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Recent years have seen an increase of interest in the dynamics of ferrimagnetic materials, in particular in the motion of domain walls [1-4]. Ferrimagnetic materials represent unique systems where the ease of manipulating the spins with applied magnetic fields is combined with exchange-driven acceleration of the internal spin dynamics. Of particular interest is the temperature range around the magnetic and spin compensation points, finely balancing both magnetic moment and angular momentum of the system, and leading to a very particular character of magnetic switching by the domain wall motion.&lt;br/&gt;Here we present our studies of the temperature-dependent domain wall dynamics in the temperature range covering both angular momentum and magnetization compensation points in garnet film, and reaching up to the Curie temperature [5]. This is made possible by the very low coercive field of the material, not exceeding 5 mT even in the close vicinity of magnetization compensation temperature. The sample used in our experiments is a single-crystal thin film of magnetic garnet. A very unusual behavior of the domain-wall dynamics is observed, such as extraordinarily high mobility of the domain walls at very low fields. Drastic changes of both domain-wall velocity and mobility by more than 2 orders of magnitude are observed across a relatively small temperature range, related to the delicate balance of magnetization and spins of iron and rare-earth sublattices [5]. Therefore, such fine tuning of the corresponding momenta could be the key for developing ultrafast ferrimagnetic spintronic devices.&lt;br/&gt;The work was supported by the Russian Foundation for Basic Research (Projects No. 18-52-16006, 18-29-27020) and the Government of the Russian Federation (Project No. 075-15-2019-1874).

2022 Joint MMM-INTERMAG

Domain wall dynamics across magnetic and spin compensation points in ferrimagnets

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Recent years have seen an increase of interest in the dynamics of ferrimagnetic materials, in particular in the motion of domain walls [1-4]. Ferrimagnetic materials represent unique systems where the ease of manipulating the spins with applied magnetic fields is combined with exchange-driven acceleration of the internal spin dynamics. Of particular interest is the temperature range around the magnetic and spin compensation points, finely balancing both magnetic moment and angular momentum of the system, and leading to a very particular character of magnetic switching by the domain wall motion. Here we present our studies of the temperature-dependent domain wall dynamics in the temperature range covering both angular momentum and magnetization compensation points in garnet film, and reaching up to the Curie temperature [5]. This is made possible by the very low coercive field of the material, not exceeding 5 mT even in the close vicinity of magnetization compensation temperature. The sample used in our experiments is a single-crystal thin film of magnetic garnet. A very unusual behavior of the domain-wall dynamics is observed, such as extraordinarily high mobility of the domain walls at very low fields. Drastic changes of both domain-wall velocity and mobility by more than 2 orders of magnitude are observed across a relatively small temperature range, related to the delicate balance of magnetization and spins of iron and rare-earth sublattices [5]. Therefore, such fine tuning of the corresponding momenta could be the key for developing ultrafast ferrimagnetic spintronic devices. The work was supported by the Russian Foundation for Basic Research (Projects No. 18-52-16006, 18-29-27020) and the Government of the Russian Federation (Project No. 075-15-2019-1874).

technical paper

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Skyrmions are topological spin textures that exhibit particle-like dynamics under current-driven forces such as spin-orbit torques (SOT). In frustrated magnets, competing exchange interactions along with the Dzyaloshinskii-Moriya interaction (DMI) can aid in stabilizing textures of different topologies, like skyrmions and antiskyrmions [1], which exhibit different motion under SOT, such as trochoidal trajectories and skyrmion-antiskyrmion pair generation, in addition to the usual rectilinear motion. Such behavior results from a departure from the frozen-core limit, where additional dynamics in the (anti)skyrmion helicity couples to the core position [2]. Here, we discuss the role of thermally driven helicity dynamics in the Brownian motion of skyrmions under weak DMI and SOT. Depending on the magnitude of the DMI, which governs the strength of the restoring force experienced by the helicity, with respect to kBT, the thermal drift of the skyrmion core under weak SOT can differ greatly from the dynamics at 0 K (Fig. 1). This behavior arises from the thermal drift and diffusion of the helicity under SOT, which is analogous to the well-known problem of Brownian motion in a tilted washboard potential, where the helicity can be assimilated to an oscillator phase in a periodic potential with a linear force term. Under weak SOT or strong DMI, we recover a ''phase-locked'' solution in which the helicity is pinned, resulting in rectlinear drift. For strong SOT or weak DMI, we find a ''free-running'' solution, where the helicity varies continuously in time and results in an amplified Brownian diffusion of the skyrmion core. In between these two regimes, thermally-activated hopping of the helicity between energy minima occurs. These results highlight the importance of helicity dynamics and may have bearing on dipole-stabilized bubbles for which drive-dependent skyrmion Hall angles [3] and low drift velocities have been reported [4].

