several (at least two for AFM vs one for FM) fields of magnetization with the geometrical curvature. This is directly related to the physical nature of the order parameter in AFMs. In contrast to FMs, where the opposite directions of the magnetization correspond to different magnetic states, the AFM order parameter is represented only by the axis of orientation, similarly to nematic directors. (33) The latter leads to specific types of domains, absent in FMs. (34,35) The staggered magnetic ordering also allows the magnetostatic interaction between neighboring AFM systems to be neglected and enhances the resonance frequencies. (36)
In this Letter, we put forth a fundamental foundation of curvilinear 1D AFMs. We explore curvature effects in a prototypical AFM system, namely, spin chain where spins are coupled via local exchange and long-range dipolar interactions. The nearest-neighbor exchange interaction brings about two geometry-induced responses: the intrinsically achiral curvilinear AFM spin chain behaves as a chiral helimagnet with a geometrically tunable DMI and a biaxial anisotropy. We show that generic curvilinear 1D AFMs exhibit the full set of Lifshitz invariants, whose strength is determined by the local torsion and curvature. We apply our theory to analyze static and dynamic responses of helical AFM spin chains to demonstrate consequences of the coupling between the geometry and the AFM order parameter. Spin chains arranged along space curves with nonzero torsion exhibit a magnetic phase transition from homogeneous to periodic states, which is tunable by controlling geometrical parameters. The appearance of the curvature-induced DMI results in the hybridization of spin wave modes in linear dynamics and opens a possibility to investigate a coherent and long-living magnon state in the DMI-induced minimum of the dispersion curve.
Model of a Curvilinear AFM
We start with a classical spin chain taking into account the AFM nearest-neighbor exchange and dipolar interaction. Its static and dynamic properties are determined by the Landau–Lifshitz equation 
with the Hamiltonian specific to the collinear intrinsically achiral AFM
(1)Here, mi is the unit magnetic moment of ith site, ℏ is the Planck constant, S is the spin length, J < 0 is the exchange integral, μ = gμBS is the total magnetic moment of one site with g being Landé factor, and μB is Bohr magneton. The dipolar field at the ith site reads Hid = −μ∑j = l+i∞[mjrij2–3rij(mj·rij)]/rij5 with rij being the radius-vector between the ith and jth sites and the distance between neighboring sites equal a. We assume that the positions of all magnetic sites are described by a space curve γ(s) with s being the arc-length characterized by the curvature κ(s) and torsion τ(s). The local reference frame can be chosen as the Frenet–Serret frame with tangential, normal, and binormal vectors eT,N,B, see Figure 1a.
with the Hamiltonian specific to the collinear intrinsically achiral AFM(1)Here, mi is the unit magnetic moment of ith site, ℏ is the Planck constant, S is the spin length, J < 0 is the exchange integral, μ = gμBS is the total magnetic moment of one site with g being Landé factor, and μB is Bohr magneton. The dipolar field at the ith site reads Hid = −μ∑j = l+i∞[mjrij2–3rij(mj·rij)]/rij5 with rij being the radius-vector between the ith and jth sites and the distance between neighboring sites equal a. We assume that the positions of all magnetic sites are described by a space curve γ(s) with s being the arc-length characterized by the curvature κ(s) and torsion τ(s). The local reference frame can be chosen as the Frenet–Serret frame with tangential, normal, and binormal vectors eT,N,B, see Figure 1a.Figure 1
Figure 1. (a) Schematics of the antiferromagnetic spin chain γ. Magnetic sublattices with magnetization mI and mII are shown by magenta and light-blue arrows. The Dzyaloshinskii vector d (dark-blue) lies in the TB plane given by the TNB basis eT,N,B. Hard and easy anisotropy axes are labeled by e1 and e3, respectively. (b) Helix spin chain with radius R and pitch P. The AFM order parameter (Néel vector) n parametrized by angles θ and ϕ is shown by the green arrow. (c) Diagram of equilibrium states for a helix spin chain. Open symbols and triangles correspond to periodic and homogeneous states, respectively, obtained in spin–lattice simulations. The solid red curve shows the boundary between the states. The dashed green line shows the asymptotic of the boundary τb ≈ 0.85κ for κ 
≪ 1. Schematics of the (d, e) homogeneous and (f, g) periodic states in the TNB reference frame. (d, f) Bloch spheres illustrate the trajectories of n. The tilt angle 
.
The continuum counterpart of the spin–lattice model is formulated on the basis of two vector fields, namely, the total magnetization m(s) = (mI + mII)/2 and Néel vector n(s) = (mI – mII)/2. The fields mI,II = mI,II(s) correspond to the two sublattices of the AFM. In the long-wave approximation, the density of Lagrangian 
, corresponding to the curvilinear AFM reads
(2a)with the overdot corresponding to the derivative with respect to time. The effective energy density 
is written as
(2b)where Ms = μ/(2a) is the magnetization of one sublattice, γ0 is the gyromagnetic ratio, Λ = 2|J|S2/a is the constant of the uniform exchange, A = |J|S2a/2 is the exchange stiffness, and K ≈ 2.7 μ2/a4 is the hard axis anisotropy constant induced by the dipolar interaction, see the Supporting Information. Model (2) is valid for K ≪Λ and the space curve γ possessing consequent turns separated by a distance significantly larger than the lattice constant a. In this approximation, |m| ≪ |n| and n can be considered as a unit director. In model (2b), the Einstein summation rule is applied and prime means derivative with respect to s. The Frenet tensor 
has four nonzero components 
and 
. The characteristic length and time scales are given by the magnetic length 
and the frequency of the AFM resonance 
with 
being the characteristic magnon speed. The exchange energy density expands into three terms, with only one, 
, possessing the form of a regular inhomogeneous exchange in straight spin chains.
, corresponding to the curvilinear AFM reads(2a)with the overdot corresponding to the derivative with respect to time. The effective energy density is written as(2b)where Ms = μ/(2a) is the magnetization of one sublattice, γ0 is the gyromagnetic ratio, Λ = 2|J|S2/a is the constant of the uniform exchange, A = |J|S2a/2 is the exchange stiffness, and K ≈ 2.7 μ2/a4 is the hard axis anisotropy constant induced by the dipolar interaction, see the Supporting Information. Model (2) is valid for K ≪Λ and the space curve γ possessing consequent turns separated by a distance significantly larger than the lattice constant a. In this approximation, |m| ≪ |n| and n can be considered as a unit director. In model (2b), the Einstein summation rule is applied and prime means derivative with respect to s. The Frenet tensor has four nonzero components and . The characteristic length and time scales are given by the magnetic length and the frequency of the AFM resonance with being the characteristic magnon speed. The exchange energy density expands into three terms, with only one, , possessing the form of a regular inhomogeneous exchange in straight spin chains.The term 
can be written as the functional form of a DMI, 
. This term is allowed in crystals with magnetic symmetry groups Cn and S4 acting on 1D magnetic textures. (15) However, its origin is not the spin–orbit interaction as for the case of intrinsic DMI but the exchange interaction. The vector d = dTeT + dBeB acts as the Dzyaloshinskii vector with components dT = 2Aτ and dB = 2Aκ. This DMI corresponds to the full set of Lifshitz invariants, allowed in a 1D magnet. The DMI vector d is linear with respect to τ and κ, which allows strong chiral effects in curvilinear 1D AFMs. The strength of the curvature-induced DMI can be estimated as the relation to the exchange stiffness. For instance, in the case of a Mn-DNA chain (A-DNA form) bent to the radius of 15 nm, the adT,B/A is about 0.05. (Magnetic parameters of Mn-DNA S = 5/2, a = 0.344 nm, and |J| = 9.6 × 10–25 J are taken from ref (37).) This value is comparable with the intrinsic chiral properties of KMnF3 used for the discussion of dynamics of 1D solitons (19,38) (aD/A = 0.036 with D being the constant of the nonuniform DMI), where ultrafast motion of AFM domain walls was predicted. (19)
can be written as the functional form of a DMI, . This term is allowed in crystals with magnetic symmetry groups Cn and S4 acting on 1D magnetic textures. (15) However, its origin is not the spin–orbit interaction as for the case of intrinsic DMI but the exchange interaction. The vector d = dTeT + dBeB acts as the Dzyaloshinskii vector with components dT = 2Aτ and dB = 2Aκ. This DMI corresponds to the full set of Lifshitz invariants, allowed in a 1D magnet. The DMI vector d is linear with respect to τ and κ, which allows strong chiral effects in curvilinear 1D AFMs. The strength of the curvature-induced DMI can be estimated as the relation to the exchange stiffness. For instance, in the case of a Mn-DNA chain (A-DNA form) bent to the radius of 15 nm, the adT,B/A is about 0.05. (Magnetic parameters of Mn-DNA S = 5/2, a = 0.344 nm, and |J| = 9.6 × 10–25 J are taken from ref (37).) This value is comparable with the intrinsic chiral properties of KMnF3 used for the discussion of dynamics of 1D solitons (19,38) (aD/A = 0.036 with D being the constant of the nonuniform DMI), where ultrafast motion of AFM domain walls was predicted. (19)In addition to the linear in τ and κ DMI terms, the expression for energy density 
contains weaker bilinear terms, representing a curvature-induced anisotropy 
whose coefficients are given by the tensor 
, κτ. It contains nondiagonal terms, causing the tilt of n within the rectifying surface formed by eT and eB. The presence of the two anisotropies (hard axis stemming from the dipolar interaction and easy axis stemming from the exchange interaction) renders a curvilinear AFM spin chain to behave as a biaxial AFM. The directions of the primary hard axis e1 and secondary easy axis e3 are determined by the diagonalization of the tensor of the total anisotropy 
with δαβ being Kronecker delta, see Figure 1a. The axis e1 lies within the rectifying surface. The anisotropy induced by the dipolar interaction is the strongest one and defines the plane, where the Néel vector rotates. The direction of the vector n within the easy plane is given by the curvature-induced anisotropy 
. The system has no competing easy axis anisotropy terms. This means that independent of the strength of 
it govern the orientation of the Néel vector even for Aκ2, Aτ2 ≪ K.
contains weaker bilinear terms, representing a curvature-induced anisotropy whose coefficients are given by the tensor , κτ. It contains nondiagonal terms, causing the tilt of n within the rectifying surface formed by eT and eB. The presence of the two anisotropies (hard axis stemming from the dipolar interaction and easy axis stemming from the exchange interaction) renders a curvilinear AFM spin chain to behave as a biaxial AFM. The directions of the primary hard axis e1 and secondary easy axis e3 are determined by the diagonalization of the tensor of the total anisotropy with δαβ being Kronecker delta, see Figure 1a. The axis e1 lies within the rectifying surface. The anisotropy induced by the dipolar interaction is the strongest one and defines the plane, where the Néel vector rotates. The direction of the vector n within the easy plane is given by the curvature-induced anisotropy . The system has no competing easy axis anisotropy terms. This means that independent of the strength of it govern the orientation of the Néel vector even for Aκ2, Aτ2 ≪ K.As a result, a generic curvilinear achiral 1D AFM will behave as a chiral helimagnet with the DMI strength and the orientation of the Néel vector determined by the geometrical parameters, i.e., curvature and torsion.
Ground State of AFM Helix Chains
To illustrate the behavior of curvilinear AFM spin chains, described by (2), we analyzed a helix chain as the prototypical curvilinear systems possessing a constant curvature and torsion. The geometry of a helix is characterized by the radius R = κ/(κ2 + τ2) and pitch P = 2πτ/(κ2 + τ2), see Figure 1b. It is convenient to introduce the angular parametrization of the Néel vector n = eTcos θ + eNsin θcos ϕ + eB sin θ sin ϕ with θ = θ(s, t) and ϕ = ϕ(s, t) being polar and azimuthal angles, respectively. Taking into account the Néel vector is a director, states with (θ, ϕ) and (π – θ, ϕ ± π) are equivalent. The linear energy density then reads
(3)As a biaxial chiral helimagnet, helix spin chains support homogeneous and periodic equilibrium states dependent on the strength of the DMI, see Figure 1c. For the case of the homogeneous state, which is realized for τ < τb(κ) ≈ 0.85κ at 
, see Figure 1d, e and the Supporting Information, the orientation of the Néel vector is given by θhom = π/2 – ψ and ϕhom = π/2, where 
and 
, 
.
(3)As a biaxial chiral helimagnet, helix spin chains support homogeneous and periodic equilibrium states dependent on the strength of the DMI, see Figure 1c. For the case of the homogeneous state, which is realized for τ < τb(κ) ≈ 0.85κ at , see Figure 1d, e and the Supporting Information, the orientation of the Néel vector is given by θhom = π/2 – ψ and ϕhom = π/2, where and , .The periodic state can be stabilized in systems possessing torsion τ > τb(κ). In the periodic state, the Néel vector is almost uniform in the plane perpendicular to the helix axis and modulated in the local reference frame, see Figure 1f, g. The emergence of the periodic state is a consequence of the exchange-induced DMI, 
, with the main contribution given by the torsion-related term dT. When the curvature is much smaller than the torsion, the state can be described as the Dzyaloshinskii spiral (39) with θper = π/2 and ϕper = −τs. The boundary between the homogeneous and periodic states τb(κ) is plotted by the solid red line in Figure 1c.
, with the main contribution given by the torsion-related term dT. When the curvature is much smaller than the torsion, the state can be described as the Dzyaloshinskii spiral (39) with θper = π/2 and ϕper = −τs. The boundary between the homogeneous and periodic states τb(κ) is plotted by the solid red line in Figure 1c.It is instructive to compare the results above with FM spin chains, where dipolar interactions induce easy axis anisotropy. In contrast to a FM helices, (24) the phase transition between the periodic and homogeneous states in AFMs has no threshold in curvature. Hence, the transition to the periodic state in the case of AFM helical chains can be observed for very small curvatures. This is a consequence of the specificity of the curvilinear AFM systems where the stability of the state is given by the weak easy axis anisotropy stemming from the exchange interaction. Therefore, effects of curvilinearity in AFMs are much stronger than in FMs.
