Ferroelectric Control of the Spin Texture in GeTe
- Christian Rinaldi*Christian Rinaldi*E-mail: [email protected]. Phone: +39-02-2399-9661.Department of Physics, Politecnico di Milano, 20133 Milano, ItalyIFN-CNR, Politecnico di Milano, 20133 Milano, ItalyMore by Christian Rinaldi
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- Sara Varotto
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- Marco Asa
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- Jagoda SławińskaJagoda SławińskaConsiglio Nazionale delle Ricerche CNR-SPIN, Sede Temporanea di Chieti, c/o Univ. “G. D’Annunzio”, 66100 Chieti, ItalyMore by Jagoda Sławińska
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- Jun FujiiJun FujiiCNR-IOM, Laboratorio TASC in Area Science Park - Basovizza, 34149 Trieste, ItalyMore by Jun Fujii
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- Giovanni VinaiGiovanni VinaiCNR-IOM, Laboratorio TASC in Area Science Park - Basovizza, 34149 Trieste, ItalyMore by Giovanni Vinai
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- Stefano CecchiStefano CecchiPaul-Drude-Institut für Festkörperelektronik, Hausvogteiplatz 5-7, 10117 Berlin, GermanyMore by Stefano Cecchi
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- Domenico Di SanteDomenico Di SanteInstitut für Theoretische Physik und Astrophysik, Universität Würzburg, Am Hubland Campus Süd, Würzburg 97074, GermanyMore by Domenico Di Sante
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- Raffaella CalarcoRaffaella CalarcoPaul-Drude-Institut für Festkörperelektronik, Hausvogteiplatz 5-7, 10117 Berlin, GermanyMore by Raffaella Calarco
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- Ivana VobornikIvana VobornikCNR-IOM, Laboratorio TASC in Area Science Park - Basovizza, 34149 Trieste, ItalyMore by Ivana Vobornik
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- Giancarlo PanaccioneGiancarlo PanaccioneCNR-IOM, Laboratorio TASC in Area Science Park - Basovizza, 34149 Trieste, ItalyMore by Giancarlo Panaccione
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- Silvia PicozziSilvia PicozziConsiglio Nazionale delle Ricerche CNR-SPIN, Sede Temporanea di Chieti, c/o Univ. “G. D’Annunzio”, 66100 Chieti, ItalyMore by Silvia Picozzi
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- Riccardo Bertacco*Riccardo Bertacco*E-mail: [email protected]. Phone: +39-02-2399-9663.Department of Physics, Politecnico di Milano, 20133 Milano, ItalyIFN-CNR, Politecnico di Milano, 20133 Milano, ItalyMore by Riccardo Bertacco
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Abstract
The electric and nonvolatile control of the spin texture in semiconductors would represent a fundamental step toward novel electronic devices combining memory and computing functionalities. Recently, GeTe has been theoretically proposed as the father compound of a new class of materials, namely ferroelectric Rashba semiconductors. They display bulk bands with giant Rashba-like splitting due to the inversion symmetry breaking arising from the ferroelectric polarization, thus allowing for the ferroelectric control of the spin. Here, we provide the experimental demonstration of the correlation between ferroelectricity and spin texture. A surface-engineering strategy is used to set two opposite predefined uniform ferroelectric polarizations, inward and outward, as monitored by piezoresponse force microscopy. Spin and angular resolved photoemission experiments show that these GeTe(111) surfaces display opposite sense of circulation of spin in bulk Rashba bands. Furthermore, we demonstrate the crafting of nonvolatile ferroelectric patterns in GeTe films at the nanoscale by using the conductive tip of an atomic force microscope. Based on the intimate link between ferroelectric polarization and spin in GeTe, ferroelectric patterning paves the way to the investigation of devices with engineered spin configurations.
While Moore’s law seems to approach its limit of validity, the search for new paradigms allowing the further improvement of the computing capabilities of electronic devices is entering a final rush. Spintronics is a promising route in this perspective, but so far, its success stories are limited to the field of memories. To enter the area of computing, devices capable of manipulating the information encoded in the spin are needed. In this sense, a lot of effort is currently carried out in the fields of spin logic, (1) magnon spintronics, (2,3) and semiconductor spintronics. (4−7) Nevertheless, about 20 years after the pioneering idea of “spin transistor” proposed by Datta and Das, (8) many practical limitations still prevent the implementation of effective transistors based on spin properties. (9) The dream remains to manipulate spins within semiconductors devices to exploit the full potential of materials with a gap for charge control, without use of auxiliary ferromagnetic materials and magnetic fields. Beyond magnetic semiconductors, (10) which still suffer from low-temperature operation and the need of external magnetic fields to control the spin texture, new materials and concepts are necessary. In this context, the recently introduced class of ferroelectric Rashba semiconductors (FERSCs), (11) whose father compound is α-GeTe, (12) is highly promising. They are semiconductors and also ferroelectrics, so that the remanent ferroelectric polarization vector breaks the inversion symmetry and determines a giant bulk Rashba k-dependent spin-splitting of the bands. (13) Remarkably, density functional theory (DFT) simulations predict that the spin direction in each sub-band should reverse upon inversion of the ferroelectric polarization, thereby allowing its electrical control. In perspective, these unique features could be exploited in novel devices (14,15) integrating memory and computing functionalities within the very same channel of a spin-transistor. (16) While ferroelectric hysteresis provides the memory functionality, spin-dependent transport phenomena in spin textures defined by ferroelectric domains can implement computing, within the very same devices.
In this paper, we address a fundamental issue on the roadmap toward the exploitation of FERSCs: the nonvolatile, but reversible, electric control of the spin texture in α-GeTe thin films down to the nanoscale, thus paving the way to the definition of unconventional spin configurations in semiconductors. The electric switching of the ferroelectric (FE) polarization has been already demonstrated in GeTe(111) films (13) and more recently in GeTe nanowires. (17) However, an experimental proof of the reversal of the spin texture (the clockwise or counterclockwise sense of circulation of spins in bulk Rashba-like bands) for opposite FE polarization is still missing. So far, only a link between the direction of the FE polarization and the spin orientation in the surface Rashba sub-bands has been reported. (13) More recently, the impact of magnetic fields on the spin texture of Mn-doped GeTe films has been investigated but always for fixed FE polarization. (18)
Here, we experimentally establish the intimate link between the orientation of the remanent ferroelectric polarization and the circulation of spin texture associated with Rashba bands in GeTe(111) thin films. First, we describe a surface engineering strategy to prepare in situ α-GeTe(111) films with uniform pristine ferroelectric polarization, outward or inward. Then, by spin- and angular-resolved photoemission spectroscopy (S-ARPES), we provide evidence for opposite sense of spin circulation of bulk Rashba bands in the two surfaces prepared with opposite FE polarization. Our results suggest the possibility of crafting the spin texture at the nanoscale in GeTe via ferroelectric patterning. In this route, we demonstrate the reversible writing of an array of nanostripes with inward and outward FE polarization, assumed to have opposite spin configurations. This represents a first example of engineered meta-material based on a ferroelectric Rashba semiconductor, suitable to implement the concept of Rashba barriers. In perspective, our results pave the way to the exploitation of GeTe in unconventional spintronic devices with pure electric control of their operation and reconfigurable computing functionalities.
The first step toward the demonstration of the link between FE state and spin texture in GeTe by S-ARPES is the initialization of the whole film, leading to a uniform pristine FE polarization pointing inward or outward. This also corresponds to the “clean blackboard” state preliminary to any patterning. In this scope, we developed a method for preparing α-GeTe(111) surfaces with opposite FE polarization, associated with different terminations. Rhombohedral α-GeTe(111) results from the stacking of Ge and Te planes, which are not equidistant and thus give rise to a net electric dipole, being Te more electronegative than Ge. (19,20)
As the energetically favored termination is generated by the breaking of long (rather than short) bonds, a Te terminated surface is expected to display a dipole pointing outward (Pout), while a Ge-terminated one will have a net dipole inward (Pin), as depicted in panels a and a′ of Figure 1. Even though calculations predict the Te-terminated GeTe(111) to be more stable than the Ge-terminated one by 60 meV Å–2, this surface energy difference is largely reduced by the presence of reconstructions, (21) vacancies, and other kind of defects, thus suggesting the possibility of stabilizing both terminations in real surfaces.
Figure 1
Figure 1. GeTe(111) surfaces with opposite FE polarization. (a, a′) Sketch of the Ge and Te planes for the Te and Ge termination, respectively. The distances given on the left refer to the unrelaxed interlayer distances. Only the topmost surface atoms of the slab are shown. The black rectangle denotes a bulk hexagonal unit cell used in DFT calculations as a building block to construct the (111) surface (rhombohedral setting, corresponding to the (0001) in the hexagonal setting). The net FE polarization Pout (Pin) (white arrows) arises from the interatomic dipoles shown with blue and red arrows. (b, b′) Piezoresponse-phase images recorded on STe (SGe) after poling with the tip at +7 V (−7 V) and −7 V (+7 V) over two concentric squares of 1.5 and 0.5 μm per side. The scale bar corresponds to 0.5 μm. (c, c′) PFM-phase signal showing the pristine polarization state and the ferroelectric hysteresis loop, as measured ex-situ on STe and SGe after the S-ARPES experiment. The controlled thermal desorption of the Te capping layer leads to a virgin-state FE polarization Pout and Pin in the two samples, respectively.
GeTe(111) films, 23 nm thick, were grown by molecular beam epitaxy (MBE) on Si(111) and then capped with 20 nm of Te to prevent contamination due to exposure to atmosphere. A reliable protocol for controlled Te-desorption in ultrahigh vacuum (UHV) has been first optimized to obtain Ge- and Te-rich surfaces with opposite polarization, as checked by X-ray photoemission spectroscopy (XPS) with Al–Kα radiation and piezoresponse force microscopy (PFM) (for details, see sections 1 and 2 of the Supporting Information). An annealing of 1 h at about 240 °C produces a Te-rich surface displaying a pristine polarization Pout, while the same annealing at 260 °C causes a complete desorption of Te (the more volatile species) and produces a Ge-rich surface with Pin. Crucial for this paper, the same method has been applied to samples prepared in situ for S-ARPES, to demonstrate that opposite FE polarization states are associated with inverse spin texture. After insertion in vacuum at the APE beamline, the samples were annealed at about 240 and 260 °C for 1 h, controlling the heater current. According to the recipe previously optimized (for details see section 2 of the Supporting Information), we obtained a first sample (STe) with a Te-rich surface and a second one (SGe) with a Ge-rich surface, as confirmed by the in situ analysis of the XPS spectra taken at 800 eV photon energy (see section 3 of the Supporting Information). In fact, from the relative intensity of the Ge 3d and Te 4d peaks, normalized to the analyzer transmission and tabulated atomic photoemission cross-sections, the average stoichiometries of STe and SGe are Ge0.39Te0.61 and Ge0.46Te0.54, respectively. The uncertainty on the relative stoichiometry is ± 0.02, and it mainly arises from the error on the estimation of the peaks’ area. Within the photoemission probing depth (∼17 Å at 800 eV photon energy), STe is clearly Te-rich, while the Ge concentration in SGe is slightly above that of GeTe films, which typically displays 10% Ge vacancies (Ge0.45Te0.55), (22,23) thus pointing toward a Ge enrichment of SGe. Data taken with Al–Kα radiation (1486.6 eV), after the beamtime, confirm that STe (SGe) is Te (Ge) rich at surface (see section 2 of the Supporting Information). Furthermore, the deconvolution of XPS spectra, using surface and bulk components (section 2 of the Supporting Information), shows that the Te (Ge) enrichment is localized at surface. Based on these considerations, in the following we will compare our ARPES data from STe and SGe with density functional theory simulations of Ge- and Te-terminated surfaces. In fact, these truncated bulk systems represent the simplest models of Te- and Ge-rich surfaces with outward and inward FE polarization.