![](https://assets.underline.io/uploads/markdown_image/1/image/4499995d079e5c36223e0c31052e4788.jpg)


Fig. 1. Comparison between SOT-driven skyrmion motion at 0 K (black line) and 50 different realisations of the Brownian motion at 10 K (colored lines), along with the average thermal drift at 10 K (purple line).

Anomalous thermal drift of skyrmions in frustrated magnets under spin-orbit torques

In order to develop energy efficient race track memory devices, it is crucial to create and controllably move chiral spin textures, namely, skyrmions in magnetic nanotrack. In recent time, intense efforts have been dedicated to understand the mechanism of domain wall pair to skyrmion conversion in different junction geometry that may fit into the memory applications [1,2]. Here, we study the mechanism of DW pair to skyrmion conversion in a typical junction geometry which consists of the combination of two narrow nanotracks (length – 800 nm, thickness – 1 nm, width varying from 20 nm to 60 nm in steps of 20 nm) and a wide track (width 200 nm). The separation between narrow channels are selected as 10 nm, 30 nm and 50 nm. The micromagnetic simulations have been performed using Ubermag to investigate the magnetization dynamics and the Zhang-Li torque evolver is implemented in Landau Lifshitz Gibert equation to drive the DWs using spin polarized current [3]. For a fixed Gilbert damping parameter (α = 0.3) and different values of non-adiabatic spin torque parameter (β = 0.2, 0.3 and 0.5) we investigate the DW to skyrmion conversion in these nanotracks. Interestingly, under the influence of spin torque, the DW pair gets converted to skyrmion only if the geometrical constraints allow the favorable instability to set in at the junction between optimally separated narrow channels and wide channel (cf. Fig. 1(a-d)) [4]. For certain width and separation between the narrow channels, the DW pair to skyrmion conversion cannot be observed for sufficiently large time scale (cf. Fig. 2(a-d)). We believe these results will be helpful in designing the skyrmion based racetrack memory where the controlled creation of skyrmion is expected to play crucial role.

![](https://assets.underline.io/uploads/markdown_image/1/image/af3301ae9ac634fc6c9411eabcfd6b01.jpg)

Fig 1: Snapshot of DW pair to skyrmions conversion from two narrow channels for α = β = 0.3, width of the narrow nanochannel = 60 nm, separation between the narrow channel = 30 nm

![](https://assets.underline.io/uploads/markdown_image/1/image/ed5b1617a9c98ac080b569cc57b93e0f.jpg)

Fig 2: DW dynamics from two channels for α = β = 0.3, width of the narrow nanochannel = 40 nm, separation between the narrow channel = 10 nm


Influence of Geometry on Domain-Wall Pair to Skyrmion Conversion in Typical Magnetic Nanochannel