Linear Dynamics
To describe linear excitations in a curved AFM helix chain, we consider the homogeneous magnetic state. The Euler–Lagrange equations for the Lagrangian (2a) are linearized by θ(s, t) = θhom + ϑ(s, t) and ϕ(s, t) = ϕhom + φ(s, t)/ sin θhom. Here, ϑ(s, t) and φ(s, t) are small deviations from the equilibrium state. The corresponding equations read
(4)where K0,3 and D3 are functions of curvature, acting as the effective anisotropy and DMI coefficients, respectively, see the Supporting Information. For a large curvature radius and small torsion, 
, K3 ≈ Aκ2 and D3 ≈ 2Aκ. The dispersion law can be written using the substitution of plane waves ϑ(s, t) = ϑk cos(ks – Ωt) and φ(s, t) = φk sin(ks – Ωt), where ϑk and φk are small amplitudes, k is the wavenumber, and Ω is frequency. The dispersion reads
(5)We note that the dispersion curve is similar to flat biaxial AFMs with DMI (19) and remains symmetric with respect to the sign of the momentum k. Yet, the geometrical tunability of the anisotropy and DMI allows to unveil new physics of collective excitations in curvilinear 1D AFMs.
(4)where K0,3 and D3 are functions of curvature, acting as the effective anisotropy and DMI coefficients, respectively, see the Supporting Information. For a large curvature radius and small torsion, , K3 ≈ Aκ2 and D3 ≈ 2Aκ. The dispersion law can be written using the substitution of plane waves ϑ(s, t) = ϑk cos(ks – Ωt) and φ(s, t) = φk sin(ks – Ωt), where ϑk and φk are small amplitudes, k is the wavenumber, and Ω is frequency. The dispersion reads(5)We note that the dispersion curve is similar to flat biaxial AFMs with DMI (19) and remains symmetric with respect to the sign of the momentum k. Yet, the geometrical tunability of the anisotropy and DMI allows to unveil new physics of collective excitations in curvilinear 1D AFMs.The spin-wave spectrum (5) superimposed with spin–lattice simulations (see the Supporting Information) is shown in Figure 2a for two helix geometries (Figure 2b). The high-frequency optical branch with q = 1 is always gapped and the change of the geometry affects only the gap due to the curvature-induced anisotropy, 
. In contrast, there is a strong qualitative impact of the curvature on the low frequency branch. While it is gapless for a straight spin chain, (40) the gap Ωq=–1gap ≈ cκ appears for any finite curvature as a results of the spin-wave hybridization, forming a low-frequency optical branch with q = −1, see Figure 2a. The curvature-induced DMI results in the emergence of a region with a negative group velocity followed by a local minimum at k = kmin on the dispersion curve with the depth δ, see Figure 2a, c. The presence of a negative group velocity is also observed for multiferroics (41) and exchange-dipolar modes in AFM thin films. (42,43) The depth of the minimum increases with κ and τ, see Figure 2d. The possibility to realize magnon ground states not in equilibrium (k ≠ 0 at minimum energy) (44) renders curvilinear 1D AFMs a flexible platform to study coherent excitations for spin superfluidity (45−47) and BEC of magnons (48−51) with taking into account a proper pumping and magnon thermodynamics.
. In contrast, there is a strong qualitative impact of the curvature on the low frequency branch. While it is gapless for a straight spin chain, (40) the gap Ωq=–1gap ≈ cκ appears for any finite curvature as a results of the spin-wave hybridization, forming a low-frequency optical branch with q = −1, see Figure 2a. The curvature-induced DMI results in the emergence of a region with a negative group velocity followed by a local minimum at k = kmin on the dispersion curve with the depth δ, see Figure 2a, c. The presence of a negative group velocity is also observed for multiferroics (41) and exchange-dipolar modes in AFM thin films. (42,43) The depth of the minimum increases with κ and τ, see Figure 2d. The possibility to realize magnon ground states not in equilibrium (k ≠ 0 at minimum energy) (44) renders curvilinear 1D AFMs a flexible platform to study coherent excitations for spin superfluidity (45−47) and BEC of magnons (48−51) with taking into account a proper pumping and magnon thermodynamics.Figure 2
Figure 2. (a) Spin-wave dispersion (5) for helical AFM spin chains with 
and two curvatures 
(black) and 
(red). The result of spin–lattice simulations is shown by the background color for a helical spin chain with the geometry with 
and 
. (b) Helix geometries calculated in a. (c) Spin-wave dispersion (5) and simulations for 
and 
. The depth of the minimum in the acoustic branch is shown by δ. (d) The depth δ for different curvatures and torsions within the homogeneous ground state (below red line, same as in Figure 1c). Dashed line corresponds to the absence of minimum.
Conclusions
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We develop a theory of curvilinear one-dimensional antiferromagnets. We demonstrate that the intrinsically achiral curvilinear AFM spin chain behaves as a biaxial chiral helimagnet with geometrically tunable DMI and anisotropy. The curvature-induced DMI results in the hybridization of magnon modes in the chain. The low-frequency branch possesses a local minimum supporting a long-living magnon state, which allows consideration of 1D curvilinear AFMs as the platform for the realization of BEC of magnons in k-space. Furthermore, the symmetry and strength of the geometry-induced DMI opens perspectives for applications in antiferromagnetic spin–orbitronics, e.g. for ultrafast dynamics of chiral domain walls. (19,38) We consider copper-based (52) and DNA-based metal–organic frameworks (53−56) as a promising materials for experimental validation of our predictions. For instance, one can expect the strength of curvature-induced DMI as adT, B/A ≈ 0.05, which is comparable with AFMs supporting chiral domain walls.
Supporting Information
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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.0c03246.
Details on analytical calculations and numerical simulations, including (i) the geometry, (ii) the model of curvilinear antiferromagnet, (iii) dipolar interaction in spin chains as an effective anisotropy (both ferromagnetic and antiferromagnetic ordering, and curvilinear antiferromagnetic spin chains), (iv) the homogeneous state of antiferromagnetic helix chains, (v) the periodic state of antiferromagnetic helix chains, (vi) the boundary between states, (vii) The ground state of antiferromagnetic flat chains, (viii) spin waves in antiferromagnetic flat chains, (ix) spin waves in antiferromagnetic helices and stability of the homogeneous state, and (x) simulations (PDF)
Terms & Conditions
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Author Information
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- Denys Makarov - Helmholtz-Zentrum Dresden-Rossendorf e.V., Institute of Ion Beam Physics and Materials Research, Dresden 01328, Germany;
http://orcid.org/0000-0002-7177-4308;
- Denis D. Sheka - Taras Shevchenko National University of Kyiv, Kyiv 01601, Ukraine;http://orcid.org/0000-0001-7311-0639;
- Oleksandr V. Pylypovskyi - Helmholtz-Zentrum Dresden-Rossendorf e.V., Institute of Ion Beam Physics and Materials Research, Dresden 01328, Germany; Taras Shevchenko National University of Kyiv, Kyiv 01601, Ukraine;http://orcid.org/0000-0002-5947-9760
- Denys Y. Kononenko - Taras Shevchenko National University of Kyiv, Kyiv 01601, Ukraine; Institute for Theoretical Solid State Physics, IFW Dresden, Dresden 01069, Germany;http://orcid.org/0000-0002-4467-730X
- Kostiantyn V. Yershov - Institute for Theoretical Solid State Physics, IFW Dresden, Dresden 01069, Germany; Bogolyubov Institute for Theoretical Physics of National Academy of Sciences of Ukraine, Kyiv 03143, Ukraine;http://orcid.org/0000-0003-2731-2808
- Artem V. Tomilo - Taras Shevchenko National University of Kyiv, Kyiv 01601, Ukraine;http://orcid.org/0000-0002-5390-2767
Acknowledgments
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We thank U. Nitzsche for technical support. D.Y.K. and K.V.Y. acknowledge financial support from UKRATOP-project (funded by BMBF under reference 01DK18002). In part, this work was supported by the Program of Fundamental Research of the Department of Physics and Astronomy of the National Academy of Sciences of Ukraine (Project 0120U100855), by the Alexander von Humboldt Foundation (Research Group Linkage Programme), DFG MA 5144/22-1, DFG MA 5144/24-1, DFG MC 9/22-1, and by Taras Shevchenko National University of Kyiv (Project 19BF052-01).
References
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This article references 56 other publications.
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- 12Zhang, X.; Liu, Q.; Luo, J.-W.; Freeman, A. J.; Zunger, A. Hidden spin polarization in inversion-symmetric bulk crystals. Nat. Phys. 2014, 10, 387– 393, DOI: 10.1038/nphys2933[Crossref], [CAS], Google Scholar12https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXmtlWntr0%253D&md5=95fe80ef57edadc61f38b7d2995617e9Hidden spin polarization in inversion-symmetric bulk crystalsZhang, Xiuwen; Liu, Qihang; Luo, Jun-Wei; Freeman, Arthur J.; Zunger, AlexNature Physics (2014), 10 (5), 387-393CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)Spin-orbit coupling can induce spin polarization in nonmagnetic 3D crystals when the inversion symmetry is broken, as manifested by the bulk Rashba and Dresselhaus effects. We establish that these spin-polarization effects originate fundamentally from specific at. site asymmetries, rather than, as generally accepted, from the asymmetry of the crystal space group. This understanding leads to the recognition that a previously overlooked hidden form of spin polarization should exist in centrosym. crystals. Although all energy bands must be doubly degenerate in centrosym. materials, we find that the two components of such doubly degenerate bands could have opposite polarizations, each spatially localized on one of the two sep. sectors forming the inversion partners. We demonstrate such hidden spin polarizations in particular centrosym. crystals by first-principles calcns. This new understanding could considerably broaden the range of currently useful spintronic materials and enable the control of spin polarization by means of operations on the at. scale.
- 13Železný, J.; Gao, H.; Výborný, K.; Zemen, J.; Mašek, J.; Manchon, A.; Wunderlich, J.; Sinova, J.; Jungwirth, T. Relativistic Néel-Order Fields Induced by Electrical Current in Antiferromagnets. Phys. Rev. Lett. 2014, 113, 157201, DOI: 10.1103/PhysRevLett.113.157201[Crossref], [PubMed], [CAS], Google Scholar13https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhvFKqsLrN&md5=13d36f741bbe1f93b73d014f35f5a6a2Relativistic Neel-order fields induced by electrical current in antiferromagnetsZelezny, J.; Gao, H.; Vyborny, K.; Zemen, J.; Masek, J.; Manchon, Aurelien; Wunderlich, J.; Sinova, Jairo; Jungwirth, T.Physical Review Letters (2014), 113 (15), 157201/1-157201/5, 5 pp.CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)We predict that a lateral elec. current in antiferromagnets can induce nonequil. Neel-order fields, i.e., fields whose sign alternates between the spin sublattices, which can trigger ultrafast spin-axis reorientation. Based on microscopic transport theory calcns. we identify staggered current-induced fields analogous to the intraband and to the intrinsic interband spin-orbit fields previously reported in ferromagnets with a broken inversion-symmetry crystal. To illustrate their rich physics and utility, we consider bulk Mn2Au with the two spin sublattices forming inversion partners, and a 2D square-lattice antiferromagnet with broken structural inversion symmetry modeled by a Rashba spin-orbit coupling. We propose an antiferromagnetic memory device with elec. writing and reading.
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- 16Qaiumzadeh, A.; Ado, I. A.; Duine, R. A.; Titov, M.; Brataas, A. Theory of the Interfacial Dzyaloshinskii-Moriya Interaction in Rashba Antiferromagnets. Phys. Rev. Lett. 2018, 120, 197202, DOI: 10.1103/PhysRevLett.120.197202[Crossref], [PubMed], [CAS], Google Scholar16https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXltVyqurw%253D&md5=0ca1baa3529c71f961398a7e8452b145Theory of the Interfacial Dzyaloshinskii-Moriya Interaction in Rashba AntiferromagnetsQaiumzadeh, Alireza; Ado, Ivan A.; Duine, Rembert A.; Titov, Mikhail; Brataas, ArnePhysical Review Letters (2018), 120 (19), 197202CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)In antiferromagnetic (AFM) thin films, broken inversion symmetry or coupling to adjacent heavy metals can induce Dzyaloshinskii-Moriya (DM) interactions. Knowledge of the DM parameters is essential for understanding and designing exotic spin structures, such as hedgehog Skyrmions and chiral Neel walls, which are attractive for use in novel information storage technologies. We introduce a framework for computing the DM interaction in two-dimensional Rashba antiferromagnets. Unlike in Rashba ferromagnets, the DM interaction is not suppressed even at low temps. The material parameters control both the strength and the sign of the interfacial DM interaction. Our results suggest a route toward controlling the DM interaction in AFM materials by means of doping and elec. fields.
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- 20Barker, J.; Tretiakov, O. A. Static and Dynamical Properties of Antiferromagnetic Skyrmions in the Presence of Applied Current and Temperature. Phys. Rev. Lett. 2016, 116, 147203, DOI: 10.1103/PhysRevLett.116.147203[Crossref], [PubMed], [CAS], Google Scholar20https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhtlOjsrnF&md5=7721fa26419ad12b93d1ba99a95fd238Static and dynamical properties of antiferromagnetic skyrmions in the presence of applied current and temperatureBarker, Joseph; Tretiakov, Oleg A.Physical Review Letters (2016), 116 (14), 147203/1-147203/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)Skyrmions are topol. protected entities in magnetic materials which have the potential to be used in spintronics for information storage and processing. However, Skyrmions in ferromagnets have some intrinsic difficulties which must be overcome to use them for spintronic applications, such as the inability to move straight along current. We show that Skyrmions can also be stabilized and manipulated in antiferromagnetic materials. An antiferromagnetic Skyrmion is a compd. topol. object with a similar but of opposite sign spin texture on each sublattice, which, e.g., results in a complete cancellation of the Magnus force. We find that the composite nature of antiferromagnetic Skyrmions gives rise to different dynamical behavior due to both an applied current and temp. effects.
- 21Shen, L.; Li, X.; Zhao, Y.; Xia, J.; Zhao, G.; Zhou, Y. Current-Induced Dynamics of the Antiferromagnetic Skyrmion and Skyrmionium. Phys. Rev. Appl. 2019, 12, 064033, DOI: 10.1103/PhysRevApplied.12.064033[Crossref], [CAS], Google Scholar21https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXjt1Sls7Y%253D&md5=10894e7c60f099ac6cd2218080901a4cCurrent-Induced Dynamics of the Antiferromagnetic Skyrmion and SkyrmioniumShen, Laichuan; Li, Xiaoguang; Zhao, Yuelei; Xia, Jing; Zhao, Guoping; Zhou, YanPhysical Review Applied (2019), 12 (6), 064033CODEN: PRAHB2; ISSN:2331-7019. (American Physical Society)Antiferromagnetic (AFM) skyrmionium composed of two topol. AFM skyrmions shares the merits of an AFM skyrmion, for example, high mobility and no skyrmion Hall effect. Here, we anal. and numerically study the dynamics of the AFM skyrmion and skyrmionium induced by spin currents. Our calcns. demonstrate that the current-induced spin-transfer torques can drive AFM skyrmion and skyrmionium with the same speed, while their steady motion speeds induced by spin-orbit torques are different. Furthermore, it is found that due to the existence of the effective AFM texture mass, the AFM skyrmion and skyrmionium obey the momentum theorem, and the time evolution of the position induced by alternating currents presents a phase. Besides, a spin torque nano-oscillator based on the AFM skyrmionium can produce high frequencies, similar to that based on the AFM skyrmion. Numerical simulations are in good agreement with the anal. solns. Our results demonstrate the inertial dynamics of the AFM skyrmion and skyrmionium and may provide guidelines for building skyrmion-based spintronic devices.