The virgin ferroelectric state of Te- and Ge-rich samples has been widely investigated by PFM, both during the optimization of the surface strategy for poling (section 1 of the Supporting Information) and after the beamtime, on samples STe and SGe. Here in particular, we report on these two samples, whose pristine FE state is crucial for the establishment of the link between FE polarization and spin texture. In Figure 1b (1b′), we show the phase signal recorded on STe (SGe) after writing a large square with +7 V (−7 V) bias on the AFM tip and then an inner square with opposite bias. FE patterns are stable over more than 24 h (section 1 of the Supporting Information), thus indicating the robustness of ferroelectricity in GeTe films. The inner square displays the same contrast (PFM phase) of the unpoled area, indicating an outward (inward) virgin ferroelectric polarization in STe (SGe). To confirm these findings, we measured the virgin curve and the full ferroelectric hysteresis loops by sweeping the PFM tip voltage. A pair of characteristic loops measured on STe and SGe are reported in panels c and c′ of Figure 1 as representative of the average response of the entire sample area probed by S-ARPES (see section 1 of the Supporting Information for details on the statistical analysis). The virgin curve measured for STe indicates the initial state is close to that obtained for negative saturating voltages, while the opposite holds for the sample SGe. This is a clear indication that STe and SGe present two opposite outward and inward virgin FE polarizations. These samples are ideal candidates for investigating the connection between FE polarization and spin texture.
In Figure 2, we show the bands dispersion and the corresponding spin texture calculated by DFT for Te- and Ge-terminated GeTe(111) surfaces displaying, respectively, Pout and Pin FE polarization that will be compared with S-ARPES from STe (Te-rich surface) and SGe (Ge-rich surface), respectively. For the sake of completeness, the spectral function for the energetically unfavorable configurations (i.e., Te-terminated surface with Pin and Ge-terminated surface with Pout) are reported in section 3 of the Supporting Information. In agreement with previous works, (21,24) we refer to bulk coordinates in terms of the rhombohedral setting (a = b = c = 4.37 Å and α = β = γ = 57.9°), such that the ferroelectric polarization points along the [111] direction of the real space and the Rashba-like dispersion of bulk bands is seen on the {111} planes of the reciprocal space around Z. However, to simulate surface aspects we adopt the more common hexagonal setting to construct the slabs (Figure 1, panels a and a′), with the ferroelectric polarization pointing along the [0001] direction. However, throughout the text, we will refer to the sample surface as GeTe(111) defined with respect to the rhombohedral cell.
Figure 2
Figure 2. DFT calculations of GeTe(111) surfaces with different terminations. (a) Density of states (spectral function) of Te-terminated GeTe(111) surface with outward polarization, projected on bulk (deep pink) and surface (yellow) principal layers calculated via Green’s functions technique for the semi-infinite model of the surface. Brighter tones of pink (yellow) bands indicate higher intensity of bulk (surface) features. High-symmetry directions used for the calculation of band dispersions are defined in panel d. (b) Corresponding k-resolved spin polarization along the high-symmetry directions. Due to its complexity, we show only the in-plane components perpendicular to k. The in-plane component parallel to wave vector is zero within the whole Brillouin zone. (c) Schematic picture of the spin texture in main bulk bands extracted from panels a and b at E = −0.5 eV; the arrows denote the direction of the in-plane projection of the spin for inner and outer bands. (a′–c′) Same as panels a–c for Ge-terminated surface, with polarization inward. The Fermi level here has been shifted to align the bulk bands of Te- and Ge-terminated surfaces. (d) Brillouin zone of hexagonal surface and bulk unit cells; the gray square marks the area displayed in panels c and c′. Dashed vertical lines in a and a′ indicate the k points used for the spin analysis reported in Figure 4.
The bulk high-symmetry directions ZU and ZA, together with the corresponding surface directions ΓM and ΓK, are shown in Figure 2d. The FE polarization is parallel to ΓZ direction of the reciprocal space, i.e., the (111) direction of the crystal. Band dispersions along high-symmetry directions are presented in Figure 2a for STe and Figure 2a′ for SGe, after projection of the spectral function on the surface layers and on the bulk in the semi-infinite model, to single out surface and bulk-like contributions.
The k-resolved spin polarization is reported in panel b for STe and b′ for SGe, in which the non-null spin components perpendicular to the wave vector are shown along the high-symmetry bulk (surface) ZA (ΓK) and ZU (ΓM) directions. While the shape of bulk Rashba sub-bands is not affected by FE polarization reversal, their spin texture is reversed, according to the main concept of FERSCs. This is evident from the comparison of the isoenergy cuts, taken at 0.5 eV below the top of the valence band, reported in panels c and c′, where arrows indicate the local spin direction. However, surface bands with Rashba splitting are very different for the two terminations. In the Te-terminated one (Pout) they display a clear Rashba-like splitting and cross the Fermi energy at higher wave vectors with respect to the bulk bands. In the Ge-terminated one (Pin), instead, the Rashba splitting of the surface bands in the gap is largely suppressed and surface bands shift toward the conduction band, without crossing the Fermi level at high momenta.
The remarkable difference between surface Rashba like bands predicted by DFT for Te- and Ge-termination has an experimental counterpart in ARPES data reported in Figure 3 for STe (panels a–h) and SGe (a′–h′). Panels a and b in Figure 3 present the experimental band dispersions along ZA and ZU for STe. Corresponding isoenergy cuts at 0, 0.25, and 0.5 eV BE in panels c–e of Figure 3 are compared with theoretical ones for a Te-terminated surface. In the following we will use a simplified distinction between “surface” and “bulk” Rashba states. Having in mind that ARPES at 20 eV probes just a few atomic layers underneath the sample surface, we identify as bulk states those displaying a sizable photon energy or kz dispersion. (13) Rigorously, these are not true bulk states but can be viewed as surface-bulk resonances (24) or simply states with sizable projection on bulk states, so they mainly reflect the bulk behavior. (25)
Figure 3
Figure 3. ARPES from Te-rich and Ge-rich samples. Panels a–h refer to the Te-rich sample STe with outward polarization. (a, b) Experimental bands dispersion collected along the principal directions ZA (kx) and ZU (ky) in the Brillouin zone. (c–e) Constant energy maps at 0, 0.25, and 0.5 eV below the Fermi energy. (f–h) Corresponding calculated constant energy maps with yellow and pink indicating the surface and bulk character of states, respectively. Panels labeled by the apex (panels a′–h′) are the same as above but for the Ge-rich sample SGe with inward polarization. The Fermi level in panels f′–h′ is chosen to be consistent with Figure 2.
Both band dispersions and isoenergy cuts from sample STe are very similar to data available in the literature for Te-terminated α-GeTe(111). (13,24,25) In agreement with DFT calculations, prominent surface bands with Rashba splitting (S1, S2) are seen at large momenta, especially along the ZA direction. A pair of outer spin split bands with 6-fold symmetry and “arms” along the equivalent ZU directions are clearly visible in the isoenergy cuts of panels c and d of Figure 3 (marked by green ticks). However, at 0.25 eV BE (Figure 3d), an inner 6-fold star (orange ticks) appears, rotated by 30 degrees with respect to the surface one, i.e., with arms along ZA. This is ascribed to the bulk-like bands (B1 and B2) evident in the band dispersion along ZU of panel b. The isoenergy cut at 0.5 eV (Figure 3e), instead, mainly reflects the symmetry of the bulk inner star because at this BE, the cut of states with surface character occurs at higher momenta.
The scenario for the SGe sample is completely different because surface states are almost absent, in agreement with DFT simulations. Indeed the prominent surface Rashba bands S1 and S2 along ZA in Figure 3a are missing in panel a′, while bulk bands B1 and B2 along ZU12 are similar in panels b and b′. The absence of S1 and S2 surface states is even more evident from the Fermi energy cut of panel 3c′, which does not display the outer 6-fold double star of panel c. Besides, the isoenergy cut at 0.25 eV (panel d′) already reflects the symmetry of bulk states, such as the inner star in Figure 3d,e from sample STe, i.e., with arms along ZA.
To summarize, ARPES data from samples STe and SGe show band dispersions in good agreement with those calculated for a Te-terminated (Pout) and Ge-terminated (Pin) surface, respectively. This represents a self-consistent proof of the reliability of our method for preparing GeTe(111) surfaces with opposite FE polarization.
In the following, we discuss the connection between the spin texture of bulk Rashba bands and the FE polarization, which is the key concept of FERSC materials. Figure 4 reports spin-resolved ARPES data from STe and SGe.
Figure 4
Figure 4. Spin-resolved ARPES from Te-rich and Ge-rich samples. Panels a–g refer to the Te-rich sample STe with outward polarization. (a) Calculated bulk bands (solid line) along ZU (ky) over the 2nd derivative of the measured band dispersion. (b, c) Spin-polarized spectra and spin asymmetry at fixed wave vector k1 indicated in panel a. The two peaks correspond to the intersection of bulk Rashba bands B1 and B2 with the vertical dashed line at k1 (panel a). (d, e) Spin-polarized spectra and spin asymmetry at opposite wave vector –k1. (f, g) Constant energy maps at 0.18 and 0.5 eV BE, corresponding to the energy of bulk bands B1 and B2 at k1, in nice agreement with the peaks of opposite spin polarizations in panels c and e. Blue and red arrows indicate the sense of circulation of spins: clockwise in the outer band and counterclockwise in the inner one. Panels a′–g′ refer to the case of the Ge-rich sample SGe. (b′–e′) Spin analysis for opposite wave vectors k2 and –k2, where the Rashba splitting is maximized. (f′, g′) Constant energy maps at 0 eV (top of B1) and 0.26 eV BE, corresponding to the energy of bulk bands B1 and B2 at k2 (panel a′). The sense of circulation of spins is opposite to that found for STe: counterclockwise in the outer band and clockwise in the inner band (panel g′).
In fact, the Rashba splitting of surface bands can be largely affected, or even suppressed, by proximity with other materials in a multilayer (26) or by the surface electric field due to screening charges. In sample STe, which displays both surface and bulk Rashba bands, we performed spin-polarized scans at fixed momenta (k1, −k1) marked in panels f and g of Figure 4, along the equivalent ZU direction at 30 degrees with respect to kx. Even though these are not the points where the Rashba splitting is maximized, for ± k1, only bulk bands B1,2 are expected to contribute to the photoemission signal at BE greater than 0.2 eV (see Figure 2a,b). The spin polarized spectra and corresponding spin-polarization are reported in panels b and c for k1 and d and e for −k1. With reference to the polarimeter quantization axis set along the negative direction of ky, at k1, we find a positive peak in the spin polarization at about 0.2 eV and a negative one at about 0.5 eV (panel c), corresponding to the crossing of the outer and inner band B1 and B2, respectively. The opposite occurs at −k1, as expected for GeTe Rashba bands. (12,24,25) The sense of circulation of spins resulting from our data is sketched in Figure 4f,g by arrows superimposed to the isoenergy cuts taken at 0.18 and 0.5 eV. In agreement with DFT calculations, for a Te-terminated (Pout) surface the sense of circulation of spins is clockwise for the outer band and counterclockwise for the inner one.
