Dynamical Torque in CoxFe3–xO4 Nanocube Thin Films Characterized by Femtosecond Magneto-Optics: A π-Shift Control of the Magnetization Precession

For spintronic devices excited by a sudden magnetic or optical perturbation, the torque acting on the magnetization plays a key role in its precession and damping. However, the torque itself can be a dynamical quantity via the time-dependent anisotropies of the system. A challenging problem for applications is then to disentangle the relative importance of various sources of anisotropies in the dynamical torque, such as the dipolar field, the crystal structure or the shape of the particular interacting magnetic nanostructures. Here, we take advantage of a range of colloidal cobalt ferrite nanocubes assembled in 2D thin films under controlled magnetic fields to demonstrate that the phase, ϕPrec, of the precession carries a strong signature of the dynamical anisotropies. Performing femtosecond magneto-optics, we show that ϕPrec displays a π-shift for a particular angle θH of an external static magnetic field, H. θH is controlled with the cobalt concentration, the laser intensity, as well as the interparticle interactions. Importantly, it is shown that the shape anisotropy, which strongly departs from those of equivalent bulk thin films or individual noninteracting nanoparticles, reveals the essential role played by the interparticle collective effects. This work shows the reliability of a noninvasive optical approach to characterize the dynamical torque in high density magnetic recording media made of organized and interacting nanoparticles.

D esigning complex nanostructures with controlled magnetic anisotropy is of utmost importance for innovative information processing technologies like spin-torque oscillators, 1,2 as well as for medical applications such as cancer therapy. 3−5 For instance, the current data storage devices use highly anisotropic ferromagnetic nanostructures that provide large densities of information. Simultaneously, a faster manipulation of the magnetization is receiving lots of attention. In that context, emerging technologies aim at combining high temporal and spatial resolutions for the study of structures with reduced dimensionality. 6 This can be achieved using femtosecond laser pulses to study and control the magnetization in a variety of nanosystems. 7−19 Among the possible colloidal magnetic nanoparticle model systems, 20−23 iron oxide nanoparticles are attractive due to the possibility to readily tailor their composition, obtain well-defined shapes, and form superstructures. 24 −28 In addition, their magneto-crystalline anisotropy can be tuned by metal doping with cobalt ions for example. 29−31 Here, considering the potentials associated with nanoparticle collective effects, we investigate ultrafast magnetization dynamics in concentrated nanoparticles assembled in twodimensional (2D) thin films. We use the cobalt content to tune the anisotropy of ferrite nanocubes (Co x Fe 3−x O 4 ), and we explore the effect of interparticle interactions by magnetically "stamping" with an external field the films during their formation. We then evidence for the first time that the precession dynamics of the magnetization in single layer cobalt ferrite nanocubes is controlled by the interplay between the time dependent magneto-crystalline and shape anisotropies. We show that the precession can oscillate with opposite phase when varying the angle of an external magnetic field θ H . This phase opposition occurs abruptly for a particular angle θ H . which depends on the concentration of Co, the laser intensity, and the degree of organization of the nanocubes.
A range of colloidal iron oxide nanocubes (nCs) with controlled cobalt doping were prepared by solution chemistry under inert nitrogen atmosphere according to a protocol detailed in the SI and based on the literature. 28,32−35 Noticing that while the use of the external magnetic field has been explored to drive nanoparticles organization 28,36−38 the effect of its orientation relative to the organization interface on the dynamics of interparticle interactions has received no attention, the nCs were deposited at a water/air interface and transferred onto quartz substrates with and without applying a magnetic field. Hereafter, the different samples are identified as Co x y . The cobalt concentration x was varied from 0 to one-third of the metal molar content with the values of x = 0, 0.15, 0.30, 0.60, and 1.00. During the formation of the films, a 4 kOe static magnetic field was applied parallel (y = Hpa) or perpendicular (y = Hpp) to the substrate plane, while y = H0 corresponds to the film preparation without field. Figure 1a displays a typical transmission electron microscopy (TEM) image of a single nC. Noticeably, the cubes tend to present a diffuse "shell" with a thickness of a few nanometers. This low electron density encapsulation is consistent with amorphous carbonaceous material remaining from the synthesis and not fully removed during the purification. The X-ray diffraction data ( Figure S2a) demonstrate the crystallinity of the nanocubes and the lattice parameter is shown to