- 22Železný, J.; Wadley, P.; Olejník, K.; Hoffmann, A.; Ohno, H. Spin transport and spin torque in antiferromagnetic devices. Nat. Phys. 2018, 14, 220– 228, DOI: 10.1038/s41567-018-0062-7[Crossref], [CAS], Google Scholar22https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXhtFGkt77F&md5=e49a6ab3baa51580956a529b76bda4a6Spin transport and spin torque in antiferromagnetic devicesZelezny, J.; Wadley, P.; Olejnik, K.; Hoffmann, A.; Ohno, H.Nature Physics (2018), 14 (3), 220-228CODEN: NPAHAX; ISSN:1745-2473. (Nature Research)Ferromagnets are key materials for sensing and memory applications. In contrast, antiferromagnets, which represent the more common form of magnetically ordered materials, have found less practical application beyond their use for establishing ref. magnetic orientations via exchange bias. This might change in the future due to the recent progress in materials research and discoveries of antiferromagnetic spintronic phenomena suitable for device applications. Exptl. demonstration of the elec. switching and detection of the Ne´el order open a route towards memory devices based on antiferromagnets. Apart from the radiation and magnetic-field hardness, memory cells fabricated from antiferromagnets can be inherently multilevel, which could be used for neuromorphic computing. Switching speeds attainable in antiferromagnets far exceed those of ferromagnetic and semiconductor memory technologies. Here, we review the recent progress in electronic spin-transport and spin-torque phenomena in antiferromagnets that are dominantly of the relativistic quantum-mech. origin. We discuss their utility in pure antiferromagnetic or hybrid ferromagnetic/antiferromagnetic memory devices.
- 23Gaididei, Y.; Kravchuk, V. P.; Sheka, D. D. Curvature Effects in Thin Magnetic Shells. Phys. Rev. Lett. 2014, 112, 257203, DOI: 10.1103/PhysRevLett.112.257203[Crossref], [PubMed], [CAS], Google Scholar23https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhs1Gjt7fM&md5=454db99e9d3f6978df05cd0278f225daCurvature effects in thin magnetic shellsGaididei, Yuri; Kravchuk, Volodymyr P.; Sheka, Denis D.Physical Review Letters (2014), 112 (25), 257203/1-257203/5, 5 pp.CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)A magnetic energy functional is derived for an arbitrary curved thin shell on the assumption that the magnetostatic effects can be reduced to an effective easy-surface anisotropy; it can be used for solving both static and dynamic problems. General static solns. are obtained in the limit of a strong anisotropy of both signs (easy-surface and easy-normal cases). It is shown that the effect of the curvature can be treated as the appearance of an effective magnetic field, which is aligned along the surface normal for the case of easy-surface anisotropy and is tangential to the surface for the case of easy-normal anisotropy. In general, the existence of such a field excludes the solns. that are strictly tangential or strictly normal to the surface. As an example, we consider static equil. solns. for a cone surface magnetization.
- 24Sheka, D. D.; Kravchuk, V. P.; Yershov, K. V.; Gaididei, Y. Torsion-induced effects in magnetic nanowires. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 92, 054417, DOI: 10.1103/PhysRevB.92.054417[Crossref], [CAS], Google Scholar24https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XislGisLo%253D&md5=850dfc3eaccb46a9ac2bdd2a548853c9Torsion-induced effects in magnetic nanowiresSheka, Denis D.; Kravchuk, Volodymyr P.; Yershov, Kostiantyn V.; Gaididei, YuriPhysical Review B: Condensed Matter and Materials Physics (2015), 92 (5), 054417/1-054417/13CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)A magnetic helix wire is one of the simplest magnetic systems which manifests properties of both curvature and torsion. Possible equil. magnetization states in the helix wire with different anisotropy directions are studied theor. There exist two equil. states in the helix wire with easy-tangential anisotropy: a quasitangential magnetization distribution in the case of relatively small curvatures and torsions, and an onion state in the opposite case. The curvature and torsion also essentially influence the spin-wave dynamics in the helix wire, acting as an effective magnetic field. Originated from a geometry-induced effective Dzyaloshinskii interaction, this magnetic field leads to a coupling between the helix chirality and the magnetochirality and breaks mirror symmetry in the spin-wave spectrum: the modification of magnon dispersion relation is linear with respect to the torsion and quadratic with respect to the curvature. All anal. predictions on magnetization statics and dynamics are well confirmed by direct spin-lattice simulations.
- 25Pylypovskyi, O. V.; Sheka, D. D.; Kravchuk, V. P.; Yershov, K. V.; Makarov, D.; Gaididei, Y. Rashba Torque Driven Domain Wall Motion in Magnetic Helices. Sci. Rep. 2016, 6, 23316, DOI: 10.1038/srep23316[Crossref], [PubMed], [CAS], Google Scholar25https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XkvVCnu7Y%253D&md5=398ebbd6984819946538931fc4527bffRashba Torque Driven Domain Wall Motion in Magnetic HelicesPylypovskyi, Oleksandr V.; Sheka, Denis D.; Kravchuk, Volodymyr P.; Yershov, Kostiantyn V.; Makarov, Denys; Gaididei, YuriScientific Reports (2016), 6 (), 23316CODEN: SRCEC3; ISSN:2045-2322. (Nature Publishing Group)Manipulation of the domain wall propagation in magnetic wires is a key practical task for a no. of devices including racetrack memory and magnetic logic. Recently, curvilinear effects emerged as an efficient mean to impact substantially the statics and dynamics of magnetic textures. Here, we demonstrate that the curvilinear form of the exchange interaction of a magnetic helix results in an effective anisotropy term and Dzyaloshinskii-Moriya interaction with a complete set of Lifshitz invariants for a one-dimensional system. In contrast to their planar counterparts, the geometrically induced modifications of the static magnetic texture of the domain walls in magnetic helixes offer unconventional means to control the wall dynamics relying on spin-orbit Rashba torque. The chiral symmetry breaking due to the Dzyaloshinskii-Moriya interaction leads to the opposite directions of the domain wall motion in left- or right-handed helixes. Furthermore, for the magnetic helixes, the emergent effective anisotropy term and Dzyaloshinskii-Moriya interaction can be attributed to the clear geometrical parameters like curvature and torsion offering intuitive understanding of the complex curvilinear effects in magnetism.
- 26Sheka, D. D.; Pylypovskyi, O. V.; Landeros, P.; Gaididei, Y.; Kákay, A.; Makarov, D. Nonlocal chiral symmetry breaking in curvilinear magnetic shells. Communications Physics 2020, 3, 128, DOI: 10.1038/s42005-020-0387-2
- 27Streubel, R.; Fischer, P.; Kronast, F.; Kravchuk, V. P.; Sheka, D. D.; Gaididei, Y.; Schmidt, O. G.; Makarov, D. Magnetism in curved geometries (Topical Review). J. Phys. D: Appl. Phys. 2016, 49, 363001, DOI: 10.1088/0022-3727/49/36/363001[Crossref], [CAS], Google Scholar27https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhvFOrtLjP&md5=88a88f4487ed4803ab3cd3decc60eb35Magnetism in curved geometriesStreubel, Robert; Fischer, Peter; Kronast, Florian; Kravchuk, Volodymyr P.; Sheka, Denis D.; Gaididei, Yuri; Schmidt, Oliver G.; Makarov, DenysJournal of Physics D: Applied Physics (2016), 49 (36), 363001/1-363001/45CODEN: JPAPBE; ISSN:0022-3727. (IOP Publishing Ltd.)Extending planar two-dimensional structures into the three-dimensional space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring the geometry of an object, e.g. its local curvature. In a generic electronic system, curvature results in the appearance of scalar and vector geometric potentials inducing anisotropic and chiral effects. In the specific case of magnetism, even in the simplest case of a curved anisotropic Heisenberg magnet, the curvilinear geometry manifests two exchange-driven interactions, namely effective anisotropy and antisym. exchange, i.e. Dzyaloshinskii-Moriya-like interaction. As a consequence, a family of novel curvature-driven effects emerges, which includes magnetochiral effects and topol. induced magnetization patterning, resulting in theor. predicted unlimited domain wall velocities, chirality symmetry breaking and Cherenkov-like effects for magnons. The broad range of altered phys. properties makes these curved architectures appealing in view of fundamental research on e.g. skyrmionic systems, magnonic crystals or exotic spin configurations. In addn. to these rich physics, the application potential of three-dimensionally shaped objects is currently being explored as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalog. devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices. These recent developments ranging from theor. predictions over fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, to their characterization using integral means as well as the development of advanced tomog. approaches are in the focus of this review.
- 28Fernández-Pacheco, A.; Streubel, R.; Fruchart, O.; Hertel, R.; Fischer, P.; Cowburn, R. P. Three-dimensional nanomagnetism. Nat. Commun. 2017, 8, 15756, DOI: 10.1038/ncomms15756[Crossref], [PubMed], [CAS], Google Scholar28https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BC1cnmslShsw%253D%253D&md5=1ac8c3c39e7c20144be54437b8f077b8Three-dimensional nanomagnetismFernandez-Pacheco Amalio; Cowburn Russell P; Streubel Robert; Fischer Peter; Fruchart Olivier; Hertel Riccardo; Fischer PeterNature communications (2017), 8 (), 15756 ISSN:.There is no expanded citation for this reference.
- 29Fischer, P.; Sanz-Hernández, D.; Streubel, R.; Fernández-Pacheco, A. Launching a new dimension with 3D magnetic nanostructures. APL Mater. 2020, 8, 010701, DOI: 10.1063/1.5134474[Crossref], [CAS], Google Scholar29https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXht1GjtLc%253D&md5=cb70d547d263a5d9890a25183bbd2e1cLaunching a new dimension with 3D magnetic nanostructuresFischer, Peter; Sanz-Hernandez, Dedalo; Streubel, Robert; Fernandez-Pacheco, AmalioAPL Materials (2020), 8 (1), 010701CODEN: AMPADS; ISSN:2166-532X. (American Institute of Physics)A review. The scientific and technol. exploration of three-dimensional magnetic nanostructures is an emerging research field that opens the path to exciting novel phys. phenomena, originating from the increased complexity in spin textures, topol., and frustration in three dimensions. One can also anticipate a tremendous potential for novel applications with those systems in a magnetic sensor and information processing technologies in terms of improved energy efficiency, processing speed, functionalities, and miniaturization of future spintronic devices. These three-dimensional structures are distinct from traditional bulk systems as they harness the scientific achievements of nanomagnetism, which aimed at lowering the dimensions down to the at. scale, but expand those now in a tailored and designed way into the third dimension. This research update provides an overview of the scientific challenges and recent progress with regard to advances in synthesis approaches and state-of-the-art nanoscale characterization techniques that are prerequisite to understand, realize, and control the properties, behavior, and functionalities of three-dimensional magnetic nanostructures. (c) 2020 American Institute of Physics.
- 30Vedmedenko, E. Y.; Kawakami, R. K.; Sheka, D.; Gambardella, P.; Kirilyuk, A.; Hirohata, A.; Binek, C.; Chubykalo-Fesenko, O. A.; Sanvito, S.; Kirby, B.; Grollier, J.; Everschor-Sitte, K.; Kampfrath, T.; You, C.-Y.; Berger, A. The 2020 Magnetism Roadmap. J. Phys. D: Appl. Phys. 2020, 53, 453001, DOI: 10.1088/1361-6463/ab9d98[Crossref], [CAS], Google Scholar30https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXisVykurbE&md5=b753b25a6da73ed203598d62d9851603The 2020 magnetism roadmapVedmedenko, E. Y.; Kawakami, R. K.; Sheka, D. D.; Gambardella, P.; Kirilyuk, A.; Hirohata, A.; Binek, C.; Chubykalo-Fesenko, O.; Sanvito, S.; Kirby, B. J.; Grollier, J.; Everschor-Sitte, K.; Kampfrath, T.; You, C-Y.; Berger, A.Journal of Physics D: Applied Physics (2020), 53 (45), 453001CODEN: JPAPBE; ISSN:0022-3727. (IOP Publishing Ltd.)Following the success and relevance of the 2014 and 2017 Magnetism Roadmap articles, this 2020 Magnetism Roadmap edition takes yet another timely look at newly relevant and highly active areas in magnetism research. The overall layout of this article is unchanged, given that it has proved the most appropriate way to convey the most relevant aspects of today's magnetism research in a wide variety of sub-fields to a broad readership. A different group of experts has again been selected for this article, representing both the breadth of new research areas, and the desire to incorporate different voices and viewpoints. The latter is esp. relevant for thistype of article, in which one's field of expertise has to be accommodated on two printed pages only, so that personal selection preferences are naturally rather more visible than in other types of articles. Most importantly, the very relevant advances in the field of magnetism research in recent years make the publication of yet another Magnetism Roadmap a very sensible and timely endeavour, allowing its authors and readers to take another broad-based, but concise look at the most significant developments in magnetism, their precise status, their challenges, and their anticipated future developments. While many of the contributions in this 2020 Magnetism Roadmap edition have significant assocns. with different aspects of magnetism, the general layout can nonetheless be classified in terms of three main themes: (i) phenomena, (ii) materials and characterization, and (iii) applications and devices. While these categories are unsurprisingly rather similar to the 2017 Roadmap, the order is different, in that the 2020 Roadmap considers phenomena first, even if their occurrences are naturally very difficult to sep. from the materials exhibiting such phenomena. Nonetheless, the specifically selected topics seemed to be best displayed in the order presented here, in particular, because many of the phenomena or geometries discussed in (i) can be found or designed into a large variety of materials, so that the progression of the article embarks from more general concepts to more specific classes of materials in the selected order. Given that applications and devices are based on both phenomena and materials, it seemed most appropriate to close the article with the application and devices section (iii) once again. The 2020 Magnetism Roadmap article contains 14 sections, all of which were written by individual authors and experts, specifically addressing a subject in terms of its status, advances, challenges and perspectives in just two pages. Evidently, this two-page format limits the depth to which each subject can be described. Nonetheless, the most relevant and key aspects of each field are touched upon, which enables the Roadmap as whole to give its readership an initial overview of and outlook into a wide variety of topics and fields in a fairly condensed format. Correspondingly, the Roadmap pursues the goal of giving each reader a brief ref. frame of relevant and current topics in modern applied magnetism research, even if not all sub-fields can be represented here. The first block of this 2020 Magnetism Roadmap, which is focussed on (i) phenomena, contains five contributions, which address the areas of interfacial Dzyaloshinskii-Moriya interactions, and two-dimensional and curvilinear magnetism, as well as spin-orbit torque phenomena and all optical magnetization reversal. All of these contributions describe cutting edge aspects of rather fundamental phys. processes and properties, assocd. with new and improved magnetic materials' properties, together with potential developments in terms of future devices and technol. As such, they form part of a widening magnetism 'phenomena reservoir' for utilization in applied magnetism and related device technol. The final block (iii) of this article focuses on such applications and device-related fields in four contributions relating to currently active areas of research, which are of course utilizing magnetic phenomena to enable specific functions. These contributions highlight the role of magnetism or spintronics in the field of neuromorphic and reservoir computing, terahertz technol., and domain wall-based logic. One aspect common to all of these application-related contributions is that they are not yet being utilized in com. available technol.; it is currently still an open question, whether or not such technol. applications will be magnetism-based at all in the future, or if other types of materials and phenomena will yet outperform magnetism. This last point is actually a very good indication of the vibrancy of applied magnetism research today, given that it demonstrates that magnetism research is able to venture into novel application fields, based upon its portfolio of phenomena, effects and materials. This materials portfolio in particular defines the central block (ii) of this article, with its five contributions interconnecting phenomena with devices, for which materials and the characterization of their properties is the decisive discriminator between purely academically interesting aspects and the true viability of real-life devices, because only available materials and their assocd. fabrication and characterization methods permit reliable technol. implementation. These five contributions specifically address magnetic films and multiferroic heterostructures for the purpose of spin electronic utilization, multi-scale materials modeling, and magnetic materials design based upon machine-learning, as well as materials characterization via polarized neutron measurements. As such, these contributions illustrate the balanced relevance of research into exptl. and modeling magnetic materials, as well the importance of sophisticated characterization methods that allow for an ever-more refined understanding of materials. As a combined and integrated article, this 2020 Magnetism Roadmap is intended to be a ref. point for current, novel and emerging research directions in modern magnetism, just as its 2014 and 2017 predecessors have been in previous years.