For SGe, the analysis of the spin texture of bulk bands is simpler, due to the lack of surface bands. In this case, we choose opposite k points (k2, −k2), along ky (ZU direction), where the maximum Rashba energy splitting (ER) of bulk bands B1,2 is expected (see Figures 2a′ and 4a′). The quantization axis of the spin polarimeter was set orthogonal to the wave vectors toward the positive kx direction. Spin-polarized spectra in Figure 4b′ display two prominent peaks with opposite spin, arising from the crossing of B1 and B2 bands at k2. Their energy splitting of about 200 meV is in good agreement with the expected value of the Rashba energy ER, according to theoretical predictions (12) and recent experimental findings. (24,25) Noteworthy is the fact that the sign of the spin polarization of the two peaks reverts when moving from k2 to −k2, as it appears from the comparison of panels b′–e′ in Figure 4. To determine the sense of circulation of spins in the outer and inner bands, we simply note that in panel c′, the peak at lower BE (outer band) has a negative polarization with respect to the quantization axis, i.e., the spin is directed along the negative direction of kx (counterclockwise rotation). The opposite holds for the peak at higher BE (inner band), so that the sense of circulation of the spin there is clockwise. The corresponding spin texture is sketched in panels f′ and g′. For a more-detailed vectorial analysis of the spin texture, see section 4 of the Supporting Information.
Crucial for the demonstration of the basic concept of FERSCs, the sense of circulation of spin in the inner and outer bands is opposite in samples STe (Figure 4g) and SGe (Figure 4g’), which display outward and inward FE polarization, respectively. This means that the spin texture is locked to the FE polarization because it reverts when the FE polarization is switched.
Having demonstrated the locking between ferroelectric polarization and spin textures, in the following we focus on the nanopatterning of ferroelectric domains. Figure 5 reports an example of a peculiar ferroelectric pattern written in a GeTe film, i.e., an array of lines with 600 nm spacing, having FE polarization inward (Pin), in a sample with uniform FE polarization outward (Pout). This pattern has been defined starting from a sample with uniform Pout, obtained by applying the surface engineering method outlined above for producing a Te-rich surface, over which a sequence of lines with opposite polarization has been written by sweeping the conductive tip of the AFM with a positive bias of +10 V. For a sweep rate of 3 μm/s, we get an average line width of about 300 nm as a result of the characteristic GeTe FE viscosity.
It is noteworthy that the pattern is stable over more than 24 h, thus pointing to the possibility of using this kind of FE patterns in spintronic devices exploiting the propagation of electrons in structure with engineered in-plane domains with opposite spin texture. Even though the direct observation of the spin in these FE nanodomains is prevented by experimental limitations of spectroscopic techniques, our S-ARPES analysis indicates that patterning of FE domains with inward or outward polarization provides a way to define also spin textures with opposite sense of rotation of spins in the Rashba bands. The FE structure of Figure 5 thus corresponds to the typical Rashba barrier device, where lines with opposite FE polarization are associated with opposite sense of circulation of spins in the Rashba bands. According to the theory of Rashba barriers, (27−29) a modulation of the resistivity for current flowing perpendicularly to the lines is expected with respect to the case of uniform FE polarization. Noteworthy, such a modulation is nonvolatile but reversible, as the uniform polarization state can be restored by electric poling. In perspective, similar structures can be designed and implemented in devices with gate electrodes, suitable for an easy and real-time manipulation of the spin texture and, in turn, of the electric conductivity. This represents the basic building block of a circuit element combining memory and computing, where the information is written in the nonvolatile ferroelectric and spin-texture pattern and computing takes place via the modulation of some spin-dependent transport property.
Figure 5
Figure 5. FE domains and spin texture patterning at the nanoscale. (a) Sketch of the writing procedure to obtain a sequence of Rashba barriers using the conductive tip of an AFM on a sample with pristine polarization outward, prepared as for sample STe above or by sweeping the tip with a negative voltage (Vtip = −10 V). Lines of inward polarization are written with opposite bias (Vtip = 10 V). The distance between lines is 600 nm, and their width about 300 nm. (b) PFM-phase signal measured along the y direction, perpendicular to the lines. (c) PFM-phase image of the ferroelectric domain pattern.
To summarize, in this Letter, we demonstrated the ferroelectric control of the spin-texture in GeTe. We developed a surface engineering strategy to prepare in situ a uniform ferroelectric polarization state, inward or outward. Through S-ARPES, we provided evidence for the intimate correlation between ferroelectric polarization and spin circulation in Rashba bands, i.e., the basis toward the possibility of crafting the spin texture via ferroelectric patterning. In this direction, by using the conductive tip of an atomic force microscope, we wrote a sequence of ferroelectric domains with inward and outward polarization expected to implement the structure of a Rashba barrier device. Noteworthy, FE domains are stable over time but can be electrically manipulated in a reversible way. These achievements pave the way to the realization of devices with gate electrodes for the real time reconfiguration of the spin structure in view of computing applications. Our findings indicate that a full electric control of the spin in a semiconductor is feasible without magnetic fields or adjacent magnetic layers. This represents a fundamental achievement toward the deployment of GeTe in spintronic devices exploiting the rich physics of Rashba effect and the additional degree of freedom arising from the electric reconfigurability of the spin texture.
Supporting Information
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.7b04829.
Additional information about the methods (sample growth, DFT calculations, angular resolved photoemission spectroscopy, and piezoresponse force microscopy), engineering of Te- and Ge-rich GeTe(111) surfaces with opposite polarization, detailed XPS characterization of Te-rich and Ge-rich samples, vectorial analysis of the spin texture of GeTe, and DFT calculations of GeTe(111) surfaces with unstable terminations. (PDF)
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Author Information
- Christian Rinaldi - Department of Physics, Politecnico di Milano, 20133 Milano, Italy; IFN-CNR, Politecnico di Milano, 20133 Milano, Italy;
http://orcid.org/0000-0001-6930-211X;
- Giovanni Vinai - CNR-IOM, Laboratorio TASC in Area Science Park - Basovizza, 34149 Trieste, Italy;http://orcid.org/0000-0003-4882-663X
- Stefano Cecchi - Paul-Drude-Institut für Festkörperelektronik, Hausvogteiplatz 5-7, 10117 Berlin, Germany;http://orcid.org/0000-0002-2243-7268
- Raffaella Calarco - Paul-Drude-Institut für Festkörperelektronik, Hausvogteiplatz 5-7, 10117 Berlin, Germany;http://orcid.org/0000-0002-5008-1617
Acknowledgments
We are grateful for helpful discussions with G. Rossi and M. Cantoni. C.R., S.V., M.A., and R.B. acknowledge financial support by the Cariplo Foundation grant no. 2013-0726 (MAGISTER) and grant no. 2013-0623 (SEARCH IV). C.R. also acknowledge the financial support by Fondazione Cariplo and Regione Lombardia via the project ECOS (grant no. 2017-1622). This work has been partly performed in the framework of the nanoscience foundry and fine analysis (NFFA-MIUR Italy) project. R.C. and S.C. thank S. Behnke and C. Stemmler for technical support at the MBE and the Leibniz Gemeinschaft within the Leibniz Competition on a project entitled “Epitaxial phase change superlattices designed for investigation of non-thermal switching” for partial funding. D.D.S. acknowledges the Deutsche Forschungsgemeinschaft (SFB 1170 ToCoTronics) and the ERC-StG-336012-Thomale-TOPOLECTRICS. This work was partially performed at Polifab, the micro- and nanofabrication facility of Politecnico di Milano.
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- 1Allwood, D. A. Science (Washington, DC, U. S.) 2005, 309 (5741), 1688– 1692, DOI: 10.1126/science.1108813Google Scholar1https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXpvFCis7Y%253D&md5=5a1a3142bd70a15a6c8dad28dd212da3Magnetic Domain-Wall LogicAllwood, D. A.; Xiong, G.; Faulkner, C. C.; Atkinson, D.; Petit, D.; Cowburn, R. P.Science (Washington, DC, United States) (2005), 309 (5741), 1688-1692CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)A review. Spintronics, in which both the spin and charge of electrons were used for logic and memory operations, promises an alternate route to traditional semiconductor electronics. A complete logic architecture can be constructed, which uses planar magnetic wires that are less than a micrometer in width. Logical NOT, logical AND, signal fan-out, and signal cross-over elements each have a simple geometric design, and they can be integrated together into one circuit. An addnl. element for data input allows information to be written to domain-wall logic circuits.
- 2Karenowska, A. D.; Chumak, A. V.; Serga, A. A.; Hillebrands, B. Handbook of Spintronics; Springer: Dordrecht Heidelberg; 2015; Vol. 11, pp 1505– 1549.Google ScholarThere is no corresponding record for this reference.
- 3Albisetti, E.; Petti, D.; Pancaldi, M.; Madami, M.; Tacchi, S.; Curtis, J.; King, W. P.; Papp, A.; Csaba, G.; Porod, W.; Vavassori, P.; Riedo, E.; Bertacco, R. Nat. Nanotechnol. 2016, 11 (6), 545– 551, DOI: 10.1038/nnano.2016.25Google Scholar3https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XjslGqtrw%253D&md5=3ea729e97907643e25a2d5922432d5b6Nanopatterning reconfigurable magnetic landscapes via thermally assisted scanning probe lithographyAlbisetti, E.; Petti, D.; Pancaldi, M.; Madami, M.; Tacchi, S.; Curtis, J.; King, W. P.; Papp, A.; Csaba, G.; Porod, W.; Vavassori, P.; Riedo, E.; Bertacco, R.Nature Nanotechnology (2016), 11 (6), 545-551CODEN: NNAABX; ISSN:1748-3387. (Nature Publishing Group)The search for novel tools to control magnetism at the nanoscale is crucial for the development of new paradigms in optics, electronics and spintronics. So far, the fabrication of magnetic nanostructures was achieved mainly through irreversible structural or chem. modifications. Here, the authors propose a new concept for creating reconfigurable magnetic nanopatterns by crafting, at the nanoscale, the magnetic anisotropy landscape of a ferromagnetic layer exchange-coupled to an antiferromagnetic layer. By performing localized field cooling with the hot tip of a scanning probe microscope, magnetic structures, with arbitrarily oriented magnetization and tunable unidirectional anisotropy, are reversibly patterned without modifying the film chem. and topog. This opens unforeseen possibilities for the development of novel metamaterials with finely tuned magnetic properties, such as reconfigurable magneto-plasmonic and magnonic crystals. In this context, the authors exptl. demonstrate spatially controlled spin wave excitation and propagation in magnetic structures patterned with the proposed method.
- 4Jansen, R. Nat. Mater. 2012, 11 (5), 400– 408, DOI: 10.1038/nmat3293Google Scholar4https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XlvVKlt7k%253D&md5=5e4fd83dfc3c064441a5b8567f257a80Silicon spintronicsJansen, RonNature Materials (2012), 11 (5), 400-408CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)A review. Worldwide efforts are underway to integrate semiconductors and magnetic materials, aiming to create a revolutionary and energy-efficient information technol. in which digital data are encoded in the spin of electrons. Implementing spin functionality in Si, the mainstream semiconductor, is vital to establish a spin-based electronics with potential to change information technol. beyond imagination. Can Si spintronics live up to the expectation. Remarkable advances in the creation and control of spin polarization in Si suggest so. Here, I review the key developments and achievements, and describe the building blocks of silicon spintronics. Unexpected and puzzling results are discussed, and open issues and challenges identified. More surprises lie ahead as Si spintronics comes of age.