slightly increase with the Co content ( Figure S2b). The surface of the nanocubes is also highly crystalline (Figure 1a and Figure  S3b,e,h). This is further illustrated by the TEM images and selected area electron diffraction (SAED) patterns obtained with the nanocubes (inset Figure 1a and Figure S3c,f,i). Overall, high-resolution electron microscope images and elemental analysis, as measured by electron energy loss spectroscopy  The 2D films transferred onto silicon substrates were investigated by scanning electron microscopy (SEM), which at low magnification showed a homogeneous distribution of the material across the substrates. At higher magnification, the films revealed more anisotropic magnetic nanoparticle islands in which morphology was influenced by the orientation of the external magnetic field applied during the organization process. As a result, quasi single layer islands grown with a parallel field were more acicular and cigar-shaped (Figure 1c), while with a perpendicular field, the islands tended to show a more circular shape ( Figure 1c). These structures are consistent with magnetic particle organizations on solid substrates obtained under controlled solvent evaporation rate and magnetic fields. 38−40 These morphologies were observed with different sizes of domains and shapes of the islands for each dopant concentration (Figures S6, S7, and S8). Figure 2a,b presents the static magnetization curves for the Co x Hpa and Co x Hpp samples, respectively, and illustrates the impact of orienting the magnetic field parallel and perpendicular to the nC film during its formation. Two important features are observed. The first is related to the measurement configuration. Measurements completed in the in-plane configuration (Figure 2a1,b1) present a the larger coercivity compared to those obtained in the perpendicular configuration (Figure 2a2,b2). The wider and more square hysteresis curves show that the sample magnetization tends to align in the plane of the nanoparticle film due to dipolar interactions between the nanocubes. 41− This was observed for all the samples. The second important feature relates to the orientation of the external magnetic field used to prepare the nanoparticle thin films. The amplitude of H c is larger and the hysteresis curves are again more square for the films formed under a parallel magnetic field (Figure 2a) than when the field was perpendicular (Figure 2b) to the film during its growth. This is due to a greater degree of particles organization in the parallel field growth case, which is also shown in the SEM analysis (Figures S6−S8), and is consistent with the distribution of the anisotropy axes leading to a decrease of the squareness of the hysteresis curves. The coercive fields and remnant magnetization values are summarized in Table S2. The coercitivity, as well as the ratio M r /M s , increases with the doping and shows a maximum for x = 0.6 (Co 20%, Figure 2a3,b3). The overall behavior is consistent with previous studies showing high coercivities for intermediate Co concentrations around 20%. 30 The decrease of the coercivity at higher concentrations is attributed to a displacement of the Co ions from octahedral to tetrahedral sites of the spinel structure, which results in a decrease of the anisotropy.
Although a few studies have considered the ultrafast magnetization dynamics of ferrite and cobalt ferrite spherical nanoparticles, 46−49 they were performed on dilute samples to avoid dipolar interactions and therefore were limited to studying the effects of size and coating of the nanoparticles. Laser-induced magnetization precession has not yet been explored in such systems. In this study, addressing the potentials arising from collective effects in concentrated samples, we investigate the ultrafast magnetization dynamics in nanoparticle thin films, which we magnetically "stamp" during the layer deposition and in which the cobalt content, hence the anisotropy, has been varied.
We performed the time-resolved magneto-optical experiments in the Faraday geometry using an amplified Ti:sapphire laser system with a repetition rate of 5 kHz. The pump and probe pulses had a duration of 120 and 150 fs, respectively. The probe beam had the fundamental wavelength of the amplifier (800 nm) while the pump was frequency doubled to 400 nm. They were both focused on the sample within a spot size of 50 and 100 μm, respectively, with an angle of incidence of 5°. The pump incident density of energy, E pump , was set in the range of 1−10 mJ·cm −2 . For each film, we measured simultaneously (i) the static transmission T, (ii) the Faraday rotation θ F , as well as their corresponding dynamical differential quantities ΔT(t)/T, and Δθ F (t)/θ F , as a function of the pump probe delay, t.

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Letter As illustrated in Figure 3a, the sample was in the xOy plane, while the pump and probe pulses were along the Oz direction. A static magnetic field, |H 0 | ≤ 3.5 kOe, was rotated in the xOz plane. The Faraday rotation, θ F , was obtained from the difference between two complementary angles of the magnetic field (θ H , and π−θ H ).