- 31Otálora, J. A.; Yan, M.; Schultheiss, H.; Hertel, R.; Kákay, A. Curvature-Induced Asymmetric Spin-Wave Dispersion. Phys. Rev. Lett. 2016, 117, 227203, DOI: 10.1103/PhysRevLett.117.227203[Crossref], [PubMed], [CAS], Google Scholar31https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXhsVWrurfI&md5=ea5b501cd63efeea6ecf68a2ffb4cd3eCurvature-induced asymmetric spin-wave dispersionOtalora, Jorge A.; Yan, Ming; Schultheiss, Helmut; Hertel, Riccardo; Kakay, AttilaPhysical Review Letters (2016), 117 (22), 227203/1-227203/6CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)In magnonics, spin waves are conceived of as electron-charge-free information carriers. Their wave behavior has established them as the key elements to achieve low power consumption, fast operative rates. and good packaging in tnagnon-based computational technologies. Hence, knowing alternative ways that reveal certain properties of their undulatory motion is an important task. Here, we show using micromagnette simulations and anal. calcns. that spin-wave propagation in ferromagnetic nanotubes is fundamentally different than in thin films. The dispersion relation is asym. regarding the sign of the wave vector, It is a purely curvature-induced effect and its fundamental origin is identified to he the classical dipole-dipole interaction. The anal. expression of the dispersion relation has the same math. form as in thin films with the Dzyalonshiinsky-Moriya interaction. Therefore. this curvature- induced effect can be seen as a "dipole-induced Dzyalonshiinsky-Moriya-like" effect.
- 32Vojkovic, S.; Carvalho-Santos, V. L.; Fonseca, J. M.; Nunez, A. S. Vortex-antivortex pairs induced by curvature in toroidal nanomagnets. J. Appl. Phys. 2017, 121, 113906, DOI: 10.1063/1.4977983[Crossref], [CAS], Google Scholar32https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXkvFWhs7c%253D&md5=faf7bb204de3e97807994e8d090c11c8Vortex-antivortex pairs induced by curvature in toroidal nanomagnetsVojkovic, Smiljan; Carvalho-Santos, Vagson L.; Fonseca, Jakson M.; Nunez, Alvaro S.Journal of Applied Physics (Melville, NY, United States) (2017), 121 (11), 113906/1-113906/7CODEN: JAPIAU; ISSN:0021-8979. (American Institute of Physics)We show that the curvature of nanomagnets can be used to induce chiral textures in the magnetization field. Among the phenomena related to the interplay between the geometry and magnetic behavior of nanomagnets, an effective curvature-induced chiral interaction has been recently predicted. In this work, it is shown that magnetization configurations consisting of two structures with opposite winding nos. (vortex and antivortex) appear as remanent states in hollow toroidal nanomagnets. It is shown that these topol. configurations are a result of a chiral interaction induced by curvature. In this way, the obtained results present a new form to produce stable vortices and antivortices by using nanomagnets with variable curvature. (c) 2017 American Institute of Physics.
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- 37Mizoguchi, K.; Tanaka, S.; Ogawa, T.; Shiobara, N.; Sakamoto, H. Magnetic study of the electronic states of B-DNA and M-DNA doped with metal ions. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 72, 033106, DOI: 10.1103/PhysRevB.72.033106[Crossref], [CAS], Google Scholar38https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXmvF2jtLc%253D&md5=54a58b35e116a0ec38edae2521d30534Magnetic study of the electronic states of B-DNA and M-DNA doped with metal ionsMizoguchi, Kenji; Tanaka, Shunsuke; Ogawa, Tasuku; Shiobara, Naofumi; Sakamoto, HirokazuPhysical Review B: Condensed Matter and Materials Physics (2005), 72 (3), 033106/1-033106/4CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)The magnetic properties of the pristine and metal ion doped DNA (DNA) of salmon are investigated with ESR (EPR), superconducting quantum interference device and energy dispersive x-ray fluorescence spectroscopy. Purified salmon DNA gives intrinsically no EPR signal, which is consistent with DNA being a semiconductor, but not with DNA having metallic or superconducting properties as reported previously. Several kinds of divalent ions (Zn, Mn, Ca,...) are used as dopants, resulting in no substantial EPR signal except in the case of Mn. This leads to the conclusion that a metal ion counterbalances two phosphate anions instead of Na counterions in B-DNA, which contradicts the metallic behavior reported previously [A. Rakitin et al, Phys. Rev. Lett. 86, 3670 (2001)].
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- 41de Sousa, R.; Moore, J. E. Optical coupling to spin waves in the cycloidal multiferroic BiFeO3. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 77, 012406, DOI: 10.1103/PhysRevB.77.012406[Crossref], [CAS], Google Scholar42https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1cXhsVGlsL8%253D&md5=0f54815cee0bace92e39b463d6a3fa18Optical coupling to spin waves in the cycloidal multiferroic BiFeO3de Sousa, Rogerio; Moore, Joel E.Physical Review B: Condensed Matter and Materials Physics (2008), 77 (1), 012406/1-012406/4CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)The magnon and optical phonon spectrum of an incommensurate multiferroic such as BiFeO3 is considered in the framework of a phenomenol. Landau theory. The resulting spin wave spectrum is quite distinct from commensurate substances due to soft mode anisotropy and magnon zone folding. The former allows elec. control of spin wave propagation via reorientation of the spontaneous ferroelec. moment. The latter gives rise to multiple magnetodielec. resonances due to the coupling of optical phonons at zero wave vector to magnons at integer multiples of the cycloid wave vector. These results show that the optical response of a multiferroic reveals much more about its magnetic excitations than previously anticipated on the basis of simpler models.
- 42Stamps, R. L.; Camley, R. E. Bulk and surface spin waves in thin-film antiferromagnets. J. Appl. Phys. 1984, 56, 3497– 3502, DOI: 10.1063/1.333915[Crossref], [CAS], Google Scholar43https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaL2MXjvVaqsw%253D%253D&md5=4206ddb695d9dc0bbf5ea748b4184f88Bulk and surface spin waves in thin-film antiferromagnetsStamps, R. L.; Camley, R. E.Journal of Applied Physics (1984), 56 (12), 3497-502CODEN: JAPIAU; ISSN:0021-8979.Antiferromagnetic bulk and surface spin waves, in the long wavelength region, on a finite thickness slab geometry. Implicit dispersion relations for both surface and bulk modes are derived, along with numerical calcns. for MnF2 and GdAlO3. The application of a magnetic field strongly localizes the surface spin wave to either the top or bottom surface of the film.
- 43Stamps, R. L.; Camley, R. E. Dipole-exchange spin-wave modes in very-thin-film antiferromagnets. Phys. Rev. B: Condens. Matter Mater. Phys. 1987, 35, 1919– 1931, DOI: 10.1103/PhysRevB.35.1919
- 44Demokritov, S. O., Slavin, A. N., Eds.; Magnonics: From Fundamentals to Applications; Topics in Applied Physics; Springer: Berlin, 2013.
- 45Yuan, W.; Zhu, Q.; Su, T.; Yao, Y.; Xing, W.; Chen, Y.; Ma, Y.; Lin, X.; Shi, J.; Shindou, R.; Xie, X. C.; Han, W. Experimental signatures of spin superfluid ground state in canted antiferromagnet Cr2O3 via nonlocal spin transport. Science Advances 2018, 4, eaat1098 DOI: 10.1126/sciadv.aat1098
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- 47Evers, M.; Nowak, U. Transport properties of spin superfluids: Comparing easy-plane ferromagnets and antiferromagnets. Phys. Rev. B: Condens. Matter Mater. Phys. 2020, 101, 184415, DOI: 10.1103/PhysRevB.101.184415
- 48Demokritov, S. O.; Demidov, V. E.; Dzyapko, O.; Melkov, G. A.; Serga, A. A.; Hillebrands, B.; Slavin, A. N. Bose–Einstein condensation of quasi-equilibrium magnons at room temperature under pumping. Nature 2006, 443, 430– 433, DOI: 10.1038/nature05117[Crossref], [PubMed], [CAS], Google Scholar49https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28XhtVSns7fN&md5=0cb4e6f4f4755490862aac5fe63d6b70Bose-Einstein condensation of quasi-equilibrium magnons at room temperature under pumpingDemokritov, S. O.; Demidov, V. E.; Dzyapko, O.; Melkov, G. A.; Serga, A. A.; Hillebrands, B.; Slavin, A. N.Nature (London, United Kingdom) (2006), 443 (7110), 430-433CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)Bose-Einstein condensation is one of the most fascinating phenomena predicted by quantum mechanics. It involves the formation of a collective quantum state composed of identical particles with integer angular momentum (bosons), if the particle d. exceeds a crit. value. To achieve Bose-Einstein condensation, one can either decrease the temp. or increase the d. of bosons. It has been predicted that a quasi-equil. system of bosons could undergo Bose-Einstein condensation even at relatively high temps., if the flow rate of energy pumped into the system exceeds a crit. value. Here we report the observation of Bose-Einstein condensation in a gas of magnons at room temp. Magnons are the quanta of magnetic excitations in a magnetically ordered ensemble of magnetic moments. In thermal equil., they can be described by Bose-Einstein statistics with zero chem. potential and a temp.-dependent d. In the expts. presented here, we show that by using a technique of microwave pumping it is possible to excite addnl. magnons and to create a gas of quasi-equil. magnons with a non-zero chem. potential. With increasing pumping intensity, the chem. potential reaches the energy of the lowest magnon state, and a Bose condensate of magnons is formed.
- 49Serga, A. A.; Tiberkevich, V. S.; Sandweg, C. W.; Vasyuchka, V. I.; Bozhko, D. A.; Chumak, A. V.; Neumann, T.; Obry, B.; Melkov, G. A.; Slavin, A. N.; Hillebrands, B. Bose–Einstein condensation in an ultra-hot gas of pumped magnons. Nat. Commun. 2014, 5, 3452, DOI: 10.1038/ncomms4452[Crossref], [PubMed], [CAS], Google Scholar50https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BC2crhslensQ%253D%253D&md5=e40378d8def1f221bc66f243e4029329Bose-Einstein condensation in an ultra-hot gas of pumped magnonsSerga Alexander A; Sandweg Christian W; Vasyuchka Vitaliy I; Chumak Andrii V; Neumann Timo; Obry Bjorn; Hillebrands Burkard; Tiberkevich Vasil S; Slavin Andrei N; Bozhko Dmytro A; Melkov Gennadii ANature communications (2014), 5 (), 3452 ISSN:.Bose-Einstein condensation of quasi-particles such as excitons, polaritons, magnons and photons is a fascinating quantum mechanical phenomenon. Unlike the Bose-Einstein condensation of real particles (like atoms), these processes do not require low temperatures, since the high densities of low-energy quasi-particles needed for the condensate to form can be produced via external pumping. Here we demonstrate that such a pumping can create remarkably high effective temperatures in a narrow spectral region of the lowest energy states in a magnon gas, resulting in strikingly unexpected transitional dynamics of Bose-Einstein magnon condensate: the density of the condensate increases immediately after the external magnon flow is switched off and initially decreases if it is switched on again. This behaviour finds explanation in a nonlinear 'evaporative supercooling' mechanism that couples the low-energy magnons overheated by pumping with all the other thermal magnons, removing the excess heat, and allowing Bose-Einstein condensate formation.