- 5Rinaldi, C.; Cantoni, M.; Petti, D.; Sottocorno, A.; Leone, M.; Caffrey, N. M.; Sanvito, S.; Bertacco, R. Adv. Mater. 2012, 24 (22), 3037– 3041, DOI: 10.1002/adma.201104256Google Scholar5https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XmtlWgsbo%253D&md5=3e1c7252d2ffbbf9c5218a6841d30f73Ge-Based Spin-Photodiodes for Room-Temperature Integrated Detection of Photon HelicityRinaldi, Christian; Cantoni, Matteo; Petti, Daniela; Sottocorno, Andrea; Leone, Marco; Caffrey, Nuala M.; Sanvito, Stefano; Bertacco, RiccardoAdvanced Materials (Weinheim, Germany) (2012), 24 (22), 3037-3041, S3037/1-S3037/10CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)The authors have demonstrated the room-temp. operation of spin-photodiodes based on epitaxial Fe/MgO/ Ge(001) heterojunctions, performing the elec. detection of spin polarization of photocarriers generated by circularly polarized photons with a wavelength of 1300 nm. An av. variation of the photocurrent of 5.9% for the complete reversal of the incident light helicity was measured both in reverse and forward bias for light pulses with intensity I0 down to 200 μW. This definitely demonstrates the full compatibility of Ge-based spin-PDs with conventional optoelectronics platforms.
- 6Sanvito, S. Nat. Phys. 2010, 6 (8), 562– 564, DOI: 10.1038/nphys1714Google Scholar6https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXpsFKlsbc%253D&md5=26128c2de4e601314a6026e7c46ad8efThe rise of spinterface scienceSanvito, StefanoNature Physics (2010), 6 (8), 562-564CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)Little is known about the mechanisms that govern the injection of spins into org. mols. A new study suggests that the metal/org. interface is key, paving the way for a new field in which interfaces are specifically designed for spin applications. This is this field of 'spinterface' science.
- 7Ciudad, D.; Gobbi, M.; Kinane, C. J.; Eich, M.; Moodera, J. S.; Hueso, L. E. Adv. Mater. 2014, 26 (45), 7561– 7567, DOI: 10.1002/adma.201401283Google Scholar7https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXitVCitb7K&md5=289ff1a7a3761e386754b40f0fd86f16Sign Control of Magnetoresistance Through Chemically Engineered InterfacesCiudad, David; Gobbi, Marco; Kinane, Christy J.; Eich, Marius; Moodera, Jagadeesh S.; Hueso, Luis E.Advanced Materials (Weinheim, Germany) (2014), 26 (45), 7561-7567CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)The sign of the magnetoresistance in org. spin valves (OSVs) with intercalated LiF layers can be tuned by simply changing the order of deposition of the different layers. Magnetic tunnel junctions (MTJs) with intercalated LiF interlayers are also characterized to show that the origin of the change of the MR in org. spin valves can be due to chem. reactions rather than hybridizations or vacuum-level changes. All the results can be explained by the formation of antiferromagnetic (AFM) difluoride layers.
- 8Datta, S.; Das, B. Appl. Phys. Lett. 1990, 56 (7), 665– 667, DOI: 10.1063/1.102730Google Scholar8https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK3cXhsVylsrc%253D&md5=63b3ec88211adfa9aa465bb41fce5e9eElectronic analog of the electro-optic modulatorDatta, Supriyo; Das, BiswajitApplied Physics Letters (1990), 56 (7), 665-7CODEN: APPLAB; ISSN:0003-6951.An electron wave analog of the electrooptic light modulator is discussed. The current modulation in the proposed structure arises from spin precession due to the spin-orbit coupling in narrow-gap semiconductors, while magnetized contacts are used to preferentially inject and detect specific spin orientations. This structure may exhibit current modulation despite multiple modes, elevated temps., or a large applied bias.
- 9Xu, Y.; Awschalom, D. D.; Nitta, J. Handbook of Spintronics, 1st ed.; Springer Publishing Company: New York, 2015.Google ScholarThere is no corresponding record for this reference.
- 10Dietl, T. Nat. Mater. 2010, 9 (12), 965– 974, DOI: 10.1038/nmat2898Google Scholar10https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXhsVGrsrjP&md5=350ebc4c60eca68ba6d4d2d4d9a2d976A ten-year perspective on dilute magnetic semiconductors and oxidesDietl, TomaszNature Materials (2010), 9 (12), 965-974CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)A review. Over the past ten years, the search for compds. combining the properties of semiconductors and ferromagnets has evolved into an important field of materials science. This endeavor was fueled by many demonstrations of remarkable low-temp. functionalities in the ferromagnetic structures (Ga,Mn)As and p-(Cd,Mn)Te, and related compds., and by the theor. prediction that magnetically doped, p-type nitride and oxide semiconductors might support ferromagnetism mediated by valence-band holes to above room temp. Indeed, ferromagnetic signatures persisting at high temps. were detected in a no. of nonmetallic systems, even under conditions in which the presence of spin ordering was not originally anticipated. Here I review recent exptl. and theor. developments, emphasizing that they not only disentangle many controversies and puzzles accumulated over the past decade but also offer new research prospects.
- 11Picozzi, S. Front. Phys. 2014, 2, 1– 5, DOI: 10.3389/fphy.2014.00010Google ScholarThere is no corresponding record for this reference.
- 12Di Sante, D.; Barone, P.; Bertacco, R.; Picozzi, S. Adv. Mater. 2013, 25 (4), 509– 513, DOI: 10.1002/adma.201203199Google Scholar12https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhsFans7rO&md5=f807b28faf2b510045e21e8cea6e9c22Electric Control of the Giant Rashba Effect in Bulk GeTeDi Sante, Domenico; Barone, Paolo; Bertacco, Riccardo; Picozzi, SilviaAdvanced Materials (Weinheim, Germany) (2013), 25 (4), 509-513CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)The authors established a link between Rashba physics and the field of ferroelectricity in single-phase materials, by predicting from first-principles a giant Rashba effect in bulk GeTe, a narrow gap ferroelec. semiconductor. The authors focus on the dependence of the spin splitting amplitude on the ferroelec. polarization, which makes the spin polarization of the current flowing in GeTe to be controllable and switchable by an elec. field. A full reversal of the spin polarization, i.e., of the Rashba parameter, can be achieved upon reversal of the ferroelec. polarization. The hysteretic nature of ferroelectricity provides a unique way to exploit the Rashba effect in novel spintronics devices with non volatile logic functions assocd. with the remanent ferroelec. states. As an example, the design of a spin FET employing a bulk GeTe channel is discussed.
- 13Liebmann, M.; Rinaldi, C.; Di Sante, D.; Kellner, J.; Pauly, C.; Wang, R. N.; Boschker, J. E.; Giussani, A.; Bertoli, S.; Cantoni, M.; Baldrati, L.; Asa, M.; Vobornik, I.; Panaccione, G.; Marchenko, D.; Sánchez-Barriga, J.; Rader, O.; Calarco, R.; Picozzi, S.; Bertacco, R.; Morgenstern, M. Adv. Mater. 2016, 28 (3), 560– 565, DOI: 10.1002/adma.201503459Google Scholar13https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXhvFens7nJ&md5=e230daec8bde40d900c87765f6f55b50Giant Rashba-Type Spin Splitting in Ferroelectric GeTe(111)Liebmann, Marcus; Rinaldi, Christian; Di Sante, Domenico; Kellner, Jens; Pauly, Christian; Wang, Rui Ning; Boschker, Jos Emiel; Giussani, Alessandro; Bertoli, Stefano; Cantoni, Matteo; Baldrati, Lorenzo; Asa, Marco; Vobornik, Ivana; Panaccione, Giancarlo; Marchenko, Dmitry; Sanchez-Barriga, Jaime; Rader, Oliver; Calarco, Raffaella; Picozzi, Silvia; Bertacco, Riccardo; Morgenstern, MarkusAdvanced Materials (Weinheim, Germany) (2016), 28 (3), 560-565CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)Here, we present spin-polarized angularly resolved photoelectron spectroscopy of GeTe(Ill) compared with d. functional theory calcns.
- 14Manchon, A.; Koo, H. C.; Nitta, J.; Frolov, S. M.; Duine, R. A. Nat. Mater. 2015, 14 (9), 871– 882, DOI: 10.1038/nmat4360Google Scholar14https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXhtlOgs7rJ&md5=c5d905d802184f6264adfe084253e249New perspectives for Rashba spin-orbit couplingManchon, A.; Koo, H. C.; Nitta, J.; Frolov, S. M.; Duine, R. A.Nature Materials (2015), 14 (9), 871-882CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)A review. In 1984, Bychkov and Rashba introduced a simple form of spin-orbit coupling to explain the peculiarities of ESR in two-dimensional semiconductors. Over the past 30 years, Rashba spin-orbit coupling has inspired a vast no. of predictions, discoveries and innovative concepts far beyond semiconductors. The past decade was particularly creative, with the realizations of manipulating spin orientation by moving electrons in space, controlling electron trajectories using spin as a steering wheel, and the discovery of new topol. classes of materials. This progress has reinvigorated the interest of physicists and materials scientists in the development of inversion asym. structures, ranging from layered graphene-like materials to cold atoms. This Review discusses relevant recent and ongoing realizations of Rashba physics in condensed matter.
- 15Hoffmann, A.; Bader, S. D. Phys. Rev. Appl. 2015, 4 (4), 47001, DOI: 10.1103/PhysRevApplied.4.047001Google Scholar15https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28Xht1Oqurk%253D&md5=ed12560c5c8a84a78011d6ee882dada1Opportunities at the frontiers of spintronicsHoffmann, Axel; Bader, Sam D.Physical Review Applied (2015), 4 (4), 047001/1-047001/18CODEN: PRAHB2; ISSN:2331-7019. (American Physical Society)The field of spintronics, or magnetic electronics, is maturing and giving rise to new subfields. These new directions involve the study of collective spin excitations and couplings of the spin system to addnl. degrees of freedom of a material, as well as metastable phenomena due to perturbations that drive the system far from equil. The interactions lead to possibilities for future applications within the realm of energy-efficient information technologies. Examples discussed herein include research opportunities assocd. with (i) various spin-orbit couplings, such as spin Hall effects, (ii) couplings to the thermal bath of a system, such as in spin Seebeck effects, (iii) spin-spin couplings, such as via induced and interacting magnon excitations, and (iv) spin-photon couplings, such as in ultrafast magnetization switching due to coherent photon pulses. These four basic frontier areas of research are giving rise to new applied disciplines known as spin orbitronics, spin caloritronics, magnonics, and spin photonics, resp. These topics are highlighted in order to stimulate interest in the new directions that spintronics research is taking and to identify open issues to pursue.
- 16Rinaldi, C.; Rojas-Sánchez, J. C.; Wang, R. N.; Fu, Y.; Oyarzun, S.; Vila, L.; Bertoli, S.; Asa, M.; Baldrati, L.; Cantoni, M.; George, J. M.; Calarco, R.; Fert, A.; Bertacco, R. APL Mater. 2016, 4 (3), 32501, DOI: 10.1063/1.4941276Google Scholar16https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XisVeiu7w%253D&md5=75ac37ebe010398bf48745e4d5afa87bEvidence for spin to charge conversion in GeTe(111)Rinaldi, C.; Rojas-Sanchez, J. C.; Wang, R. N.; Fu, Y.; Oyarzun, S.; Vila, L.; Bertoli, S.; Asa, M.; Baldrati, L.; Cantoni, M.; George, J.-M.; Calarco, R.; Fert, A.; Bertacco, R.APL Materials (2016), 4 (3), 032501/1-032501/6CODEN: AMPADS; ISSN:2166-532X. (American Institute of Physics)GeTe has been predicted to be the father compd. of a new class of multifunctional materials, ferroelec. Rashba semiconductors, displaying a coupling between spin-dependent k-splitting and ferroelectricity. In this paper, we report on epitaxial Fe/GeTe(111) heterostructures grown by mol. beam epitaxy. Spin-pumping expts. have been performed in a radio-frequency cavity by pumping a spin current from the Fe layer into GeTe at the Fe ferromagnetic resonance and detecting the transverse charge current originated in the slab due to spin-to-charge conversion. Preliminary expts. indicate that a clear spin to charge conversion exists, thus unveiling the potential of GeTe for spin-orbitronics. (c) 2016 American Institute of Physics.