For their applications in spintronics, skyrmions need to be controlled one by one, and therefore appear as excitations over a uniform ground state. This is why in most demonstrations, the application of an external field is required. In this study, we show by fine-tuning the micromagnetic parameters, through their control by the ferromagnetic layer thickness, multilayers can be optimized to host zero field skyrmion excitations. We study Pt/Co/Au based heterostructures with varying Co thickness t. Close to the spin reorientation transition (t = 1.6 nm), the domain wall energy vanishes and the ground state is a stripe phase. To favor the uniform state, t is reduced to increase the magnetic anisotropy, until samples show a 100% remanence. Below 1.45 nm, skyrmions could be obtained and stabilized during the magnetization reversal process, and remain stable at zero field. This bistable situation offers a perfect playground to study current-induced nucleation in zero field, which we study in the vicinity of a point contact. Starting from a uniform state, current pulses lead to the formation of magnetic textures. However, to avoid the formation of elongated structures, similar to stripes, Co thickness needs to be further reduced. At 1.2 nm, the magnetic anisotropy is sufficiently large to cut elongated structures into well-defined skyrmions, which could be obtained with good reproducibility. Their topological nature is proven through the observation of the skyrmion Hall effect: depending on the orientation of the initial state, skyrmions are deflected in one or the other directions. Velocities of about 50 m/s induced by SOT, using a current density of 3.7 x 1012 A/m2 in 1µm wide tracks were also observed. This opens an important perspective towards skyrmionic devices at zero field, in particular concerning stacks that are not sensitive to external fields such as ferrimagnets and antiferromagnets. Figure: Zero field MFM images of 3 µm wide magnetic nanotracks, after successive application of 3.7 x 1012 A/m2, 3 ns long current pulses starting from a saturated track. In the first serie (a-c) the sample is initially magnetized downward, in the second one (d-f), it is magnetized upward, evidencing the gyrotropic deflection.

![](https://assets.underline.io/uploads/markdown_image/1/image/15d074009eea6ac625bfde657bff2eb1.jpg)

Figure: Zero field MFM images of 3 µm wide magnetic nanotracks, after successive application of 3.7 x 1012 A/m2, 3 ns long current pulses starting from a saturated track. In the first serie (a-c) the sample is initially magnetized downward, in the second one (d-f), it is magnetized upward, evidencing the gyrotropic deflection.

Current induced skyrmion nucleation at zero field

Magnetic skyrmions present interesting and unique pseudo-particle behaviors which arises from their topological protection [1-2]. Key among these behaviors is their resonant dynamics, under microwave fields, which include both breathing and gyration modes. Due to their small size, and magnetic-only contrast of skyrmions, coupled with high frequency dynamics – in the GHz regime – it is challenging to do in-situ measurements on these excitations. This work reports the use of small angle neutron scattering (SANS) to capture the dynamics of hybrid skyrmions stabilized in Fe/Gd multilayers by means of dipolar interactions. Using perpendicular DC fields and in-plane RF fields, we explored the gyration modes of hybrid skyrmions away, below, at, and above resonance [Fig.1(a-d)]. We find the dynamic modes of hybrid skyrmions contribute to the SANS signal in two ways: first, the scattered neutrons incur additional transverse momentum as a result of scattering from a moving source, and second, the gyration skyrmions disrupt ordering of the lattice giving rise to enhancement form-factor scattering. Ferromagnetic resonance measurements confirm the RF and DC field conditions for these gyration modes. Our results offer new insights into the nanoscale dynamics of magnetic skyrmions and present a unique use of SANS to probe magnetization dynamics.

![](https://assets.underline.io/uploads/markdown_image/1/image/a7eefda0d3ae85f8c787ee1cd94ec130.jpg)

Fig.1 2D SANS pattern of magnetic skyrmions under different magnetic fields and excitation frequencies: (a) Static state (H=0, RF=0), (b) below-resonance state (H=150 mT, RF=1.2 GHz), (c) at-resonance state (H=150 mT, RF=1.3 GHz) and (d) above-resonance state (H=150 mT, RF=1.4 GHz). All 2D images are plotted with the same intensity scale.