- 50Clausen, P.; Bozhko, D. A.; Vasyuchka, V. I.; Hillebrands, B.; Melkov, G. A.; Serga, A. A. Stimulated thermalization of a parametrically driven magnon gas as a prerequisite for Bose–Einstein magnon condensation. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 91, 220402(R) DOI: 10.1103/PhysRevB.91.220402
- 51Bozhko, D. A.; Serga, A. A.; Clausen, P.; Vasyuchka, V. I.; Heussner, F.; Melkov, G. A.; Pomyalov, A.; L’vov, V. S.; Hillebrands, B. Supercurrent in a room-temperature Bose–Einstein magnon condensate. Nat. Phys. 2016, 12, 1057– 1062, DOI: 10.1038/nphys3838[Crossref], [CAS], Google Scholar52https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28Xht1ygs7%252FI&md5=49a77c9ff2eb446ddbce588241925e63Supercurrent in a room-temperature Bose-Einstein magnon condensateBozhko, Dmytro A.; Serga, Alexander A.; Clausen, Peter; Vasyuchka, Vitaliy I.; Heussner, Frank; Melkov, Gennadii A.; Pomyalov, Anna; L'vov, Victor S.; Hillebrands, BurkardNature Physics (2016), 12 (11), 1057-1062CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)A supercurrent is a macroscopic effect of a phase-induced collective motion of a quantum condensate. So far, exptl. obsd. supercurrent phenomena such as supercond. and superfluidity have been restricted to cryogenic temps. Here, we report on the discovery of a supercurrent in a Bose-Einstein magnon condensate prepd. in a room-temp. ferrimagnetic film. The magnon condensate is formed in a parametrically pumped magnon gas and is subject to a thermal gradient created by local laser heating of the film. The appearance of the supercurrent, which is driven by a thermally induced phase shift in the condensate wavefunction, is evidenced by anal. of the temporal evolution of the magnon d. measured by means of Brillouin light scattering spectroscopy. Our findings offer opportunities for the investigation of room-temp. macroscopic quantum phenomena and their potential applications at ambient conditions.
- 52Zhang, X.; Li, B.; Zhang, J. An Efficient Strategy for Self-Assembly of DNA-Mimic Homochiral 1D Helical Cu(II) Chain from Achiral Flexible Ligand by Spontaneous Resolution. Inorg. Chem. 2016, 55, 3378– 3383, DOI: 10.1021/acs.inorgchem.5b02785[ACS Full Text
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- 54Yamaguchi, K.; Taniguchi, T.; Kawakami, T.; Hamamoto, T.; Okumura, M. Possibilities of magnetic modifications of DNA wires, sheets and related materials. Polyhedron 2005, 24, 2758– 2766, DOI: 10.1016/j.poly.2005.03.132[Crossref], [CAS], Google Scholar55https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXhtFymtrnE&md5=569921e3c679fb0a7938281e7dafa645Possibilities of magnetic modifications of DNA wires, sheets and related materialsYamaguchi, K.; Taniguchi, T.; Kawakami, T.; Hamamoto, T.; Okumura, M.Polyhedron (2005), 24 (16-17), 2758-2766CODEN: PLYHDE; ISSN:0277-5387. (Elsevier B.V.)Our theor. efforts towards mol.-based magnetic conductors and superconductors on the basis of ab initio Hamiltonians and effective model Hamiltonians are summarized in relation to recently developed DNA-based mol. materials. Guanine and adenine derivs. coupling with org. radicals (R) are investigated as possible π-R components. In order to elucidate electronic and magnetic properties of these species, effective exchange integrals (Jab) for magnetic clusters are calcd. by ab initio hybrid d. functional methods. Theor. possibilities of org. magnetic conductors and the org. solenoid are elucidated on the basis of these models in self-assembled DNA wires, sheets and related materials. Implications of the calcd. results are finally discussed in order to obtain a unified picture of many p-d, π-d and π-R mol.-based systems with strong electron correlations.
- 55Mizoguchi, K.; Tanaka, S.; Ojima, M.; Sano, S.; Nagatori, M.; Sakamoto, H.; Yonezawa, Y.; Aoki, Y.; Sato, H.; Furukawa, K.; Nakamura, T. AF-like Ground State of Mn-DNA and Charge Transfer from Fe to Base-π-Band in Fe-DNA. J. Phys. Soc. Jpn. 2007, 76, 043801, DOI: 10.1143/JPSJ.76.043801[Crossref], [CAS], Google Scholar56https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXls1ansrY%253D&md5=78be548e5a8095f42132879739cbd122AF-like ground state of Mn-DNA and charge transfer from Fe to base-π-band in Fe-DNAMizoguchi, Kenji; Tanaka, Shunsuke; Ojima, Masaya; Sano, Sayaka; Nagatori, Mai; Sakamoto, Hirokazu; Yonezawa, Yuki; Aoki, Yuji; Sato, Hideyuki; Furukawa, Kou; Nakamura, ToshikazuJournal of the Physical Society of Japan (2007), 76 (4), 043801/1-043801/4CODEN: JUPSAU; ISSN:0031-9015. (Physical Society of Japan)The electronics states of M-DNA doped with M = Mg, Ca, Zn, Mn, Fe are investigated mainly with magnetic properties. In the "wet" condition the Mn ions of Mn-DNA form a 1-D chain in the center of a DNA double helix, as evidenced from the formation of the unnatural base pair combination with M, poly(dA)-M-poly(dC), but in the "dry" condition they form a 3-D network with the antiferromagnetic ground state around 0.4 K with the superexchange coupling via water mols. The valence of 3+ is found only in Fe-DNA, from which the base π-band obtains π charge carriers.
- 56Samanta, P. K.; Pati, S. K. Structural and Magnetic Properties of a Variety of Transition Metal Incorporated DNA Double Helices. Chem. - Eur. J. 2014, 20, 1760– 1764, DOI: 10.1002/chem.201302628[Crossref], [PubMed], [CAS], Google Scholar57https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXms1em&md5=801fd4344d346cc7396b2dbc1aa0fb14Structural and Magnetic Properties of a Variety of Transition Metal Incorporated DNA Double HelixesSamanta, Pralok K.; Pati, Swapan K.Chemistry - A European Journal (2014), 20 (6), 1760-1764CODEN: CEUJED; ISSN:0947-6539. (Wiley-VCH Verlag GmbH & Co. KGaA)By using d. functional theory calcns., the structural, energetic, magnetic, and optical properties for a variety of transition metal (M = Mn, Fe, Co, Ni and Cu) ions incorporated modified-DNA (M-DNA) double helixes was studied. The DNA is modified with either hydroxypyridone (H) or bis(salicylaldehyde)ethylenediamine (S-en) metalated bases. The formation of extended M-O network leading to the ferromagnetic interactions for the case of H-DNA for all the metal ions were found. More ordered stacking arrangement was found for S-en-DNA. The authors calc. the exchange coupling const. (J) considering Heisenberg Hamiltonian for quant. description of magnetic interactions. The ferromagnetic and antiferromagnetic interactions were obtained by varying different transition metal ions. The extent of the magnetic interaction depends on the no. of transition metal ions. Optical profiles show peaks <2 eV, a clear signature of spin-spin coupling.
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Abstract
Figure 1
Figure 1. (a) Schematics of the antiferromagnetic spin chain γ. Magnetic sublattices with magnetization mI and mII are shown by magenta and light-blue arrows. The Dzyaloshinskii vector d (dark-blue) lies in the TB plane given by the TNB basis eT,N,B. Hard and easy anisotropy axes are labeled by e1 and e3, respectively. (b) Helix spin chain with radius R and pitch P. The AFM order parameter (Néel vector) n parametrized by angles θ and ϕ is shown by the green arrow. (c) Diagram of equilibrium states for a helix spin chain. Open symbols and triangles correspond to periodic and homogeneous states, respectively, obtained in spin–lattice simulations. The solid red curve shows the boundary between the states. The dashed green line shows the asymptotic of the boundary τb ≈ 0.85κ for κ
≪ 1. Schematics of the (d, e) homogeneous and (f, g) periodic states in the TNB reference frame. (d, f) Bloch spheres illustrate the trajectories of n. The tilt angle .Figure 2
Figure 2. (a) Spin-wave dispersion (5) for helical AFM spin chains with
and two curvatures (black) and (red). The result of spin–lattice simulations is shown by the background color for a helical spin chain with the geometry with and . (b) Helix geometries calculated in a. (c) Spin-wave dispersion (5) and simulations for and . The depth of the minimum in the acoustic branch is shown by δ. (d) The depth δ for different curvatures and torsions within the homogeneous ground state (below red line, same as in Figure 1c). Dashed line corresponds to the absence of minimum.References
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- 9Gomonay, O.; Jungwirth, T.; Sinova, J. Concepts of antiferromagnetic spintronics. Phys. Status Solidi RRL 2017, 11, 1700022, DOI: 10.1002/pssr.201700022
- 10Šmejkal, L.; Mokrousov, Y.; Yan, B.; MacDonald, A. H. Topological antiferromagnetic spintronics. Nat. Phys. 2018, 14, 242– 251, DOI: 10.1038/s41567-018-0064-5[Crossref], [CAS], Google Scholar10https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXhtFGkt7%252FO&md5=c77da6f5409ca15f24d112c49da023faTopological antiferromagnetic spintronicsSmejkal, Libor; Mokrousov, Yuriy; Yan, Binghai; MacDonald, Allan H.Nature Physics (2018), 14 (3), 242-251CODEN: NPAHAX; ISSN:1745-2473. (Nature Research)A Review. The recent demonstrations of elec. manipulation and detection of antiferromagnetic spins have opened up a new chapter in the story of spintronics. Here, we review the emerging research field that is exploring the links between antiferromagnetic spintronics and topol. structures in real and momentum space. Active topics include proposals to realize Majorana fermions in antiferromagnetic topol. superconductors, to control topol. protection and Dirac points by manipulating antiferromagnetic order parameters, and to exploit the anomalous and topol. Hall effects of zero-net-moment antiferromagnets. We explain the basic concepts behind these proposals, and discuss potential applications of topol. antiferromagnetic spintronics.
- 11Manchon, A.; Železný, J.; Miron, I. M.; Jungwirth, T.; Sinova, J.; Thiaville, A.; Garello, K.; Gambardella, P. Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems. Rev. Mod. Phys. 2019, 91, 035004, DOI: 10.1103/RevModPhys.91.035004[Crossref], [CAS], Google Scholar11https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXit1Clt7%252FI&md5=3a4ff9ca1163b200226e9d78d2772516Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systemsManchon, A.; Zelezny, J.; Miron, I. M.; Jungwirth, T.; Sinova, J.; Thiaville, A.; Garello, K.; Gambardella, P.Reviews of Modern Physics (2019), 91 (3), 035004CODEN: RMPHAT; ISSN:1539-0756. (American Physical Society)Spin-orbit coupling in inversion-asym. magnetic crystals and structures has emerged as a powerful tool to generate complex magnetic textures, interconvert charge and spin under applied current, and control magnetization dynamics. Current-induced spin-orbit torques mediate the transfer of angular momentum from the lattice to the spin system, leading to sustained magnetic oscillations or switching of ferromagnetic as well as antiferromagnetic structures. The manipulation of magnetic order, domain walls, and skyrmions by spin-orbit torques provides evidence of the microscopic interactions between charge and spin in a variety of materials and opens novel strategies to design spintronic devices with potentially high impact in data storage, nonvolatile logic, and magnonic applications. This paper reviews recent progress in the field of spin orbitronics, focusing on theor. models, material properties, and exptl. results obtained on bulk noncentrosym. conductors and multilayer heterostructures, including metals, semiconductors, and topol. insulator systems. Relevant aspects for improving the understanding and optimizing the efficiency of nonequil. spin-orbit phenomena in future nanoscale devices are also discussed.
- 12Zhang, X.; Liu, Q.; Luo, J.-W.; Freeman, A. J.; Zunger, A. Hidden spin polarization in inversion-symmetric bulk crystals. Nat. Phys. 2014, 10, 387– 393, DOI: 10.1038/nphys2933[Crossref], [CAS], Google Scholar12https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXmtlWntr0%253D&md5=95fe80ef57edadc61f38b7d2995617e9Hidden spin polarization in inversion-symmetric bulk crystalsZhang, Xiuwen; Liu, Qihang; Luo, Jun-Wei; Freeman, Arthur J.; Zunger, AlexNature Physics (2014), 10 (5), 387-393CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)Spin-orbit coupling can induce spin polarization in nonmagnetic 3D crystals when the inversion symmetry is broken, as manifested by the bulk Rashba and Dresselhaus effects. We establish that these spin-polarization effects originate fundamentally from specific at. site asymmetries, rather than, as generally accepted, from the asymmetry of the crystal space group. This understanding leads to the recognition that a previously overlooked hidden form of spin polarization should exist in centrosym. crystals. Although all energy bands must be doubly degenerate in centrosym. materials, we find that the two components of such doubly degenerate bands could have opposite polarizations, each spatially localized on one of the two sep. sectors forming the inversion partners. We demonstrate such hidden spin polarizations in particular centrosym. crystals by first-principles calcns. This new understanding could considerably broaden the range of currently useful spintronic materials and enable the control of spin polarization by means of operations on the at. scale.
- 13Železný, J.; Gao, H.; Výborný, K.; Zemen, J.; Mašek, J.; Manchon, A.; Wunderlich, J.; Sinova, J.; Jungwirth, T. Relativistic Néel-Order Fields Induced by Electrical Current in Antiferromagnets. Phys. Rev. Lett. 2014, 113, 157201, DOI: 10.1103/PhysRevLett.113.157201[Crossref], [PubMed], [CAS], Google Scholar13https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhvFKqsLrN&md5=13d36f741bbe1f93b73d014f35f5a6a2Relativistic Neel-order fields induced by electrical current in antiferromagnetsZelezny, J.; Gao, H.; Vyborny, K.; Zemen, J.; Masek, J.; Manchon, Aurelien; Wunderlich, J.; Sinova, Jairo; Jungwirth, T.Physical Review Letters (2014), 113 (15), 157201/1-157201/5, 5 pp.CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)We predict that a lateral elec. current in antiferromagnets can induce nonequil. Neel-order fields, i.e., fields whose sign alternates between the spin sublattices, which can trigger ultrafast spin-axis reorientation. Based on microscopic transport theory calcns. we identify staggered current-induced fields analogous to the intraband and to the intrinsic interband spin-orbit fields previously reported in ferromagnets with a broken inversion-symmetry crystal. To illustrate their rich physics and utility, we consider bulk Mn2Au with the two spin sublattices forming inversion partners, and a 2D square-lattice antiferromagnet with broken structural inversion symmetry modeled by a Rashba spin-orbit coupling. We propose an antiferromagnetic memory device with elec. writing and reading.