- 17Nukala, P.; Ren, M.; Agarwal, R.; Berger, J.; Liu, G.; Johnson, A. T. C.; Agarwal, R. Nat. Commun. 2017, 8 (1), 15033, DOI: 10.1038/ncomms15033Google Scholar17https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXmtFCrsb0%253D&md5=85b46d3dff168d89e0b614fd33924f2dInverting polar domains via electrical pulsing in metallic germanium tellurideNukala, Pavan; Ren, Mingliang; Agarwal, Rahul; Berger, Jacob; Liu, Gerui; Johnson, A. T. Charlie; Agarwal, RiteshNature Communications (2017), 8 (), 15033CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)Germanium telluride (GeTe) is both polar and metallic, an unusual combination of properties in any material system. The large concn. of free-carriers in GeTe precludes the coupling of external elec. field with internal polarization, rendering it ineffective for conventional ferroelec. applications and polarization switching. Here we investigate alternate ways of coupling the polar domains in GeTe to external elec. stimuli through optical second harmonic generation polarimetry and in situ TEM elec. testing on single-cryst. GeTe nanowires. We show that anti-phase boundaries, created from current pulses (heat shocks), invert the polarization of selective domains resulting in reorganization of certain 71° domain boundaries into 109° boundaries. These boundaries subsequently interact and evolve with the partial dislocations, which migrate from domain to domain with the carrier-wind force (elec. current). This work suggests that current pulses and carrier-wind force could be external stimuli for domain engineering in ferroelecs. with significant current leakage.
- 18Krempasky, J.; Weber, A. P.; Pilet, N.; Warnicke, P.; Ebert, H.; Muff, S.; Bisti, F.; Fanciulli, M.; Volfova, H.; Springholz, G. Nat. Commun. 2016, 7 (May), 13071, DOI: 10.1038/ncomms13071Google Scholar18https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhslGrtr%252FK&md5=53e09dfa31075fe26e5e942e9f6120a4Entanglement and manipulation of the magnetic and spin-orbit order in multiferroic Rashba semiconductorsKrempasky, J.; Muff, S.; Bisti, F.; Fanciulli, M.; Volfova, H.; Weber, A. P.; Pilet, N.; Warnicke, P.; Ebert, H.; Braun, J.; Bertran, F.; Volobuev, V. V.; Minar, J.; Springholz, G.; Dil, J. H.; Strocov, V. N.Nature Communications (2016), 7 (), 13071CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)Entanglement of the spin-orbit and magnetic order in multiferroic materials bears a strong potential for engineering novel electronic and spintronic devices. Here, we explore the electron and spin structure of ferroelec. α-GeTe thin films doped with ferromagnetic Mn impurities to achieve its multiferroic functionality. We use bulk-sensitive soft-X-ray angle-resolved photoemission spectroscopy (SX-ARPES) to follow hybridization of the GeTe valence band with the Mn dopants. We observe a gradual opening of the Zeeman gap in the bulk Rashba bands around the Dirac point with increase of the Mn concn., indicative of the ferromagnetic order, at persistent Rashba splitting. Furthermore, subtle details regarding the spin-orbit and magnetic order entanglement are deduced from spin-resolved ARPES measurements. We identify antiparallel orientation of the ferroelec. and ferromagnetic polarization, and altering of the Rashba-type spin helicity by magnetic switching. Our exptl. results are supported by first-principles calcns. of the electron and spin structure.
- 19Chattopadhyay, T.; Boucherle, J. X.; VonSchnering, H. G. J. Phys. C: Solid State Phys. 1987, 20 (10), 1431– 1440, DOI: 10.1088/0022-3719/20/10/012Google Scholar19https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaL2sXit1Crtbo%253D&md5=ad6cfe022cefeee3a70cc55d89174e08Neutron diffraction study on the structural phase transition in germanium monotellurideChattopadhyay, T.; Boucherle, J. X.; Von Schnering, H. G.Journal of Physics C: Solid State Physics (1987), 20 (10), 1431-40CODEN: JPSOAW; ISSN:0022-3719.The structural phase transition in GeTe was investigated by neutron diffraction at 295-716 K. Accurate positional and thermal parameters were obtained as a function of temp. both in the rhombohedral R3m phase (binary analog of gray As structure A7) and in the cubic Fm3m phase (NaCl-type, B1). The temp. variation of the rhombohedral distortion and the relative shifts of the Ge and Te substructures show that the structural phase transition in GeTe is a displacive type.
- 20Rabe, K. M.; Joannopoulos, J. D. Phys. Rev. B: Condens. Matter Mater. Phys. 1987, 36 (12), 6631– 6639, DOI: 10.1103/PhysRevB.36.6631Google Scholar20https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaL2sXmt1Kgtro%253D&md5=8d15482101cc762bac77b108dff2301aTheory of the structural phase transition of germanium tellurideRabe, K. M.; Joannopoulos, J. D.Physical Review B: Condensed Matter and Materials Physics (1987), 36 (12), 6631-9CODEN: PRBMDO; ISSN:0163-1829.A completely ab initio theor. investigation of the rocksalt-rhombohedral structural phase transition of GeTe is described. Starting from an anharmonic lattice Hamiltonian, a model Hamiltonian that includes coupling of the order parameter to long-wavelength strain is constructed. The parameters appearing in the model were calcd. using the self-consistent ab initio pseudopotential total-energy method. The phase transition in the model system was studied through a momentum-space renormalization-group-theory approach, leading to the prediction of a fluctuation driven 1st-order transition at 657 ± 100 K. The strain coupling is crucial in detg. the 1st-order character of the transition.
- 21Deringer, V. L.; Lumeij, M.; Dronskowski, R. J. Phys. Chem. C 2012, 116 (29), 15801– 15811, DOI: 10.1021/jp304455zGoogle Scholar21https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XptFSrtL0%253D&md5=01241f8d272def0339b92c6f84c8ecc3Ab Initio Modeling of α-GeTe(111) SurfacesDeringer, Volker L.; Lumeij, Marck; Dronskowski, RichardJournal of Physical Chemistry C (2012), 116 (29), 15801-15811CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)D.-functional theory (DFT) computations are reported for the (111) crystal surfaces of the phase-change material germanium telluride in its stable rhombohedral modification (dubbed α-GeTe). Atomic structures and surface energies are evaluated using a custom-tailored slab model and periodic plane-wave basis sets in the PBE-GGA approxn. Independent of the chem. surrounding, a pristine Te-covered (111) surface is energetically favorable among competing models, whereas a purely Ge-terminated surface is about 60 meV Å-2 higher in energy and predicted to undergo a structural reconstruction. Several at. motifs for such reconstructions lie closely together energetically and are expected to coexist at finite temps. Formation of Ge vacancies in the subsurface layers is investigated in detail. Scanning tunneling microscopy (STM) images are simulated from the DFT wave functions for comparison with expts. to be performed in the foreseeable future.
- 22Wuttig, M.; Lüsebrink, D.; Wamwangi, D.; Wełnic, W.; Gilleßen, M.; Dronskowski, R. Nat. Mater. 2007, 6 (2), 122– 128, DOI: 10.1038/nmat1807Google Scholar22https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXhtFyiu70%253D&md5=55224cf3c5b3f7febfe9aa7ce5d970deThe role of vacancies and local distortions in the design of new phase-change materialsWuttig, Matthias; Luesebrink, Daniel; Wamwangi, Daniel; Welnic, Wojciech; Gillessen, Michael; Dronskowski, RichardNature Materials (2007), 6 (2), 122-128CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)Phase-change materials are of tremendous technol. importance ranging from optical data storage to electronic memories. Despite this interest, many fundamental properties of phase-change materials, such as the role of vacancies, remain poorly understood. 'GeSbTe'-based phase-change materials contain vacancy concns. around 10% in their metastable cryst. structure. By using d.-functional theory, the origin of these vacancies was clarified and the most stable cryst. phases with rocksalt-like structures were characterized by large vacancy concns. and local distortions. The ease by which vacancies are formed is explained by the need to annihilate energetically unfavorable antibonding Ge-Te and Sb-Te interactions in the highest occupied bands. Understanding how the interplay between vacancies and local distortions lowers the total energy helps to design novel phase-change materials as evidenced by new exptl. data.
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- 25Elmers, H. J.; Wallauer, R.; Liebmann, M.; Kellner, J.; Morgenstern, M.; Wang, R. N.; Boschker, J. E.; Calarco, R.; Sánchez-Barriga, J.; Rader, O.; Kutnyakhov, D.; Chernov, S. V.; Medjanik, K.; Tusche, C.; Ellguth, M.; Volfova, H.; Borek, S.; Braun, J.; Minár, J.; Ebert, H.; Schönhense, G. Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 94 (20), 201403, DOI: 10.1103/PhysRevB.94.201403Google ScholarThere is no corresponding record for this reference.
- 26Oyarzún, S.; Nandy, A. K.; Rortais, F.; Rojas-Sánchez, J. C.; Dau, M. T.; Noël, P.; Laczkowski, P.; Pouget, S.; Okuno, H.; Vila, L.; Vergnaud, C.; Beigné, C.; Marty, A.; Attané, J. P.; Gambarelli, S.; George, J. M.; Jaffrès, H.; Blügel, S.; Jamet, M. Nat. Commun. 2016, 7, 13857, DOI: 10.1038/ncomms13857Google Scholar26https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XitFamsbnL&md5=6a9118eb9225b1a3a7a1980ed025bad5Evidence for spin-to-charge conversion by Rashba coupling in metallic states at the Fe/Ge(111) interfaceOyarzun, S.; Nandy, A. K.; Rortais, F.; Rojas-Sanchez, J.-C.; Dau, M.-T.; Noel, P.; Laczkowski, P.; Pouget, S.; Okuno, H.; Vila, L.; Vergnaud, C.; Beigne, C.; Marty, A.; Attane, J.-P.; Gambarelli, S.; George, J.-M.; Jaffres, H.; Blugel, S.; Jamet, M.Nature Communications (2016), 7 (), 13857CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)The spin-orbit coupling relating the electron spin and momentum allows for spin generation, detection and manipulation. It thus fulfils the three basic functions of the spin field-effect transistor. However, the spin Hall effect in bulk germanium is too weak to produce spin currents, whereas large Rashba effect at Ge(111) surfaces covered with heavy metals could generate spin-polarized currents. The Rashba spin splitting can actually be as large as hundreds of meV. Here we show a giant spin-to-charge conversion in metallic states at the Fe/Ge(111) interface due to the Rashba coupling. We generate very large charge currents by direct spin pumping into the interface states from 20 K to room temp. The presence of these metallic states at the Fe/Ge(111) interface is demonstrated by first-principles electronic structure calcns. By this, we demonstrate how to take advantage of the spin-orbit coupling for the development of the spin field-effect transistor.