The absorption of the laser pulses by the nCs leads to an initial rise of the electrons and spins temperatures, which subsequently equilibrate with the lattice in a picosecond time scale. 7 This temperature rise modifies the effective magnetic field leading to a precession of the magnetization which was measured for several angles, θ H , as shown in Figure 3b for the sample Co 0. 3 Hpa . For each angle θ H , the corresponding phase and period of the precession were obtained and are displayed in Figure 3c. It shows two important features. First, an abrupt change of the precession phase, ϕ Prec , occurs around θ H ≈ 25°. As demonstrated later, it results from the competition between the temperature dependent cubic magneto-crystalline anisotropy of the individual nanoparticles and the time-dependent demagnetizing field modified by the change of the magnetization modulus, which in the present case is a signature of the interaction between the nanocubes. Second, the precession period, Ω Prec , continuously increases as θ H decreases. It is also due to dipolar interactions between the nanoparticles. Figure 4 presents the detailed analysis of the impact on the magnetization precession of the magneto-crystalline anisotropy controlled with Co-doping (Figure 4a), the degree of organization of the nCs (Figure 4b), as well as the density of energy of the pump laser E pump (Figure 4c). In Figure 4a, Co 0. 3 Hpa and Co 0.6 Hpa display an abrupt change of the precession phase around θ H = 25°for a pump density of excitation E pump = 3.6 mJ cm −2 . At low cobalt concentration (x ≤ 0.15), the small amplitude of the precession signal does not allow reliable extraction of phase and frequency for θ H ≤ 20°. It should be emphasized that this situation occurs for low Co doping due to the lower anisotropy of the nCs as seen in Figure 2a3,b3. However, if a change of the precession phase is present, the angle θ H of low Co concentrations samples is reduced by at least 5°with respect to Co 0.3 Hpa and Co 0.6 Hpa . As discussed theoretically hereafter, the abrupt change of phase for θ H results from a temperature related variation of the magnetic anisotropies.
The degree of organization of magnetic nanoparticles can be influenced by the presence of a magnetic field during a layer deposition. This can lead to a change in the dipolar interactions between the particles within the resulting structure. The phase of the precession for the x = 0.3 samples exposed to different magnetic fields during the film formation are displayed in Figure 4b. The use of a static magnetic field parallel to the substrate plane (Hpa) during the sample deposition decreases θ H by about 5°compared to Hpp and H0 deposition configurations. This is due to a lower degree of organization of the nCs as shown by SEM ( Figures S7 and S8) which reduces the dipolar interactions between the nCs leading to a weaker demagnetizing field.
As shown in Figure 4c, the π-phase shift occurs for two different angles θ H when varying E pump . It is due to the different origins of the shape and magneto-crystalline anisotropies that show distinct temperature dependencies. The former has a quadratic variation with the magnitude of the magnetization, while the latter has been shown for cobalt ferrites nanoparticles to vary exponentially with the square of the temperature. 30,50 The magnetization precession has been modeled using the Landau−Lifshitz−Gilbert (LLG) equation (eq 1) coupled to the three temperature model (TTM) accounting for the dynamics of the charges, spins, and lattice temperatures (T e , T s , T l ) as shown in eq 2  (2) where γ 0 , α, and T S are the gyromagnetic factor, the damping parameter, and the spin temperature, respectively. In the TTM, C e , C s , and C l are the electronic, magnetic, and lattice contributions to the specific heat, G el , G es , and G sl are the electron−lattice, electron−spin, and spin−lattice coupling constants and τ diff stands for the heat diffusion to the environment. We consider an equivalent reference system as the experimental geometry with the sample being in the xOy plane (see Figure 1a) and the axes of the cubic anisotropy along the system referential. An external magnetic field can be rotated in the xOy plane. In eq 3, the free energy, E, includes three contributions: cubic magneto-crystalline energy, Zeeman

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Letter energy, and demagnetizing energy accounting for the shape anisotropy of the single layer nanoparticles. where K 1 and K 2 are the magneto-crystalline anisotropy constants, a i are the cosine directions with i = x, y, z, μ 0 is the vacuum magnetic permeability, and H i is the static applied magnetic field components in ith direction. The time dependent effective field, where T c is the Curie temperature. The temperature variation of K 1 has been considered to be analogous to one measured for cobalt ferrite nanoparticles at high temperatures, that is, K 1 (T) = K 1 (0)exp(−αT 2 ). Figure 5 shows the effect of these parameters for a direct comparison with the experimental results ( Figure 3). Figure 5a displays the simulated magnetization dynamics projected on the Oz axis (M z ) obtained for a system corresponding to the sample Co 0.3 Hpa . In the calculations, the room temperature SQUID measurements have been used to determine the M s values. The interparticle dipolar interactions within the nC layer were introduced as an average demagnetizing field corresponding to the shape anisotropy of a continuous film with infinite lateral dimension, that is, N x = N y = 0; N z = 1, where N x , N y , and N z are the demagnetization factors. K 1 was the only adjustable parameter, selected such that θ H lies between 20°and 25°. Its value is close to the ones deduced from the SQUID measurements detailed in Section SI.III.3of the Supporting Information.