- 14Dzialoshinskii, I. E. Thermodynamic theory of “weak” ferromagnetism in antiferromagnetic substances. Sov. Phys. JETP 1957, 5, 1259– 1272
- 15Bogdanov, A. N.; Yablonskiĭ, D. A. Thermodynamically stable “vortices” in magnetically ordered crystals. The mixed state of magnets. Zh. Eksp. Teor. Fiz. 1989, 95, 178– 182
- 16Qaiumzadeh, A.; Ado, I. A.; Duine, R. A.; Titov, M.; Brataas, A. Theory of the Interfacial Dzyaloshinskii-Moriya Interaction in Rashba Antiferromagnets. Phys. Rev. Lett. 2018, 120, 197202, DOI: 10.1103/PhysRevLett.120.197202[Crossref], [PubMed], [CAS], Google Scholar16https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXltVyqurw%253D&md5=0ca1baa3529c71f961398a7e8452b145Theory of the Interfacial Dzyaloshinskii-Moriya Interaction in Rashba AntiferromagnetsQaiumzadeh, Alireza; Ado, Ivan A.; Duine, Rembert A.; Titov, Mikhail; Brataas, ArnePhysical Review Letters (2018), 120 (19), 197202CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)In antiferromagnetic (AFM) thin films, broken inversion symmetry or coupling to adjacent heavy metals can induce Dzyaloshinskii-Moriya (DM) interactions. Knowledge of the DM parameters is essential for understanding and designing exotic spin structures, such as hedgehog Skyrmions and chiral Neel walls, which are attractive for use in novel information storage technologies. We introduce a framework for computing the DM interaction in two-dimensional Rashba antiferromagnets. Unlike in Rashba ferromagnets, the DM interaction is not suppressed even at low temps. The material parameters control both the strength and the sign of the interfacial DM interaction. Our results suggest a route toward controlling the DM interaction in AFM materials by means of doping and elec. fields.
- 17Dzyaloshinskii, I. E. Theory of Helicoidal Structures in Antiferromagnets. I. Nonmetals. Sov. Phys. JETP 1964, 19, 960– 971
- 18Bogdanov, A. N.; Rößler, U. K.; Wolf, M.; Müller, K.-H. Magnetic structures and reorientation transitions in noncentrosymmetric uniaxial antiferromagnets. Phys. Rev. B: Condens. Matter Mater. Phys. 2002, 66, 214410, DOI: 10.1103/PhysRevB.66.214410[Crossref], [CAS], Google Scholar18https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3sXhvFCjtQ%253D%253D&md5=48236b99c6a0cae1f7696a0fe294c6b5Magnetic structures and reorientation transitions in noncentrosymmetric uniaxial antiferromagnetsBogdanov, A. N.; Rossler, U. K.; Wolf, M.; Muller, K.-H.Physical Review B: Condensed Matter and Materials Physics (2002), 66 (21), 214410/1-214410/16CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)A phenomenol. theory of magnetic states in noncentrosym. tetragonal antiferromagnets is developed, which has to include homogeneous and inhomogeneous terms (Lifshitz invariants) derived from Dzyaloshinskii-Moriya couplings. Magnetic properties of this class of antiferromagnets with low crystal symmetry are discussed in relation to the recently detected compds. Ba2CuGe2O7 and K2V3O8. Crystallog. symmetry and magnetic ordering in these systems allow the simultaneous occurrence of chiral inhomogeneous magnetic structures and weak ferromagnetism. Incommensurate magnetic structures, chiral helixes, with a rotation of the staggered magnetization accompanied by oscillations of the total magnetization, are possible. Field-induced reorientation transitions into modulated states have been studied and corresponding phase diagrams are constructed. Structures of magnetic defects (domain-walls and vortices) are discussed. In particular, vortices, i.e., localized nonsingular line defects, are stabilized by inhomogeneous Dzyaloshinskii-Moriya interactions in uniaxial noncentrosym. antiferromagnets.
- 19Qaiumzadeh, A.; Kristiansen, L. A.; Brataas, A. Controlling chiral domain walls in antiferromagnets using spin-wave helicity. Phys. Rev. B: Condens. Matter Mater. Phys. 2018, 97, 020402(R) DOI: 10.1103/PhysRevB.97.020402
- 20Barker, J.; Tretiakov, O. A. Static and Dynamical Properties of Antiferromagnetic Skyrmions in the Presence of Applied Current and Temperature. Phys. Rev. Lett. 2016, 116, 147203, DOI: 10.1103/PhysRevLett.116.147203[Crossref], [PubMed], [CAS], Google Scholar20https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhtlOjsrnF&md5=7721fa26419ad12b93d1ba99a95fd238Static and dynamical properties of antiferromagnetic skyrmions in the presence of applied current and temperatureBarker, Joseph; Tretiakov, Oleg A.Physical Review Letters (2016), 116 (14), 147203/1-147203/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)Skyrmions are topol. protected entities in magnetic materials which have the potential to be used in spintronics for information storage and processing. However, Skyrmions in ferromagnets have some intrinsic difficulties which must be overcome to use them for spintronic applications, such as the inability to move straight along current. We show that Skyrmions can also be stabilized and manipulated in antiferromagnetic materials. An antiferromagnetic Skyrmion is a compd. topol. object with a similar but of opposite sign spin texture on each sublattice, which, e.g., results in a complete cancellation of the Magnus force. We find that the composite nature of antiferromagnetic Skyrmions gives rise to different dynamical behavior due to both an applied current and temp. effects.
- 21Shen, L.; Li, X.; Zhao, Y.; Xia, J.; Zhao, G.; Zhou, Y. Current-Induced Dynamics of the Antiferromagnetic Skyrmion and Skyrmionium. Phys. Rev. Appl. 2019, 12, 064033, DOI: 10.1103/PhysRevApplied.12.064033[Crossref], [CAS], Google Scholar21https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXjt1Sls7Y%253D&md5=10894e7c60f099ac6cd2218080901a4cCurrent-Induced Dynamics of the Antiferromagnetic Skyrmion and SkyrmioniumShen, Laichuan; Li, Xiaoguang; Zhao, Yuelei; Xia, Jing; Zhao, Guoping; Zhou, YanPhysical Review Applied (2019), 12 (6), 064033CODEN: PRAHB2; ISSN:2331-7019. (American Physical Society)Antiferromagnetic (AFM) skyrmionium composed of two topol. AFM skyrmions shares the merits of an AFM skyrmion, for example, high mobility and no skyrmion Hall effect. Here, we anal. and numerically study the dynamics of the AFM skyrmion and skyrmionium induced by spin currents. Our calcns. demonstrate that the current-induced spin-transfer torques can drive AFM skyrmion and skyrmionium with the same speed, while their steady motion speeds induced by spin-orbit torques are different. Furthermore, it is found that due to the existence of the effective AFM texture mass, the AFM skyrmion and skyrmionium obey the momentum theorem, and the time evolution of the position induced by alternating currents presents a phase. Besides, a spin torque nano-oscillator based on the AFM skyrmionium can produce high frequencies, similar to that based on the AFM skyrmion. Numerical simulations are in good agreement with the anal. solns. Our results demonstrate the inertial dynamics of the AFM skyrmion and skyrmionium and may provide guidelines for building skyrmion-based spintronic devices.
- 22Železný, J.; Wadley, P.; Olejník, K.; Hoffmann, A.; Ohno, H. Spin transport and spin torque in antiferromagnetic devices. Nat. Phys. 2018, 14, 220– 228, DOI: 10.1038/s41567-018-0062-7[Crossref], [CAS], Google Scholar22https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXhtFGkt77F&md5=e49a6ab3baa51580956a529b76bda4a6Spin transport and spin torque in antiferromagnetic devicesZelezny, J.; Wadley, P.; Olejnik, K.; Hoffmann, A.; Ohno, H.Nature Physics (2018), 14 (3), 220-228CODEN: NPAHAX; ISSN:1745-2473. (Nature Research)Ferromagnets are key materials for sensing and memory applications. In contrast, antiferromagnets, which represent the more common form of magnetically ordered materials, have found less practical application beyond their use for establishing ref. magnetic orientations via exchange bias. This might change in the future due to the recent progress in materials research and discoveries of antiferromagnetic spintronic phenomena suitable for device applications. Exptl. demonstration of the elec. switching and detection of the Ne´el order open a route towards memory devices based on antiferromagnets. Apart from the radiation and magnetic-field hardness, memory cells fabricated from antiferromagnets can be inherently multilevel, which could be used for neuromorphic computing. Switching speeds attainable in antiferromagnets far exceed those of ferromagnetic and semiconductor memory technologies. Here, we review the recent progress in electronic spin-transport and spin-torque phenomena in antiferromagnets that are dominantly of the relativistic quantum-mech. origin. We discuss their utility in pure antiferromagnetic or hybrid ferromagnetic/antiferromagnetic memory devices.
- 23Gaididei, Y.; Kravchuk, V. P.; Sheka, D. D. Curvature Effects in Thin Magnetic Shells. Phys. Rev. Lett. 2014, 112, 257203, DOI: 10.1103/PhysRevLett.112.257203[Crossref], [PubMed], [CAS], Google Scholar23https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhs1Gjt7fM&md5=454db99e9d3f6978df05cd0278f225daCurvature effects in thin magnetic shellsGaididei, Yuri; Kravchuk, Volodymyr P.; Sheka, Denis D.Physical Review Letters (2014), 112 (25), 257203/1-257203/5, 5 pp.CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)A magnetic energy functional is derived for an arbitrary curved thin shell on the assumption that the magnetostatic effects can be reduced to an effective easy-surface anisotropy; it can be used for solving both static and dynamic problems. General static solns. are obtained in the limit of a strong anisotropy of both signs (easy-surface and easy-normal cases). It is shown that the effect of the curvature can be treated as the appearance of an effective magnetic field, which is aligned along the surface normal for the case of easy-surface anisotropy and is tangential to the surface for the case of easy-normal anisotropy. In general, the existence of such a field excludes the solns. that are strictly tangential or strictly normal to the surface. As an example, we consider static equil. solns. for a cone surface magnetization.
- 24Sheka, D. D.; Kravchuk, V. P.; Yershov, K. V.; Gaididei, Y. Torsion-induced effects in magnetic nanowires. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 92, 054417, DOI: 10.1103/PhysRevB.92.054417[Crossref], [CAS], Google Scholar24https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XislGisLo%253D&md5=850dfc3eaccb46a9ac2bdd2a548853c9Torsion-induced effects in magnetic nanowiresSheka, Denis D.; Kravchuk, Volodymyr P.; Yershov, Kostiantyn V.; Gaididei, YuriPhysical Review B: Condensed Matter and Materials Physics (2015), 92 (5), 054417/1-054417/13CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)A magnetic helix wire is one of the simplest magnetic systems which manifests properties of both curvature and torsion. Possible equil. magnetization states in the helix wire with different anisotropy directions are studied theor. There exist two equil. states in the helix wire with easy-tangential anisotropy: a quasitangential magnetization distribution in the case of relatively small curvatures and torsions, and an onion state in the opposite case. The curvature and torsion also essentially influence the spin-wave dynamics in the helix wire, acting as an effective magnetic field. Originated from a geometry-induced effective Dzyaloshinskii interaction, this magnetic field leads to a coupling between the helix chirality and the magnetochirality and breaks mirror symmetry in the spin-wave spectrum: the modification of magnon dispersion relation is linear with respect to the torsion and quadratic with respect to the curvature. All anal. predictions on magnetization statics and dynamics are well confirmed by direct spin-lattice simulations.
- 25Pylypovskyi, O. V.; Sheka, D. D.; Kravchuk, V. P.; Yershov, K. V.; Makarov, D.; Gaididei, Y. Rashba Torque Driven Domain Wall Motion in Magnetic Helices. Sci. Rep. 2016, 6, 23316, DOI: 10.1038/srep23316[Crossref], [PubMed], [CAS], Google Scholar25https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XkvVCnu7Y%253D&md5=398ebbd6984819946538931fc4527bffRashba Torque Driven Domain Wall Motion in Magnetic HelicesPylypovskyi, Oleksandr V.; Sheka, Denis D.; Kravchuk, Volodymyr P.; Yershov, Kostiantyn V.; Makarov, Denys; Gaididei, YuriScientific Reports (2016), 6 (), 23316CODEN: SRCEC3; ISSN:2045-2322. (Nature Publishing Group)Manipulation of the domain wall propagation in magnetic wires is a key practical task for a no. of devices including racetrack memory and magnetic logic. Recently, curvilinear effects emerged as an efficient mean to impact substantially the statics and dynamics of magnetic textures. Here, we demonstrate that the curvilinear form of the exchange interaction of a magnetic helix results in an effective anisotropy term and Dzyaloshinskii-Moriya interaction with a complete set of Lifshitz invariants for a one-dimensional system. In contrast to their planar counterparts, the geometrically induced modifications of the static magnetic texture of the domain walls in magnetic helixes offer unconventional means to control the wall dynamics relying on spin-orbit Rashba torque. The chiral symmetry breaking due to the Dzyaloshinskii-Moriya interaction leads to the opposite directions of the domain wall motion in left- or right-handed helixes. Furthermore, for the magnetic helixes, the emergent effective anisotropy term and Dzyaloshinskii-Moriya interaction can be attributed to the clear geometrical parameters like curvature and torsion offering intuitive understanding of the complex curvilinear effects in magnetism.
- 26Sheka, D. D.; Pylypovskyi, O. V.; Landeros, P.; Gaididei, Y.; Kákay, A.; Makarov, D. Nonlocal chiral symmetry breaking in curvilinear magnetic shells. Communications Physics 2020, 3, 128, DOI: 10.1038/s42005-020-0387-2
- 27Streubel, R.; Fischer, P.; Kronast, F.; Kravchuk, V. P.; Sheka, D. D.; Gaididei, Y.; Schmidt, O. G.; Makarov, D. Magnetism in curved geometries (Topical Review). J. Phys. D: Appl. Phys. 2016, 49, 363001, DOI: 10.1088/0022-3727/49/36/363001[Crossref], [CAS], Google Scholar27https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhvFOrtLjP&md5=88a88f4487ed4803ab3cd3decc60eb35Magnetism in curved geometriesStreubel, Robert; Fischer, Peter; Kronast, Florian; Kravchuk, Volodymyr P.; Sheka, Denis D.; Gaididei, Yuri; Schmidt, Oliver G.; Makarov, DenysJournal of Physics D: Applied Physics (2016), 49 (36), 363001/1-363001/45CODEN: JPAPBE; ISSN:0022-3727. (IOP Publishing Ltd.)Extending planar two-dimensional structures into the three-dimensional space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring the geometry of an object, e.g. its local curvature. In a generic electronic system, curvature results in the appearance of scalar and vector geometric potentials inducing anisotropic and chiral effects. In the specific case of magnetism, even in the simplest case of a curved anisotropic Heisenberg magnet, the curvilinear geometry manifests two exchange-driven interactions, namely effective anisotropy and antisym. exchange, i.e. Dzyaloshinskii-Moriya-like interaction. As a consequence, a family of novel curvature-driven effects emerges, which includes magnetochiral effects and topol. induced magnetization patterning, resulting in theor. predicted unlimited domain wall velocities, chirality symmetry breaking and Cherenkov-like effects for magnons. The broad range of altered phys. properties makes these curved architectures appealing in view of fundamental research on e.g. skyrmionic systems, magnonic crystals or exotic spin configurations. In addn. to these rich physics, the application potential of three-dimensionally shaped objects is currently being explored as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalog. devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices. These recent developments ranging from theor. predictions over fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, to their characterization using integral means as well as the development of advanced tomog. approaches are in the focus of this review.