- 27Gong, S. J.; Yang, Z. Q. J. Appl. Phys. 2007, 102 (3). 033706 DOI: 10.1063/1.2767373Google Scholar27https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXpt1CktrY%253D&md5=13d63e587e728f0c1631c0ddcd31eaafSpin filtering implemented through Rashba spin-orbit coupling and weak magnetic modulationsGong, S. J.; Yang, Z. Q.Journal of Applied Physics (2007), 102 (3), 033706/1-033706/4CODEN: JAPIAU; ISSN:0021-8979. (American Institute of Physics)We present two theor. schemes for spin filters in one-dimensional semiconductor quantum wires with spatially modulated Rashba spin-orbit couplings (SOCs) and weak magnetic potentials. In the first scheme, the SOC is periodic and the weak magnetic potential is applied uniformly along the wire. Full spin polarizations with opposite signs are obtained within two sepd. energy intervals. In the second scheme, the weak magnetic potential is periodic while the SOC is uniform. An ideal neg./pos. switching effect for spin polarization is realized by tuning the strength of SOC. The roles of SOC, magnetic potential, and their joint action on the spin filters are analyzed.
- 28Xiao, X. B.; Li, X. M.; Chen, Y. G. Phys. B 2009, 404 (21), 4159– 4161, DOI: 10.1016/j.physb.2009.07.192Google Scholar28https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXhtlansrnJ&md5=ba5bac684b4b56389f2f9e450b7a4989Electron transport of a quantum wire with spatially periodic spin-orbit couplingXiao, X. B.; Li, X. M.; Chen, Y. G.Physica B: Condensed Matter (Amsterdam, Netherlands) (2009), 404 (21), 4159-4161CODEN: PHYBE3; ISSN:0921-4526. (Elsevier B.V.)Electron transport properties of an ideal one-dimensional (1D) quantum wire are studied including spatially periodic Rashba spin-orbit coupling (SOC) and Dresselhaus SOC. By comparing with the previous work, two transmission gaps appear in the transmission probability of electrons and their widths are also broadened dramatically. Moreover, it is found that their widths are sensitive not only to the strength of SOCs but also to the length ratio of SOCs segment and non-SOCs segment. In addn., a circle-type' transmission behavior has been found by tuning the strength of SOCs continuously. Our results may extend the previous work and provide an more effective method to manipulate the current in nanoelec. devices.
- 29Zhang, L.; Brusheim, P.; Xu, H. Q. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 72 (4), 45347, DOI: 10.1103/PhysRevB.72.045347Google Scholar29https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXmvF2htbY%253D&md5=a239a4c232d6e58b3faedf420b360a95Multimode electron transport through quantum waveguides with spin-orbit interaction modulation: Applications of the scattering matrix formalismZhang, Lebo; Brusheim, P.; Xu, H. Q.Physical Review B: Condensed Matter and Materials Physics (2005), 72 (4), 045347/1-045347/9CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)We present a formulation of the scattering matrix method for spin-dependent electron transport in a quantum waveguide with spin-orbit interaction (SOI). All the required Hamiltonian matrixes needed in the implementation of the formulation are represented in a basis of the transverse spatial eigenstates and the spin eigenstates of the leads. Thus the method has great flexibility and can be easily applied to systems with complex geometrical structure, potential distribution, and SOI strength profile. Also, the method is numerically stable and can be used to treat spin-dependent multisubband scattering processes accurately. We have applied the method to the spin-dependent electron transport in quasi-one-dimensional (Q1D) conductors, with a region of the Rashba SOI of uniform strength and with a region contg. a Rashba SOI superlattice, made from a semiconductor heterostructure. The total conductance, spin-dependent conductances, and spin polarization of the system are calcd. for a fully spin-polarized electron beam injected from a lead into the SOI region. For the Q1D conductor with a single region of the Rashba SOI, it is found that when the Fermi energy is set at a value, for which the total conductance is at a plateau, the spin-dependent conductances show regular oscillations with increasing SOI strength. This is approx. true even when the total conductance is at a high plateau and thus multiple subbands in the waveguide are open for conduction. However, when the Fermi energy is set at a value close to the onset of a subband (with the subband index n ≥ 2), the spin-polarized conductances plotted against the SOI strength and the SOI region length show sharp resonance features or complex fluctuations. These irregular conductance characteristics arise from SOI-induced strong coupling between subbands. For the Q1D conductor modulated by an array of strong Rashba SOI stripes, the total conductance shows regular superlattice behavior, while the spin-dependent conductances show complex behavior with regions of slow oscillations and regions of rapid oscillations. As in the Q1D conductor with a single SOI region, the slow oscillations are found in the energy regions where the total conductance is at plateaus. However, the rapid oscillations appear at energies close to the onsets of subbands with the subband index n ≥ 2. These oscillations originate from strong spin scattering by localized states formed in the SOI-modulated superlattice region.
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Abstract
Figure 1
Figure 1. GeTe(111) surfaces with opposite FE polarization. (a, a′) Sketch of the Ge and Te planes for the Te and Ge termination, respectively. The distances given on the left refer to the unrelaxed interlayer distances. Only the topmost surface atoms of the slab are shown. The black rectangle denotes a bulk hexagonal unit cell used in DFT calculations as a building block to construct the (111) surface (rhombohedral setting, corresponding to the (0001) in the hexagonal setting). The net FE polarization Pout (Pin) (white arrows) arises from the interatomic dipoles shown with blue and red arrows. (b, b′) Piezoresponse-phase images recorded on STe (SGe) after poling with the tip at +7 V (−7 V) and −7 V (+7 V) over two concentric squares of 1.5 and 0.5 μm per side. The scale bar corresponds to 0.5 μm. (c, c′) PFM-phase signal showing the pristine polarization state and the ferroelectric hysteresis loop, as measured ex-situ on STe and SGe after the S-ARPES experiment. The controlled thermal desorption of the Te capping layer leads to a virgin-state FE polarization Pout and Pin in the two samples, respectively.
Figure 2
Figure 2. DFT calculations of GeTe(111) surfaces with different terminations. (a) Density of states (spectral function) of Te-terminated GeTe(111) surface with outward polarization, projected on bulk (deep pink) and surface (yellow) principal layers calculated via Green’s functions technique for the semi-infinite model of the surface. Brighter tones of pink (yellow) bands indicate higher intensity of bulk (surface) features. High-symmetry directions used for the calculation of band dispersions are defined in panel d. (b) Corresponding k-resolved spin polarization along the high-symmetry directions. Due to its complexity, we show only the in-plane components perpendicular to k. The in-plane component parallel to wave vector is zero within the whole Brillouin zone. (c) Schematic picture of the spin texture in main bulk bands extracted from panels a and b at E = −0.5 eV; the arrows denote the direction of the in-plane projection of the spin for inner and outer bands. (a′–c′) Same as panels a–c for Ge-terminated surface, with polarization inward. The Fermi level here has been shifted to align the bulk bands of Te- and Ge-terminated surfaces. (d) Brillouin zone of hexagonal surface and bulk unit cells; the gray square marks the area displayed in panels c and c′. Dashed vertical lines in a and a′ indicate the k points used for the spin analysis reported in Figure 4.
Figure 3
Figure 3. ARPES from Te-rich and Ge-rich samples. Panels a–h refer to the Te-rich sample STe with outward polarization. (a, b) Experimental bands dispersion collected along the principal directions ZA (kx) and ZU (ky) in the Brillouin zone. (c–e) Constant energy maps at 0, 0.25, and 0.5 eV below the Fermi energy. (f–h) Corresponding calculated constant energy maps with yellow and pink indicating the surface and bulk character of states, respectively. Panels labeled by the apex (panels a′–h′) are the same as above but for the Ge-rich sample SGe with inward polarization. The Fermi level in panels f′–h′ is chosen to be consistent with Figure 2.
Figure 4
Figure 4. Spin-resolved ARPES from Te-rich and Ge-rich samples. Panels a–g refer to the Te-rich sample STe with outward polarization. (a) Calculated bulk bands (solid line) along ZU (ky) over the 2nd derivative of the measured band dispersion. (b, c) Spin-polarized spectra and spin asymmetry at fixed wave vector k1 indicated in panel a. The two peaks correspond to the intersection of bulk Rashba bands B1 and B2 with the vertical dashed line at k1 (panel a). (d, e) Spin-polarized spectra and spin asymmetry at opposite wave vector –k1. (f, g) Constant energy maps at 0.18 and 0.5 eV BE, corresponding to the energy of bulk bands B1 and B2 at k1, in nice agreement with the peaks of opposite spin polarizations in panels c and e. Blue and red arrows indicate the sense of circulation of spins: clockwise in the outer band and counterclockwise in the inner one. Panels a′–g′ refer to the case of the Ge-rich sample SGe. (b′–e′) Spin analysis for opposite wave vectors k2 and –k2, where the Rashba splitting is maximized. (f′, g′) Constant energy maps at 0 eV (top of B1) and 0.26 eV BE, corresponding to the energy of bulk bands B1 and B2 at k2 (panel a′). The sense of circulation of spins is opposite to that found for STe: counterclockwise in the outer band and clockwise in the inner band (panel g′).
Figure 5
Figure 5. FE domains and spin texture patterning at the nanoscale. (a) Sketch of the writing procedure to obtain a sequence of Rashba barriers using the conductive tip of an AFM on a sample with pristine polarization outward, prepared as for sample STe above or by sweeping the tip with a negative voltage (Vtip = −10 V). Lines of inward polarization are written with opposite bias (Vtip = 10 V). The distance between lines is 600 nm, and their width about 300 nm. (b) PFM-phase signal measured along the y direction, perpendicular to the lines. (c) PFM-phase image of the ferroelectric domain pattern.
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- 10Dietl, T. Nat. Mater. 2010, 9 (12), 965– 974, DOI: 10.1038/nmat2898Google Scholar10https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXhsVGrsrjP&md5=350ebc4c60eca68ba6d4d2d4d9a2d976A ten-year perspective on dilute magnetic semiconductors and oxidesDietl, TomaszNature Materials (2010), 9 (12), 965-974CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)A review. Over the past ten years, the search for compds. combining the properties of semiconductors and ferromagnets has evolved into an important field of materials science. This endeavor was fueled by many demonstrations of remarkable low-temp. functionalities in the ferromagnetic structures (Ga,Mn)As and p-(Cd,Mn)Te, and related compds., and by the theor. prediction that magnetically doped, p-type nitride and oxide semiconductors might support ferromagnetism mediated by valence-band holes to above room temp. Indeed, ferromagnetic signatures persisting at high temps. were detected in a no. of nonmetallic systems, even under conditions in which the presence of spin ordering was not originally anticipated. Here I review recent exptl. and theor. developments, emphasizing that they not only disentangle many controversies and puzzles accumulated over the past decade but also offer new research prospects.
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- 12Di Sante, D.; Barone, P.; Bertacco, R.; Picozzi, S. Adv. Mater. 2013, 25 (4), 509– 513, DOI: 10.1002/adma.201203199Google Scholar12https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhsFans7rO&md5=f807b28faf2b510045e21e8cea6e9c22Electric Control of the Giant Rashba Effect in Bulk GeTeDi Sante, Domenico; Barone, Paolo; Bertacco, Riccardo; Picozzi, SilviaAdvanced Materials (Weinheim, Germany) (2013), 25 (4), 509-513CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)The authors established a link between Rashba physics and the field of ferroelectricity in single-phase materials, by predicting from first-principles a giant Rashba effect in bulk GeTe, a narrow gap ferroelec. semiconductor. The authors focus on the dependence of the spin splitting amplitude on the ferroelec. polarization, which makes the spin polarization of the current flowing in GeTe to be controllable and switchable by an elec. field. A full reversal of the spin polarization, i.e., of the Rashba parameter, can be achieved upon reversal of the ferroelec. polarization. The hysteretic nature of ferroelectricity provides a unique way to exploit the Rashba effect in novel spintronics devices with non volatile logic functions assocd. with the remanent ferroelec. states. As an example, the design of a spin FET employing a bulk GeTe channel is discussed.