The influence of the doping, the dipolar interactions (via N z ) and the pump intensity I pump are presented in Figure 6 and correspond to the experimental results in Figure 4. Figure 6a displays the π-phase shift of the precession as observed experimentally in Figure 4a for x = 0.3 and 0.6. However, while the experimental transient measurements performed on samples with x ≤ 0.15 did not allow reliable ϕ Prec values to be extracted, the modeling show that the angle θ H of low Co concentrations samples is reduced by 5°with respect to that obtained for x = 0.3. The K 1 value for Co 0. 15 Hpa was set to 73% of that used for Co 0. 3 Hpa and corresponds to the values extracted from SQUID measurements. Figure 6b shows a variation of θ H of about 5°for N z = 1.0 and 0.8, corresponding to the samples Co 0. 3 Hpa and Co 0.3 Hpp , respectively. The corresponding decrease of θ H is attributed to a reduction of the demagnetizing field with respect to the magneto-crystalline anisotropy. Two limit cases can be distinguished for the shape anisotropy, characterized by the ratio N x /N z = N y /N z , corresponding to two opposite interaction regimes. For N x = N y = N z = 1/3 the nanocubes can be considered as isolated with their typical cubic symmetry, while N z = 1, N x = N y = 0 corresponds to the bulk thin film limit. The intermediate situations correspond to an assembly of interacting particles that can be taken into account, for example, via different filling factors. In the following, we study the behavior of the π-phase shift associated with this intermediate regime of interaction. To investigate this issue it is important to consider the minimization of the free energy in the static case for various parameters, θ H and E pump or equivalently T S , which is the equilibrium temperature between the charges, spins and lattice (considered as being achieved at time t = 10 ps in the following). Figure S14b shows the calculated change of magnetization orientation [θ M (300 K) − θ M (500 K)] as a function of the external field direction θ H . The set of curves correspond to different anisotropies from N z = 1 (bulk thin film) to N z = 1/3 (isolated nanocube) when the temperature increases from 300 to 500 K. For each curve, θ M changes sign for a value θ H of θ H that corresponds to the π-phase shift and that is plotted in Figure S14c. To evaluate which regime of interaction we have to consider for our nanocube layers, we made the same analysis for different temperatures. As shown in Figure S14d, the obtained set of curves (for 350 ≤ T S ≤ 600 K) allows a range of anisotropy ratios N x /N y to be defined to correspond to a range of critical angles θ H (see shaded area in Figure S14d), compatible with the experimental results of Figure 4c. For the observed angle θ H = 25°in Figure 4c, the

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Letter anisotropy is different from the pure bulk thin film (N x = 0, N z = 1) and from the isolated cubes (N x = N z = 1/3). This study clearly establishes the effect of interparticle interactions via the shape anisotropy. At the end of Section SI−IV.1in the Supporting Information, we show that the above considerations are valid for the temperatures of the sample derived either from the three temperature model and Curie−Weiss law or by the estimation of the temperature increase due to the sample absorption.
The experimental results of Figure 4c show that, when increasing E pump by a factor 3, θ H decreases by 5°. This relatively large variation of θ H with E pump can be advantageously used for controlling the phase of magnetic oscillators with laser intensity.
Let us now briefly consider the effect of disorder of the orientations of the nanocubes in the xOy plane (ϕ angle). In Section SI−IV.2 in the Supporting Information, an analysis has been performed over 138 nanocubes with a distribution of orientations corresponding to the disorder measured by SEM ( Figure S7a1). Figure S15 shows that the corresponding distribution of angles θ H is very narrow. Indeed, the mean square value of 1.6°around θ H = 24°shows that the disorder does not essentially modify the π-phase shift behavior described above.
In conclusion, we have shown that a π-phase shift of the magnetization precession induced by femtosecond laser pulses in cobalt ferrite nanocubes occurs for particular angles of an applied external magnetic field. Its origin is demonstrated to be related to the competition between the temperature-dependent magneto-crystalline anisotropy of the nanocubes and the temperature-dependent demagnetizing field associated with the collective interactions between particles. These parameters can be tuned with the doping of the nanocubes and the intralayer interactions, controlled at the time of the nanocube preparation and of their assembly, respectively. In addition, we have shown that the phase of the precession can be controlled by the intensity of the pump laser field. Our results bring valuable insights into the understanding of magnetization dynamics in confined magnetic nanosystems useful for applications in data storage and local magnetic sensing.