- 28Fernández-Pacheco, A.; Streubel, R.; Fruchart, O.; Hertel, R.; Fischer, P.; Cowburn, R. P. Three-dimensional nanomagnetism. Nat. Commun. 2017, 8, 15756, DOI: 10.1038/ncomms15756[Crossref], [PubMed], [CAS], Google Scholar28https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BC1cnmslShsw%253D%253D&md5=1ac8c3c39e7c20144be54437b8f077b8Three-dimensional nanomagnetismFernandez-Pacheco Amalio; Cowburn Russell P; Streubel Robert; Fischer Peter; Fruchart Olivier; Hertel Riccardo; Fischer PeterNature communications (2017), 8 (), 15756 ISSN:.There is no expanded citation for this reference.
- 29Fischer, P.; Sanz-Hernández, D.; Streubel, R.; Fernández-Pacheco, A. Launching a new dimension with 3D magnetic nanostructures. APL Mater. 2020, 8, 010701, DOI: 10.1063/1.5134474[Crossref], [CAS], Google Scholar29https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXht1GjtLc%253D&md5=cb70d547d263a5d9890a25183bbd2e1cLaunching a new dimension with 3D magnetic nanostructuresFischer, Peter; Sanz-Hernandez, Dedalo; Streubel, Robert; Fernandez-Pacheco, AmalioAPL Materials (2020), 8 (1), 010701CODEN: AMPADS; ISSN:2166-532X. (American Institute of Physics)A review. The scientific and technol. exploration of three-dimensional magnetic nanostructures is an emerging research field that opens the path to exciting novel phys. phenomena, originating from the increased complexity in spin textures, topol., and frustration in three dimensions. One can also anticipate a tremendous potential for novel applications with those systems in a magnetic sensor and information processing technologies in terms of improved energy efficiency, processing speed, functionalities, and miniaturization of future spintronic devices. These three-dimensional structures are distinct from traditional bulk systems as they harness the scientific achievements of nanomagnetism, which aimed at lowering the dimensions down to the at. scale, but expand those now in a tailored and designed way into the third dimension. This research update provides an overview of the scientific challenges and recent progress with regard to advances in synthesis approaches and state-of-the-art nanoscale characterization techniques that are prerequisite to understand, realize, and control the properties, behavior, and functionalities of three-dimensional magnetic nanostructures. (c) 2020 American Institute of Physics.
- 30Vedmedenko, E. Y.; Kawakami, R. K.; Sheka, D.; Gambardella, P.; Kirilyuk, A.; Hirohata, A.; Binek, C.; Chubykalo-Fesenko, O. A.; Sanvito, S.; Kirby, B.; Grollier, J.; Everschor-Sitte, K.; Kampfrath, T.; You, C.-Y.; Berger, A. The 2020 Magnetism Roadmap. J. Phys. D: Appl. Phys. 2020, 53, 453001, DOI: 10.1088/1361-6463/ab9d98[Crossref], [CAS], Google Scholar30https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXisVykurbE&md5=b753b25a6da73ed203598d62d9851603The 2020 magnetism roadmapVedmedenko, E. Y.; Kawakami, R. K.; Sheka, D. D.; Gambardella, P.; Kirilyuk, A.; Hirohata, A.; Binek, C.; Chubykalo-Fesenko, O.; Sanvito, S.; Kirby, B. J.; Grollier, J.; Everschor-Sitte, K.; Kampfrath, T.; You, C-Y.; Berger, A.Journal of Physics D: Applied Physics (2020), 53 (45), 453001CODEN: JPAPBE; ISSN:0022-3727. (IOP Publishing Ltd.)Following the success and relevance of the 2014 and 2017 Magnetism Roadmap articles, this 2020 Magnetism Roadmap edition takes yet another timely look at newly relevant and highly active areas in magnetism research. The overall layout of this article is unchanged, given that it has proved the most appropriate way to convey the most relevant aspects of today's magnetism research in a wide variety of sub-fields to a broad readership. A different group of experts has again been selected for this article, representing both the breadth of new research areas, and the desire to incorporate different voices and viewpoints. The latter is esp. relevant for thistype of article, in which one's field of expertise has to be accommodated on two printed pages only, so that personal selection preferences are naturally rather more visible than in other types of articles. Most importantly, the very relevant advances in the field of magnetism research in recent years make the publication of yet another Magnetism Roadmap a very sensible and timely endeavour, allowing its authors and readers to take another broad-based, but concise look at the most significant developments in magnetism, their precise status, their challenges, and their anticipated future developments. While many of the contributions in this 2020 Magnetism Roadmap edition have significant assocns. with different aspects of magnetism, the general layout can nonetheless be classified in terms of three main themes: (i) phenomena, (ii) materials and characterization, and (iii) applications and devices. While these categories are unsurprisingly rather similar to the 2017 Roadmap, the order is different, in that the 2020 Roadmap considers phenomena first, even if their occurrences are naturally very difficult to sep. from the materials exhibiting such phenomena. Nonetheless, the specifically selected topics seemed to be best displayed in the order presented here, in particular, because many of the phenomena or geometries discussed in (i) can be found or designed into a large variety of materials, so that the progression of the article embarks from more general concepts to more specific classes of materials in the selected order. Given that applications and devices are based on both phenomena and materials, it seemed most appropriate to close the article with the application and devices section (iii) once again. The 2020 Magnetism Roadmap article contains 14 sections, all of which were written by individual authors and experts, specifically addressing a subject in terms of its status, advances, challenges and perspectives in just two pages. Evidently, this two-page format limits the depth to which each subject can be described. Nonetheless, the most relevant and key aspects of each field are touched upon, which enables the Roadmap as whole to give its readership an initial overview of and outlook into a wide variety of topics and fields in a fairly condensed format. Correspondingly, the Roadmap pursues the goal of giving each reader a brief ref. frame of relevant and current topics in modern applied magnetism research, even if not all sub-fields can be represented here. The first block of this 2020 Magnetism Roadmap, which is focussed on (i) phenomena, contains five contributions, which address the areas of interfacial Dzyaloshinskii-Moriya interactions, and two-dimensional and curvilinear magnetism, as well as spin-orbit torque phenomena and all optical magnetization reversal. All of these contributions describe cutting edge aspects of rather fundamental phys. processes and properties, assocd. with new and improved magnetic materials' properties, together with potential developments in terms of future devices and technol. As such, they form part of a widening magnetism 'phenomena reservoir' for utilization in applied magnetism and related device technol. The final block (iii) of this article focuses on such applications and device-related fields in four contributions relating to currently active areas of research, which are of course utilizing magnetic phenomena to enable specific functions. These contributions highlight the role of magnetism or spintronics in the field of neuromorphic and reservoir computing, terahertz technol., and domain wall-based logic. One aspect common to all of these application-related contributions is that they are not yet being utilized in com. available technol.; it is currently still an open question, whether or not such technol. applications will be magnetism-based at all in the future, or if other types of materials and phenomena will yet outperform magnetism. This last point is actually a very good indication of the vibrancy of applied magnetism research today, given that it demonstrates that magnetism research is able to venture into novel application fields, based upon its portfolio of phenomena, effects and materials. This materials portfolio in particular defines the central block (ii) of this article, with its five contributions interconnecting phenomena with devices, for which materials and the characterization of their properties is the decisive discriminator between purely academically interesting aspects and the true viability of real-life devices, because only available materials and their assocd. fabrication and characterization methods permit reliable technol. implementation. These five contributions specifically address magnetic films and multiferroic heterostructures for the purpose of spin electronic utilization, multi-scale materials modeling, and magnetic materials design based upon machine-learning, as well as materials characterization via polarized neutron measurements. As such, these contributions illustrate the balanced relevance of research into exptl. and modeling magnetic materials, as well the importance of sophisticated characterization methods that allow for an ever-more refined understanding of materials. As a combined and integrated article, this 2020 Magnetism Roadmap is intended to be a ref. point for current, novel and emerging research directions in modern magnetism, just as its 2014 and 2017 predecessors have been in previous years.
- 31Otálora, J. A.; Yan, M.; Schultheiss, H.; Hertel, R.; Kákay, A. Curvature-Induced Asymmetric Spin-Wave Dispersion. Phys. Rev. Lett. 2016, 117, 227203, DOI: 10.1103/PhysRevLett.117.227203[Crossref], [PubMed], [CAS], Google Scholar31https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXhsVWrurfI&md5=ea5b501cd63efeea6ecf68a2ffb4cd3eCurvature-induced asymmetric spin-wave dispersionOtalora, Jorge A.; Yan, Ming; Schultheiss, Helmut; Hertel, Riccardo; Kakay, AttilaPhysical Review Letters (2016), 117 (22), 227203/1-227203/6CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)In magnonics, spin waves are conceived of as electron-charge-free information carriers. Their wave behavior has established them as the key elements to achieve low power consumption, fast operative rates. and good packaging in tnagnon-based computational technologies. Hence, knowing alternative ways that reveal certain properties of their undulatory motion is an important task. Here, we show using micromagnette simulations and anal. calcns. that spin-wave propagation in ferromagnetic nanotubes is fundamentally different than in thin films. The dispersion relation is asym. regarding the sign of the wave vector, It is a purely curvature-induced effect and its fundamental origin is identified to he the classical dipole-dipole interaction. The anal. expression of the dispersion relation has the same math. form as in thin films with the Dzyalonshiinsky-Moriya interaction. Therefore. this curvature- induced effect can be seen as a "dipole-induced Dzyalonshiinsky-Moriya-like" effect.
- 32Vojkovic, S.; Carvalho-Santos, V. L.; Fonseca, J. M.; Nunez, A. S. Vortex-antivortex pairs induced by curvature in toroidal nanomagnets. J. Appl. Phys. 2017, 121, 113906, DOI: 10.1063/1.4977983[Crossref], [CAS], Google Scholar32https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXkvFWhs7c%253D&md5=faf7bb204de3e97807994e8d090c11c8Vortex-antivortex pairs induced by curvature in toroidal nanomagnetsVojkovic, Smiljan; Carvalho-Santos, Vagson L.; Fonseca, Jakson M.; Nunez, Alvaro S.Journal of Applied Physics (Melville, NY, United States) (2017), 121 (11), 113906/1-113906/7CODEN: JAPIAU; ISSN:0021-8979. (American Institute of Physics)We show that the curvature of nanomagnets can be used to induce chiral textures in the magnetization field. Among the phenomena related to the interplay between the geometry and magnetic behavior of nanomagnets, an effective curvature-induced chiral interaction has been recently predicted. In this work, it is shown that magnetization configurations consisting of two structures with opposite winding nos. (vortex and antivortex) appear as remanent states in hollow toroidal nanomagnets. It is shown that these topol. configurations are a result of a chiral interaction induced by curvature. In this way, the obtained results present a new form to produce stable vortices and antivortices by using nanomagnets with variable curvature. (c) 2017 American Institute of Physics.
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- 37Mizoguchi, K.; Tanaka, S.; Ogawa, T.; Shiobara, N.; Sakamoto, H. Magnetic study of the electronic states of B-DNA and M-DNA doped with metal ions. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 72, 033106, DOI: 10.1103/PhysRevB.72.033106[Crossref], [CAS], Google Scholar38https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXmvF2jtLc%253D&md5=54a58b35e116a0ec38edae2521d30534Magnetic study of the electronic states of B-DNA and M-DNA doped with metal ionsMizoguchi, Kenji; Tanaka, Shunsuke; Ogawa, Tasuku; Shiobara, Naofumi; Sakamoto, HirokazuPhysical Review B: Condensed Matter and Materials Physics (2005), 72 (3), 033106/1-033106/4CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)The magnetic properties of the pristine and metal ion doped DNA (DNA) of salmon are investigated with ESR (EPR), superconducting quantum interference device and energy dispersive x-ray fluorescence spectroscopy. Purified salmon DNA gives intrinsically no EPR signal, which is consistent with DNA being a semiconductor, but not with DNA having metallic or superconducting properties as reported previously. Several kinds of divalent ions (Zn, Mn, Ca,...) are used as dopants, resulting in no substantial EPR signal except in the case of Mn. This leads to the conclusion that a metal ion counterbalances two phosphate anions instead of Na counterions in B-DNA, which contradicts the metallic behavior reported previously [A. Rakitin et al, Phys. Rev. Lett. 86, 3670 (2001)].
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- 41de Sousa, R.; Moore, J. E. Optical coupling to spin waves in the cycloidal multiferroic BiFeO3. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 77, 012406, DOI: 10.1103/PhysRevB.77.012406[Crossref], [CAS], Google Scholar42https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1cXhsVGlsL8%253D&md5=0f54815cee0bace92e39b463d6a3fa18Optical coupling to spin waves in the cycloidal multiferroic BiFeO3de Sousa, Rogerio; Moore, Joel E.Physical Review B: Condensed Matter and Materials Physics (2008), 77 (1), 012406/1-012406/4CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)The magnon and optical phonon spectrum of an incommensurate multiferroic such as BiFeO3 is considered in the framework of a phenomenol. Landau theory. The resulting spin wave spectrum is quite distinct from commensurate substances due to soft mode anisotropy and magnon zone folding. The former allows elec. control of spin wave propagation via reorientation of the spontaneous ferroelec. moment. The latter gives rise to multiple magnetodielec. resonances due to the coupling of optical phonons at zero wave vector to magnons at integer multiples of the cycloid wave vector. These results show that the optical response of a multiferroic reveals much more about its magnetic excitations than previously anticipated on the basis of simpler models.