In-situ GHz Dynamics of Skyrmions Probed with SANS

Skyrmions have clear advantages for future spintronic devices over domain walls in terms of information carrying and storage, however there are still many open questions left and inherent challenges in the transition to applications. Here we study the effect of an additional interfacial spin-transfer torque (ISTT) [1], as well as the well-established spin-orbit torque (SOT), on skyrmion collections [2] – group of skyrmions dense enough that they are not isolated from one another – in magnetic multilayers, by comparing modelling using Boris [3], with experimental results. We show that skyrmion collective motion has additional effects not reproduced when compared to modelled isolated skyrmions [1]. In particular, as the skyrmion collection density increases the effect of local disorder is reduced, leading to reduced threshold current densities, and a sharper dependence of skyrmion Hall Angle (SkHA) on velocity in the depinning regime, in agreement with experimental results. When including both the ISTT and SOT, the small SkHA observed in experiment are in good agreement, also explaining the observed diameter-independent SkHA [4], as seen in Figure 1. Contrary to the model which considers the SOT as the only driving torque, and which predicts a monotonically increasing SkHA with decreasing diameter, inclusion of ISTT results in SkHA closely aligned to experimental results, particularly when the effect of local disorder and skyrmion-skyrmion interactions are taken into account. Our results shed further light on collective current-driven skyrmion motion in magnetic multilayers and highlight the significance of the ISTT in understanding current-driven skyrmion motion in magnetic multilayers.

![](https://assets.underline.io/uploads/markdown_image/1/image/219d9cf02b4f240924efc702e30f317a.jpg)

Figure 1. Collective SkHA dependence on skyrmion diameter for (a) N = 50 Sk/µm2 and (b) N = 100 Sk/µm2. (c) Experimentally obtained SkHA from skyrmion collections with a range of diameters with an average current density of 2×1011 A/m2. The overlaid dashed and solid lines show the ideal isolated skyrmion case – independent of current density – for the SOT and ISTT+SOT, respectively. The solid blue line in panel (b) represents a Savitzky-Golay fit to the simulated skyrmion motion, for a current density of Jc = 2×1011 A/m2.

Collective Skyrmion Motion Under the Influence of an Additional Interfacial Spin-Transfer Torque

Co/Gd based synthetic ferrimagnets have received considerable attention owing to the coexistence of both pronounced spin-orbitronic effects and all-optical switching (AOS), allowing for novel, hybrid devices [1,2]. Previous studies [3,4] have shown that spin-orbit torque (SOT) driven domain wall motion in these 3d-4f ferrimagnets system is most efficient at angular momentum compensation. Following this notion, in this study, we explore the stack engineering of Co/Gd based synthetic ferrimagnets to achieve high SOT driven domain wall motion at room temperature[5]. Here, we experimentally demonstrate that magnetization compensation can be achieved and tuned by varying layer thicknesses in Co/Gd(x)/Co/Gd quadlayer systems (see inset of Fig. 1), which shows AOS in the full range of Gd thickness[5]. Fig. 1 (a) shows the coercivity and polar magneto-optical Kerr effect (MOKE)-signal in such a quadlayer system where the middle Gd layer is wedged. The sign change of the MOKE signal and divergence of the coercivity indicate a compensated system. The CIDWM velocity as a function of Gd thickness of this stack has been investigated, after structuring a series of domain wall conduits from another wedge sample grown in the same batch. In Fig. 1 (b) it can be observed that for low to moderate current densities the optimum in the velocity can be found at compensation. As the current density is increased the optimum in the velocity is found to shift towards larger Gd thicknesses, likely due to the difference in temperature dependence of the magnetization in Co and Gd leading to a shift in the compensation thickness due to joule heating during the applied current pulses. Our study shows a significant improvement of the room temperature domain wall velocity in synthetic ferrimagnetic systems through stack engineering. Further studies to explore the role of the weak exchange link provided by the proximity induced Gd magnetization profile are in progress.

![](https://assets.underline.io/uploads/markdown_image/1/image/abbc4d28d2f8fc22cfb8a86256cef998.jpg)

Fig. 1: Coercivity, polar MOKE signal (a) and current-driven domain wall velocity (b) as a function of Gd thickness in a Pt(4)/Co(0.6)/Gd(x)/Co(0.7)/Gd(1.5) multilayer system (thicknesses in nm in parenthesis), and x indicates Gd layer thickness.