- 13Liebmann, M.; Rinaldi, C.; Di Sante, D.; Kellner, J.; Pauly, C.; Wang, R. N.; Boschker, J. E.; Giussani, A.; Bertoli, S.; Cantoni, M.; Baldrati, L.; Asa, M.; Vobornik, I.; Panaccione, G.; Marchenko, D.; Sánchez-Barriga, J.; Rader, O.; Calarco, R.; Picozzi, S.; Bertacco, R.; Morgenstern, M. Adv. Mater. 2016, 28 (3), 560– 565, DOI: 10.1002/adma.201503459Google Scholar13https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXhvFens7nJ&md5=e230daec8bde40d900c87765f6f55b50Giant Rashba-Type Spin Splitting in Ferroelectric GeTe(111)Liebmann, Marcus; Rinaldi, Christian; Di Sante, Domenico; Kellner, Jens; Pauly, Christian; Wang, Rui Ning; Boschker, Jos Emiel; Giussani, Alessandro; Bertoli, Stefano; Cantoni, Matteo; Baldrati, Lorenzo; Asa, Marco; Vobornik, Ivana; Panaccione, Giancarlo; Marchenko, Dmitry; Sanchez-Barriga, Jaime; Rader, Oliver; Calarco, Raffaella; Picozzi, Silvia; Bertacco, Riccardo; Morgenstern, MarkusAdvanced Materials (Weinheim, Germany) (2016), 28 (3), 560-565CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)Here, we present spin-polarized angularly resolved photoelectron spectroscopy of GeTe(Ill) compared with d. functional theory calcns.
- 14Manchon, A.; Koo, H. C.; Nitta, J.; Frolov, S. M.; Duine, R. A. Nat. Mater. 2015, 14 (9), 871– 882, DOI: 10.1038/nmat4360Google Scholar14https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXhtlOgs7rJ&md5=c5d905d802184f6264adfe084253e249New perspectives for Rashba spin-orbit couplingManchon, A.; Koo, H. C.; Nitta, J.; Frolov, S. M.; Duine, R. A.Nature Materials (2015), 14 (9), 871-882CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)A review. In 1984, Bychkov and Rashba introduced a simple form of spin-orbit coupling to explain the peculiarities of ESR in two-dimensional semiconductors. Over the past 30 years, Rashba spin-orbit coupling has inspired a vast no. of predictions, discoveries and innovative concepts far beyond semiconductors. The past decade was particularly creative, with the realizations of manipulating spin orientation by moving electrons in space, controlling electron trajectories using spin as a steering wheel, and the discovery of new topol. classes of materials. This progress has reinvigorated the interest of physicists and materials scientists in the development of inversion asym. structures, ranging from layered graphene-like materials to cold atoms. This Review discusses relevant recent and ongoing realizations of Rashba physics in condensed matter.
- 15Hoffmann, A.; Bader, S. D. Phys. Rev. Appl. 2015, 4 (4), 47001, DOI: 10.1103/PhysRevApplied.4.047001Google Scholar15https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28Xht1Oqurk%253D&md5=ed12560c5c8a84a78011d6ee882dada1Opportunities at the frontiers of spintronicsHoffmann, Axel; Bader, Sam D.Physical Review Applied (2015), 4 (4), 047001/1-047001/18CODEN: PRAHB2; ISSN:2331-7019. (American Physical Society)The field of spintronics, or magnetic electronics, is maturing and giving rise to new subfields. These new directions involve the study of collective spin excitations and couplings of the spin system to addnl. degrees of freedom of a material, as well as metastable phenomena due to perturbations that drive the system far from equil. The interactions lead to possibilities for future applications within the realm of energy-efficient information technologies. Examples discussed herein include research opportunities assocd. with (i) various spin-orbit couplings, such as spin Hall effects, (ii) couplings to the thermal bath of a system, such as in spin Seebeck effects, (iii) spin-spin couplings, such as via induced and interacting magnon excitations, and (iv) spin-photon couplings, such as in ultrafast magnetization switching due to coherent photon pulses. These four basic frontier areas of research are giving rise to new applied disciplines known as spin orbitronics, spin caloritronics, magnonics, and spin photonics, resp. These topics are highlighted in order to stimulate interest in the new directions that spintronics research is taking and to identify open issues to pursue.
- 16Rinaldi, C.; Rojas-Sánchez, J. C.; Wang, R. N.; Fu, Y.; Oyarzun, S.; Vila, L.; Bertoli, S.; Asa, M.; Baldrati, L.; Cantoni, M.; George, J. M.; Calarco, R.; Fert, A.; Bertacco, R. APL Mater. 2016, 4 (3), 32501, DOI: 10.1063/1.4941276Google Scholar16https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XisVeiu7w%253D&md5=75ac37ebe010398bf48745e4d5afa87bEvidence for spin to charge conversion in GeTe(111)Rinaldi, C.; Rojas-Sanchez, J. C.; Wang, R. N.; Fu, Y.; Oyarzun, S.; Vila, L.; Bertoli, S.; Asa, M.; Baldrati, L.; Cantoni, M.; George, J.-M.; Calarco, R.; Fert, A.; Bertacco, R.APL Materials (2016), 4 (3), 032501/1-032501/6CODEN: AMPADS; ISSN:2166-532X. (American Institute of Physics)GeTe has been predicted to be the father compd. of a new class of multifunctional materials, ferroelec. Rashba semiconductors, displaying a coupling between spin-dependent k-splitting and ferroelectricity. In this paper, we report on epitaxial Fe/GeTe(111) heterostructures grown by mol. beam epitaxy. Spin-pumping expts. have been performed in a radio-frequency cavity by pumping a spin current from the Fe layer into GeTe at the Fe ferromagnetic resonance and detecting the transverse charge current originated in the slab due to spin-to-charge conversion. Preliminary expts. indicate that a clear spin to charge conversion exists, thus unveiling the potential of GeTe for spin-orbitronics. (c) 2016 American Institute of Physics.
- 17Nukala, P.; Ren, M.; Agarwal, R.; Berger, J.; Liu, G.; Johnson, A. T. C.; Agarwal, R. Nat. Commun. 2017, 8 (1), 15033, DOI: 10.1038/ncomms15033Google Scholar17https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXmtFCrsb0%253D&md5=85b46d3dff168d89e0b614fd33924f2dInverting polar domains via electrical pulsing in metallic germanium tellurideNukala, Pavan; Ren, Mingliang; Agarwal, Rahul; Berger, Jacob; Liu, Gerui; Johnson, A. T. Charlie; Agarwal, RiteshNature Communications (2017), 8 (), 15033CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)Germanium telluride (GeTe) is both polar and metallic, an unusual combination of properties in any material system. The large concn. of free-carriers in GeTe precludes the coupling of external elec. field with internal polarization, rendering it ineffective for conventional ferroelec. applications and polarization switching. Here we investigate alternate ways of coupling the polar domains in GeTe to external elec. stimuli through optical second harmonic generation polarimetry and in situ TEM elec. testing on single-cryst. GeTe nanowires. We show that anti-phase boundaries, created from current pulses (heat shocks), invert the polarization of selective domains resulting in reorganization of certain 71° domain boundaries into 109° boundaries. These boundaries subsequently interact and evolve with the partial dislocations, which migrate from domain to domain with the carrier-wind force (elec. current). This work suggests that current pulses and carrier-wind force could be external stimuli for domain engineering in ferroelecs. with significant current leakage.
- 18Krempasky, J.; Weber, A. P.; Pilet, N.; Warnicke, P.; Ebert, H.; Muff, S.; Bisti, F.; Fanciulli, M.; Volfova, H.; Springholz, G. Nat. Commun. 2016, 7 (May), 13071, DOI: 10.1038/ncomms13071Google Scholar18https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhslGrtr%252FK&md5=53e09dfa31075fe26e5e942e9f6120a4Entanglement and manipulation of the magnetic and spin-orbit order in multiferroic Rashba semiconductorsKrempasky, J.; Muff, S.; Bisti, F.; Fanciulli, M.; Volfova, H.; Weber, A. P.; Pilet, N.; Warnicke, P.; Ebert, H.; Braun, J.; Bertran, F.; Volobuev, V. V.; Minar, J.; Springholz, G.; Dil, J. H.; Strocov, V. N.Nature Communications (2016), 7 (), 13071CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)Entanglement of the spin-orbit and magnetic order in multiferroic materials bears a strong potential for engineering novel electronic and spintronic devices. Here, we explore the electron and spin structure of ferroelec. α-GeTe thin films doped with ferromagnetic Mn impurities to achieve its multiferroic functionality. We use bulk-sensitive soft-X-ray angle-resolved photoemission spectroscopy (SX-ARPES) to follow hybridization of the GeTe valence band with the Mn dopants. We observe a gradual opening of the Zeeman gap in the bulk Rashba bands around the Dirac point with increase of the Mn concn., indicative of the ferromagnetic order, at persistent Rashba splitting. Furthermore, subtle details regarding the spin-orbit and magnetic order entanglement are deduced from spin-resolved ARPES measurements. We identify antiparallel orientation of the ferroelec. and ferromagnetic polarization, and altering of the Rashba-type spin helicity by magnetic switching. Our exptl. results are supported by first-principles calcns. of the electron and spin structure.
- 19Chattopadhyay, T.; Boucherle, J. X.; VonSchnering, H. G. J. Phys. C: Solid State Phys. 1987, 20 (10), 1431– 1440, DOI: 10.1088/0022-3719/20/10/012Google Scholar19https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaL2sXit1Crtbo%253D&md5=ad6cfe022cefeee3a70cc55d89174e08Neutron diffraction study on the structural phase transition in germanium monotellurideChattopadhyay, T.; Boucherle, J. X.; Von Schnering, H. G.Journal of Physics C: Solid State Physics (1987), 20 (10), 1431-40CODEN: JPSOAW; ISSN:0022-3719.The structural phase transition in GeTe was investigated by neutron diffraction at 295-716 K. Accurate positional and thermal parameters were obtained as a function of temp. both in the rhombohedral R3m phase (binary analog of gray As structure A7) and in the cubic Fm3m phase (NaCl-type, B1). The temp. variation of the rhombohedral distortion and the relative shifts of the Ge and Te substructures show that the structural phase transition in GeTe is a displacive type.
- 20Rabe, K. M.; Joannopoulos, J. D. Phys. Rev. B: Condens. Matter Mater. Phys. 1987, 36 (12), 6631– 6639, DOI: 10.1103/PhysRevB.36.6631Google Scholar20https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaL2sXmt1Kgtro%253D&md5=8d15482101cc762bac77b108dff2301aTheory of the structural phase transition of germanium tellurideRabe, K. M.; Joannopoulos, J. D.Physical Review B: Condensed Matter and Materials Physics (1987), 36 (12), 6631-9CODEN: PRBMDO; ISSN:0163-1829.A completely ab initio theor. investigation of the rocksalt-rhombohedral structural phase transition of GeTe is described. Starting from an anharmonic lattice Hamiltonian, a model Hamiltonian that includes coupling of the order parameter to long-wavelength strain is constructed. The parameters appearing in the model were calcd. using the self-consistent ab initio pseudopotential total-energy method. The phase transition in the model system was studied through a momentum-space renormalization-group-theory approach, leading to the prediction of a fluctuation driven 1st-order transition at 657 ± 100 K. The strain coupling is crucial in detg. the 1st-order character of the transition.