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- 43Stamps, R. L.; Camley, R. E. Dipole-exchange spin-wave modes in very-thin-film antiferromagnets. Phys. Rev. B: Condens. Matter Mater. Phys. 1987, 35, 1919– 1931, DOI: 10.1103/PhysRevB.35.1919
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- 45Yuan, W.; Zhu, Q.; Su, T.; Yao, Y.; Xing, W.; Chen, Y.; Ma, Y.; Lin, X.; Shi, J.; Shindou, R.; Xie, X. C.; Han, W. Experimental signatures of spin superfluid ground state in canted antiferromagnet Cr2O3 via nonlocal spin transport. Science Advances 2018, 4, eaat1098 DOI: 10.1126/sciadv.aat1098
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- 47Evers, M.; Nowak, U. Transport properties of spin superfluids: Comparing easy-plane ferromagnets and antiferromagnets. Phys. Rev. B: Condens. Matter Mater. Phys. 2020, 101, 184415, DOI: 10.1103/PhysRevB.101.184415
- 48Demokritov, S. O.; Demidov, V. E.; Dzyapko, O.; Melkov, G. A.; Serga, A. A.; Hillebrands, B.; Slavin, A. N. Bose–Einstein condensation of quasi-equilibrium magnons at room temperature under pumping. Nature 2006, 443, 430– 433, DOI: 10.1038/nature05117[Crossref], [PubMed], [CAS], Google Scholar49https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28XhtVSns7fN&md5=0cb4e6f4f4755490862aac5fe63d6b70Bose-Einstein condensation of quasi-equilibrium magnons at room temperature under pumpingDemokritov, S. O.; Demidov, V. E.; Dzyapko, O.; Melkov, G. A.; Serga, A. A.; Hillebrands, B.; Slavin, A. N.Nature (London, United Kingdom) (2006), 443 (7110), 430-433CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)Bose-Einstein condensation is one of the most fascinating phenomena predicted by quantum mechanics. It involves the formation of a collective quantum state composed of identical particles with integer angular momentum (bosons), if the particle d. exceeds a crit. value. To achieve Bose-Einstein condensation, one can either decrease the temp. or increase the d. of bosons. It has been predicted that a quasi-equil. system of bosons could undergo Bose-Einstein condensation even at relatively high temps., if the flow rate of energy pumped into the system exceeds a crit. value. Here we report the observation of Bose-Einstein condensation in a gas of magnons at room temp. Magnons are the quanta of magnetic excitations in a magnetically ordered ensemble of magnetic moments. In thermal equil., they can be described by Bose-Einstein statistics with zero chem. potential and a temp.-dependent d. In the expts. presented here, we show that by using a technique of microwave pumping it is possible to excite addnl. magnons and to create a gas of quasi-equil. magnons with a non-zero chem. potential. With increasing pumping intensity, the chem. potential reaches the energy of the lowest magnon state, and a Bose condensate of magnons is formed.
- 49Serga, A. A.; Tiberkevich, V. S.; Sandweg, C. W.; Vasyuchka, V. I.; Bozhko, D. A.; Chumak, A. V.; Neumann, T.; Obry, B.; Melkov, G. A.; Slavin, A. N.; Hillebrands, B. Bose–Einstein condensation in an ultra-hot gas of pumped magnons. Nat. Commun. 2014, 5, 3452, DOI: 10.1038/ncomms4452[Crossref], [PubMed], [CAS], Google Scholar50https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BC2crhslensQ%253D%253D&md5=e40378d8def1f221bc66f243e4029329Bose-Einstein condensation in an ultra-hot gas of pumped magnonsSerga Alexander A; Sandweg Christian W; Vasyuchka Vitaliy I; Chumak Andrii V; Neumann Timo; Obry Bjorn; Hillebrands Burkard; Tiberkevich Vasil S; Slavin Andrei N; Bozhko Dmytro A; Melkov Gennadii ANature communications (2014), 5 (), 3452 ISSN:.Bose-Einstein condensation of quasi-particles such as excitons, polaritons, magnons and photons is a fascinating quantum mechanical phenomenon. Unlike the Bose-Einstein condensation of real particles (like atoms), these processes do not require low temperatures, since the high densities of low-energy quasi-particles needed for the condensate to form can be produced via external pumping. Here we demonstrate that such a pumping can create remarkably high effective temperatures in a narrow spectral region of the lowest energy states in a magnon gas, resulting in strikingly unexpected transitional dynamics of Bose-Einstein magnon condensate: the density of the condensate increases immediately after the external magnon flow is switched off and initially decreases if it is switched on again. This behaviour finds explanation in a nonlinear 'evaporative supercooling' mechanism that couples the low-energy magnons overheated by pumping with all the other thermal magnons, removing the excess heat, and allowing Bose-Einstein condensate formation.
- 50Clausen, P.; Bozhko, D. A.; Vasyuchka, V. I.; Hillebrands, B.; Melkov, G. A.; Serga, A. A. Stimulated thermalization of a parametrically driven magnon gas as a prerequisite for Bose–Einstein magnon condensation. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 91, 220402(R) DOI: 10.1103/PhysRevB.91.220402
- 51Bozhko, D. A.; Serga, A. A.; Clausen, P.; Vasyuchka, V. I.; Heussner, F.; Melkov, G. A.; Pomyalov, A.; L’vov, V. S.; Hillebrands, B. Supercurrent in a room-temperature Bose–Einstein magnon condensate. Nat. Phys. 2016, 12, 1057– 1062, DOI: 10.1038/nphys3838[Crossref], [CAS], Google Scholar52https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28Xht1ygs7%252FI&md5=49a77c9ff2eb446ddbce588241925e63Supercurrent in a room-temperature Bose-Einstein magnon condensateBozhko, Dmytro A.; Serga, Alexander A.; Clausen, Peter; Vasyuchka, Vitaliy I.; Heussner, Frank; Melkov, Gennadii A.; Pomyalov, Anna; L'vov, Victor S.; Hillebrands, BurkardNature Physics (2016), 12 (11), 1057-1062CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)A supercurrent is a macroscopic effect of a phase-induced collective motion of a quantum condensate. So far, exptl. obsd. supercurrent phenomena such as supercond. and superfluidity have been restricted to cryogenic temps. Here, we report on the discovery of a supercurrent in a Bose-Einstein magnon condensate prepd. in a room-temp. ferrimagnetic film. The magnon condensate is formed in a parametrically pumped magnon gas and is subject to a thermal gradient created by local laser heating of the film. The appearance of the supercurrent, which is driven by a thermally induced phase shift in the condensate wavefunction, is evidenced by anal. of the temporal evolution of the magnon d. measured by means of Brillouin light scattering spectroscopy. Our findings offer opportunities for the investigation of room-temp. macroscopic quantum phenomena and their potential applications at ambient conditions.
- 52Zhang, X.; Li, B.; Zhang, J. An Efficient Strategy for Self-Assembly of DNA-Mimic Homochiral 1D Helical Cu(II) Chain from Achiral Flexible Ligand by Spontaneous Resolution. Inorg. Chem. 2016, 55, 3378– 3383, DOI: 10.1021/acs.inorgchem.5b02785[ACS Full Text], [CAS], Google Scholar53https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XksV2gsL8%253D&md5=bdcba11500b8b8360129b979502ee433An Efficient Strategy for Self-Assembly of DNA-Mimic Homochiral 1D Helical Cu(II) Chain from Achiral Flexible Ligand by Spontaneous ResolutionZhang, Xiaoying; Li, Bo; Zhang, JingpingInorganic Chemistry (2016), 55 (7), 3378-3383CODEN: INOCAJ; ISSN:0020-1669. (American Chemical Society)Four helical copper complexes Cu[NCN2]2Hhmp (1), Cu[NCN2]2Hhmp∞ (2), L-Cu4[NCN2]2hmp4CH3COO2· CH3CN∞ (3a), and D-Cu4[NCN2]2hmp4CH3COO2· CH3CN∞ (3b) Hhmp = 2-hydroxymethylpyridine have been prepd. toward a mimic DNA structure. By changing the solvent and supplementary ligand, the structures can be successfully tuned from quasi-double-helical complex 1 to racemic 1D single helix complex 2, then the right 3a)-/left 3b-handed double helixes. The topologies of 3a and 3b may be considered as a mimic of DNA, where the Cu-O bonds between the two strands replace the hydrogen-bonding interactions in DNA. Solid-state CD spectra confirmed that 3a and 3b are optically active, resp. Magnetic measurements for 1-3 indicated all complexes to be antiferromagnetic interactions. The best fitting results to the magnetic susceptibilities were J = -0.80 cm-1, g = 2.11 for 1 and J1 = -9.22 cm-1, J2 = 3.56 cm-1, J3 = -9.49 cm-1, g = 2.27 for 3.
- 53Zhang, H. Y.; Calzolari, A.; Di Felice, R. On the Magnetic Alignment of Metal Ions in a DNA-Mimic Double Helix. J. Phys. Chem. B 2005, 109, 15345– 15348, DOI: 10.1021/jp052202t[ACS Full Text], [CAS], Google Scholar54https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXmtlGrsLc%253D&md5=36fe09b0363b65a6b55fddaa6e10c24aOn the Magnetic Alignment of Metal Ions in a DNA-Mimic Double HelixZhang, Hou Yu; Calzolari, Arrigo; Di Felice, RosaJournal of Physical Chemistry B (2005), 109 (32), 15345-15348CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)We computed by spin-polarized DFT the structure and the electronic properties of an infinite periodic wire constituted of planar Cu-bridged hydroxypyridone chelator base pairs and of a similarly stacked finite dimer. The Cu centers undergo electronic hybridization with the bases. There is an unpaired spin per plane, and the majority-spins manifest ordering: The ferromagnetic and antiferromagnetic phases are energetically degenerate. The total magnetization of the ferromagnetic wire depends linearly on the no. of planes in the stack. The combination of interplane spin coupling and intraplane metal-hydroxypyridone coupling makes this system very appealing for electronic and magnetic device exploitation.
- 54Yamaguchi, K.; Taniguchi, T.; Kawakami, T.; Hamamoto, T.; Okumura, M. Possibilities of magnetic modifications of DNA wires, sheets and related materials. Polyhedron 2005, 24, 2758– 2766, DOI: 10.1016/j.poly.2005.03.132[Crossref], [CAS], Google Scholar55https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXhtFymtrnE&md5=569921e3c679fb0a7938281e7dafa645Possibilities of magnetic modifications of DNA wires, sheets and related materialsYamaguchi, K.; Taniguchi, T.; Kawakami, T.; Hamamoto, T.; Okumura, M.Polyhedron (2005), 24 (16-17), 2758-2766CODEN: PLYHDE; ISSN:0277-5387. (Elsevier B.V.)Our theor. efforts towards mol.-based magnetic conductors and superconductors on the basis of ab initio Hamiltonians and effective model Hamiltonians are summarized in relation to recently developed DNA-based mol. materials. Guanine and adenine derivs. coupling with org. radicals (R) are investigated as possible π-R components. In order to elucidate electronic and magnetic properties of these species, effective exchange integrals (Jab) for magnetic clusters are calcd. by ab initio hybrid d. functional methods. Theor. possibilities of org. magnetic conductors and the org. solenoid are elucidated on the basis of these models in self-assembled DNA wires, sheets and related materials. Implications of the calcd. results are finally discussed in order to obtain a unified picture of many p-d, π-d and π-R mol.-based systems with strong electron correlations.
- 55Mizoguchi, K.; Tanaka, S.; Ojima, M.; Sano, S.; Nagatori, M.; Sakamoto, H.; Yonezawa, Y.; Aoki, Y.; Sato, H.; Furukawa, K.; Nakamura, T. AF-like Ground State of Mn-DNA and Charge Transfer from Fe to Base-π-Band in Fe-DNA. J. Phys. Soc. Jpn. 2007, 76, 043801, DOI: 10.1143/JPSJ.76.043801[Crossref], [CAS], Google Scholar56https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXls1ansrY%253D&md5=78be548e5a8095f42132879739cbd122AF-like ground state of Mn-DNA and charge transfer from Fe to base-π-band in Fe-DNAMizoguchi, Kenji; Tanaka, Shunsuke; Ojima, Masaya; Sano, Sayaka; Nagatori, Mai; Sakamoto, Hirokazu; Yonezawa, Yuki; Aoki, Yuji; Sato, Hideyuki; Furukawa, Kou; Nakamura, ToshikazuJournal of the Physical Society of Japan (2007), 76 (4), 043801/1-043801/4CODEN: JUPSAU; ISSN:0031-9015. (Physical Society of Japan)The electronics states of M-DNA doped with M = Mg, Ca, Zn, Mn, Fe are investigated mainly with magnetic properties. In the "wet" condition the Mn ions of Mn-DNA form a 1-D chain in the center of a DNA double helix, as evidenced from the formation of the unnatural base pair combination with M, poly(dA)-M-poly(dC), but in the "dry" condition they form a 3-D network with the antiferromagnetic ground state around 0.4 K with the superexchange coupling via water mols. The valence of 3+ is found only in Fe-DNA, from which the base π-band obtains π charge carriers.
- 56Samanta, P. K.; Pati, S. K. Structural and Magnetic Properties of a Variety of Transition Metal Incorporated DNA Double Helices. Chem. - Eur. J. 2014, 20, 1760– 1764, DOI: 10.1002/chem.201302628[Crossref], [PubMed], [CAS], Google Scholar57https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXms1em&md5=801fd4344d346cc7396b2dbc1aa0fb14Structural and Magnetic Properties of a Variety of Transition Metal Incorporated DNA Double HelixesSamanta, Pralok K.; Pati, Swapan K.Chemistry - A European Journal (2014), 20 (6), 1760-1764CODEN: CEUJED; ISSN:0947-6539. (Wiley-VCH Verlag GmbH & Co. KGaA)By using d. functional theory calcns., the structural, energetic, magnetic, and optical properties for a variety of transition metal (M = Mn, Fe, Co, Ni and Cu) ions incorporated modified-DNA (M-DNA) double helixes was studied. The DNA is modified with either hydroxypyridone (H) or bis(salicylaldehyde)ethylenediamine (S-en) metalated bases. The formation of extended M-O network leading to the ferromagnetic interactions for the case of H-DNA for all the metal ions were found. More ordered stacking arrangement was found for S-en-DNA. The authors calc. the exchange coupling const. (J) considering Heisenberg Hamiltonian for quant. description of magnetic interactions. The ferromagnetic and antiferromagnetic interactions were obtained by varying different transition metal ions. The extent of the magnetic interaction depends on the no. of transition metal ions. Optical profiles show peaks <2 eV, a clear signature of spin-spin coupling.
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ARTICLE SECTIONSThe Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.0c03246.
Details on analytical calculations and numerical simulations, including (i) the geometry, (ii) the model of curvilinear antiferromagnet, (iii) dipolar interaction in spin chains as an effective anisotropy (both ferromagnetic and antiferromagnetic ordering, and curvilinear antiferromagnetic spin chains), (iv) the homogeneous state of antiferromagnetic helix chains, (v) the periodic state of antiferromagnetic helix chains, (vi) the boundary between states, (vii) The ground state of antiferromagnetic flat chains, (viii) spin waves in antiferromagnetic flat chains, (ix) spin waves in antiferromagnetic helices and stability of the homogeneous state, and (x) simulations (PDF)
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