![](https://assets.underline.io/uploads/markdown_image/1/image/439e7460be2e15697bd7be423caa409c.jpg)

Fig. 1 (a) The XRD pattern and (b) the FC magnetic moment as a function of temperature at 100 Oe, of LNMO films. The sample numbers represent the annealing time in minutes.

Fast Current-Induced Domain Wall Motion in Compensated Co/Gd Quadlayers

In recent years, there was an increased interest in using antiferromagnetic (AFM) materials for THz frequency sources. The operation of such AFM structures is based on the AFM resonance, which can have THz frequencies, exceeding the frequency ferromagnetic (FM) resonances by order of magnitude [1,2]. Recent experiments showed that it is possible to generate such signal in AFM FeRh/Pt bi-layers by optically exciting them with a sub-picosecond laser pulse [3]. The signal in the AFM state can be originated from a partial phase transition induced by the laser heat from the AF to the FM phase [4]. Such transformation occurs on a sub picosecond time scale [5-7]. Using atomistic simulations, it is possible to reproduce such transition by including both the bilinear and biquadratic exchanges in the Hamiltonian [7,8]. However, to model larger spatial structures, a coarse-grained model for the dynamic of the magnetization is desirable. Here, we present a micromagnetic formulation to model the magnetization dynamics and phase transition in FeRh at low and high temperatures, including the transition near the Curie temperature. The formulation is based on a mean field approximation (MFA), where each macrospin is modeled by two coupled sublattices, including the atomistic biquadratic interactions described as a micromagnetic inter-sublattice molecular field with a cubic dependence of the magnetization. To validate the model, we compare our simulations of the phase transitions in the static and dynamic case with the existing literature. The results show an agreement with the experiments and atomistic modeling, displaying the characteristic hysteretic behavior for the magnetization (Fig. 1), and a similar dynamic response to an external thermal pulse (Fig.2).

![](https://assets.underline.io/uploads/markdown_image/1/image/514f2aed032312bb7acd410db166547c.jpg)

Equilibrium magnetization as a function of temperature.

![](https://assets.underline.io/uploads/markdown_image/1/image/25e2660f89da1d9cb11ba63fe22f9af2.jpg)

Dynamic response of the magnetization to an optical pulse (shaded area) for different values of the atomistic damping coefficient α

Macromagnetic Simulation of AFM-FM phase transition in FeRh using a modified Landau-Lifshitz-Bloch Equation

Synthetic antiferromagnets (SAFs) are of interest in a wide variety of spintronic applications owing to their net zero magnetisation and inherent tunability arising from control over complex stacking sequences [1]. They show very fast domain wall (DW) motion in response to spin torques [2]. Here we describe current-driven DW motion in an SAF with stack structure Ta/[Ru/Pt/CoB/Ru/Pt/CoFeB]×5/Ru/Pt which displays both perpendicular magnetic anisotropy (PMA) and the Dzyaloshinskii-Moriya interaction (DMI). The alternating CoB and CoFeB layers had their thicknesses adjusted to give net zero magnetisation (as determined by SQUID-VSM) for applied fields up to ~500 Oe. They were patterned into 2 µm wide wires with Cu leads attached to each end. These were fabricated on Si3N4 membranes to permit imaging of DW motion using scanning x-ray transmission microscopy. The distinct chemical composition of the two sublattices means that we could use the element specificity of this technique to observe the CoFeB separately whilst imaging at the Fe L3 edge, whilst contrast at the Co L3 edge is dominated by the other sublattice. Inverted domain structures observed at these two edges, as shown in Fig. 1, confirm the SAF ordering of the layers. Current pulses drive domain wall motion, as shown in Fig. 2, with velocities up to ~ 20 m/s achieved at current densities as low as 4 × 1011 A/m2.

![](https://assets.underline.io/uploads/markdown_image/1/image/d87de30dbef334ff75e4447e90cf2feb.jpg)

Fig. 1: STXM images acquired at zero field the Co and Fe L3 edges, which probe different sublattices of the SAF. A finger-shaped Cu lead is visible on the left. 1 µm scale bar.