- 21Deringer, V. L.; Lumeij, M.; Dronskowski, R. J. Phys. Chem. C 2012, 116 (29), 15801– 15811, DOI: 10.1021/jp304455zGoogle Scholar21https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XptFSrtL0%253D&md5=01241f8d272def0339b92c6f84c8ecc3Ab Initio Modeling of α-GeTe(111) SurfacesDeringer, Volker L.; Lumeij, Marck; Dronskowski, RichardJournal of Physical Chemistry C (2012), 116 (29), 15801-15811CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)D.-functional theory (DFT) computations are reported for the (111) crystal surfaces of the phase-change material germanium telluride in its stable rhombohedral modification (dubbed α-GeTe). Atomic structures and surface energies are evaluated using a custom-tailored slab model and periodic plane-wave basis sets in the PBE-GGA approxn. Independent of the chem. surrounding, a pristine Te-covered (111) surface is energetically favorable among competing models, whereas a purely Ge-terminated surface is about 60 meV Å-2 higher in energy and predicted to undergo a structural reconstruction. Several at. motifs for such reconstructions lie closely together energetically and are expected to coexist at finite temps. Formation of Ge vacancies in the subsurface layers is investigated in detail. Scanning tunneling microscopy (STM) images are simulated from the DFT wave functions for comparison with expts. to be performed in the foreseeable future.
- 22Wuttig, M.; Lüsebrink, D.; Wamwangi, D.; Wełnic, W.; Gilleßen, M.; Dronskowski, R. Nat. Mater. 2007, 6 (2), 122– 128, DOI: 10.1038/nmat1807Google Scholar22https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXhtFyiu70%253D&md5=55224cf3c5b3f7febfe9aa7ce5d970deThe role of vacancies and local distortions in the design of new phase-change materialsWuttig, Matthias; Luesebrink, Daniel; Wamwangi, Daniel; Welnic, Wojciech; Gillessen, Michael; Dronskowski, RichardNature Materials (2007), 6 (2), 122-128CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)Phase-change materials are of tremendous technol. importance ranging from optical data storage to electronic memories. Despite this interest, many fundamental properties of phase-change materials, such as the role of vacancies, remain poorly understood. 'GeSbTe'-based phase-change materials contain vacancy concns. around 10% in their metastable cryst. structure. By using d.-functional theory, the origin of these vacancies was clarified and the most stable cryst. phases with rocksalt-like structures were characterized by large vacancy concns. and local distortions. The ease by which vacancies are formed is explained by the need to annihilate energetically unfavorable antibonding Ge-Te and Sb-Te interactions in the highest occupied bands. Understanding how the interplay between vacancies and local distortions lowers the total energy helps to design novel phase-change materials as evidenced by new exptl. data.
- 23Perumal, K. Epitaxial Growth of Ge-Sb-Te based Phase Change Materials, Humboldt-Universität zu Berlin , 2013.Google ScholarThere is no corresponding record for this reference.
- 24Krempasky, J.; Muff, S.; Pilet, N.; Landolt, G.; Radovi, M.; Shi, M.; Kriegner, D.; Hol, V.; Braun, J.; Dil, J. H. Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 94, 205111, DOI: 10.1103/PhysRevB.94.205111Google ScholarThere is no corresponding record for this reference.
- 25Elmers, H. J.; Wallauer, R.; Liebmann, M.; Kellner, J.; Morgenstern, M.; Wang, R. N.; Boschker, J. E.; Calarco, R.; Sánchez-Barriga, J.; Rader, O.; Kutnyakhov, D.; Chernov, S. V.; Medjanik, K.; Tusche, C.; Ellguth, M.; Volfova, H.; Borek, S.; Braun, J.; Minár, J.; Ebert, H.; Schönhense, G. Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 94 (20), 201403, DOI: 10.1103/PhysRevB.94.201403Google ScholarThere is no corresponding record for this reference.
- 26Oyarzún, S.; Nandy, A. K.; Rortais, F.; Rojas-Sánchez, J. C.; Dau, M. T.; Noël, P.; Laczkowski, P.; Pouget, S.; Okuno, H.; Vila, L.; Vergnaud, C.; Beigné, C.; Marty, A.; Attané, J. P.; Gambarelli, S.; George, J. M.; Jaffrès, H.; Blügel, S.; Jamet, M. Nat. Commun. 2016, 7, 13857, DOI: 10.1038/ncomms13857Google Scholar26https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XitFamsbnL&md5=6a9118eb9225b1a3a7a1980ed025bad5Evidence for spin-to-charge conversion by Rashba coupling in metallic states at the Fe/Ge(111) interfaceOyarzun, S.; Nandy, A. K.; Rortais, F.; Rojas-Sanchez, J.-C.; Dau, M.-T.; Noel, P.; Laczkowski, P.; Pouget, S.; Okuno, H.; Vila, L.; Vergnaud, C.; Beigne, C.; Marty, A.; Attane, J.-P.; Gambarelli, S.; George, J.-M.; Jaffres, H.; Blugel, S.; Jamet, M.Nature Communications (2016), 7 (), 13857CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)The spin-orbit coupling relating the electron spin and momentum allows for spin generation, detection and manipulation. It thus fulfils the three basic functions of the spin field-effect transistor. However, the spin Hall effect in bulk germanium is too weak to produce spin currents, whereas large Rashba effect at Ge(111) surfaces covered with heavy metals could generate spin-polarized currents. The Rashba spin splitting can actually be as large as hundreds of meV. Here we show a giant spin-to-charge conversion in metallic states at the Fe/Ge(111) interface due to the Rashba coupling. We generate very large charge currents by direct spin pumping into the interface states from 20 K to room temp. The presence of these metallic states at the Fe/Ge(111) interface is demonstrated by first-principles electronic structure calcns. By this, we demonstrate how to take advantage of the spin-orbit coupling for the development of the spin field-effect transistor.
- 27Gong, S. J.; Yang, Z. Q. J. Appl. Phys. 2007, 102 (3). 033706 DOI: 10.1063/1.2767373Google Scholar27https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXpt1CktrY%253D&md5=13d63e587e728f0c1631c0ddcd31eaafSpin filtering implemented through Rashba spin-orbit coupling and weak magnetic modulationsGong, S. J.; Yang, Z. Q.Journal of Applied Physics (2007), 102 (3), 033706/1-033706/4CODEN: JAPIAU; ISSN:0021-8979. (American Institute of Physics)We present two theor. schemes for spin filters in one-dimensional semiconductor quantum wires with spatially modulated Rashba spin-orbit couplings (SOCs) and weak magnetic potentials. In the first scheme, the SOC is periodic and the weak magnetic potential is applied uniformly along the wire. Full spin polarizations with opposite signs are obtained within two sepd. energy intervals. In the second scheme, the weak magnetic potential is periodic while the SOC is uniform. An ideal neg./pos. switching effect for spin polarization is realized by tuning the strength of SOC. The roles of SOC, magnetic potential, and their joint action on the spin filters are analyzed.
- 28Xiao, X. B.; Li, X. M.; Chen, Y. G. Phys. B 2009, 404 (21), 4159– 4161, DOI: 10.1016/j.physb.2009.07.192Google Scholar28https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXhtlansrnJ&md5=ba5bac684b4b56389f2f9e450b7a4989Electron transport of a quantum wire with spatially periodic spin-orbit couplingXiao, X. B.; Li, X. M.; Chen, Y. G.Physica B: Condensed Matter (Amsterdam, Netherlands) (2009), 404 (21), 4159-4161CODEN: PHYBE3; ISSN:0921-4526. (Elsevier B.V.)Electron transport properties of an ideal one-dimensional (1D) quantum wire are studied including spatially periodic Rashba spin-orbit coupling (SOC) and Dresselhaus SOC. By comparing with the previous work, two transmission gaps appear in the transmission probability of electrons and their widths are also broadened dramatically. Moreover, it is found that their widths are sensitive not only to the strength of SOCs but also to the length ratio of SOCs segment and non-SOCs segment. In addn., a circle-type' transmission behavior has been found by tuning the strength of SOCs continuously. Our results may extend the previous work and provide an more effective method to manipulate the current in nanoelec. devices.
- 29Zhang, L.; Brusheim, P.; Xu, H. Q. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 72 (4), 45347, DOI: 10.1103/PhysRevB.72.045347Google Scholar29https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXmvF2htbY%253D&md5=a239a4c232d6e58b3faedf420b360a95Multimode electron transport through quantum waveguides with spin-orbit interaction modulation: Applications of the scattering matrix formalismZhang, Lebo; Brusheim, P.; Xu, H. Q.Physical Review B: Condensed Matter and Materials Physics (2005), 72 (4), 045347/1-045347/9CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)We present a formulation of the scattering matrix method for spin-dependent electron transport in a quantum waveguide with spin-orbit interaction (SOI). All the required Hamiltonian matrixes needed in the implementation of the formulation are represented in a basis of the transverse spatial eigenstates and the spin eigenstates of the leads. Thus the method has great flexibility and can be easily applied to systems with complex geometrical structure, potential distribution, and SOI strength profile. Also, the method is numerically stable and can be used to treat spin-dependent multisubband scattering processes accurately. We have applied the method to the spin-dependent electron transport in quasi-one-dimensional (Q1D) conductors, with a region of the Rashba SOI of uniform strength and with a region contg. a Rashba SOI superlattice, made from a semiconductor heterostructure. The total conductance, spin-dependent conductances, and spin polarization of the system are calcd. for a fully spin-polarized electron beam injected from a lead into the SOI region. For the Q1D conductor with a single region of the Rashba SOI, it is found that when the Fermi energy is set at a value, for which the total conductance is at a plateau, the spin-dependent conductances show regular oscillations with increasing SOI strength. This is approx. true even when the total conductance is at a high plateau and thus multiple subbands in the waveguide are open for conduction. However, when the Fermi energy is set at a value close to the onset of a subband (with the subband index n ≥ 2), the spin-polarized conductances plotted against the SOI strength and the SOI region length show sharp resonance features or complex fluctuations. These irregular conductance characteristics arise from SOI-induced strong coupling between subbands. For the Q1D conductor modulated by an array of strong Rashba SOI stripes, the total conductance shows regular superlattice behavior, while the spin-dependent conductances show complex behavior with regions of slow oscillations and regions of rapid oscillations. As in the Q1D conductor with a single SOI region, the slow oscillations are found in the energy regions where the total conductance is at plateaus. However, the rapid oscillations appear at energies close to the onsets of subbands with the subband index n ≥ 2. These oscillations originate from strong spin scattering by localized states formed in the SOI-modulated superlattice region.
Supporting Information
Supporting Information
ARTICLE SECTIONSThe Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.7b04829.
Additional information about the methods (sample growth, DFT calculations, angular resolved photoemission spectroscopy, and piezoresponse force microscopy), engineering of Te- and Ge-rich GeTe(111) surfaces with opposite polarization, detailed XPS characterization of Te-rich and Ge-rich samples, vectorial analysis of the spin texture of GeTe, and DFT calculations of GeTe(111) surfaces with unstable terminations. (PDF)
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