![](https://assets.underline.io/uploads/markdown_image/1/image/04b915124bc7866fb80c310fb03a761b.jpg)

Fig. 2: DW velocity against current density measured using 5 ns current pulses.

Current-Driven Domain Wall Motion in a Synthetic Antiferromagnet Multilayer

We show that antiperovskite Mn4N transforms from ferri- to ferromagnetism at room temperature (RT) when the Mn content is decreased by the addition of non-magnetic In atoms. Mn4N films have attracted increasing attention as candidates for the current induced domain wall motion (CIDWM) devices. They have a small magnetization (Ms ~ 100 kA/m [1]) and perpendicular magnetic anisotropy, contributing to high CIDWM mobility with low threshold current. In addition, Mn4-xNixN [2] and Mn4-xCoxN [3] epitaxial films have x-dependent magnetic compensation (MC) points at RT, probed by X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) measurements. In Mn4-xNixN nanowires at the vicinity of the MC, we demonstrated ultrafast and efficient CIDWM (3,000 m/s with j=1.2×1012 A/m2) by pure spin transfer torque at RT [4]. In this work, we focused on Mn4-xInxN epitaxial films as new candidates for such materials [5]. We grew 25nm-thick Mn4-xInxN films (x=0, 0.15 and 0.27) on MgO(001) by MBE. XAS and XMCD measurements were performed at the twin APPLE II undulator beam line BL16A of KEK-PF in Japan. Figure 1 shows XAS and XMCD spectra of Mn-L2,3 absorption edges of the samples. In the XAS spectra of all the samples, distinct shoulders marked by arrows appear at about 2 eV above the main L3 edges, which are caused by fcc-Mn(II) atoms [3]. In the XMCD spectrum of Mn4N(x=0), corner-site Mn(I) and fcc-Mn(II) atoms are attributable to peaks α and β, respectively [3]. Their different signs show that the magnetic moments of Mn(I) and Mn(II) are aligned antiparallel. When the In composition x increases up to 0.27, the sign of peak β reverses while that of peak α remains unchanged. It means that the magnetic moment of Mn(II) reverses and now aligns parallel to that of Mn(I), showing a ferri-to-ferromagnetic transition at RT. Figure 2 shows the anomalous Hall effect (AHE) curves at RT. The sign reversal of ρAHE reconfirms the reversal of the magnetic moment of Mn(II) between x = 0.15 and 0.27 in Fig. 1.

![](https://assets.underline.io/uploads/markdown_image/1/image/26c9e42c0a4ba29f78f74bc6894e54cc.jpg)

Fig. 1 XAS and XMCD spectra at Mn-L2,3edges in (a) Mn4N, (b) Mn3.85In0.15N and (c) Mn3.85In0.27N.

![](https://assets.underline.io/uploads/markdown_image/1/image/cfe5232aa05ae86551424552fbca083a.jpg)

Fig. 2 Anomalous Hall effect curves of Mn4−xInxN (x=0.15 and 0.27) films on MgO(001).

Making ferrimagnetic Mn4N ferromagnetic by non-magnetic element doping

Magnetic domain walls (DWs) in ferromagnetic nanostrips with perpendicular magnetic anisotropy have widely been a subject of research, not only due to its intrinsic fundamental interest but also to develop spintronic devices where information is coded in domains between walls [1,2]. To that purpose, ferrimagnetic materials (FiM) are recently attracting much attention due to their fast DW dynamics, almost zero interaction with external fields and a wide availability in nature. Controlling the current-driven DW along curved FiMs strips is essential to develop DW-based circuitry, but it faces problems such as DW distortion [3]. A proper design for the strip geometry may overcome these problems, as shape is intimately connected with DW motion via spin currents and interfacial phenomena in the structure. Studying the influence of temperature (or composition) is also key for developing real applications. Therefore, understanding the influence of shape and temperature to fully control the DW motion is nowadays a fundamental topic in spintronics research. In this work we perform a micromagnetic (μm) study on DW motion in ring-like FiM strips, characterising DW terminal velocities and inertial times, as a function of temperature, width, curvature of the strip (see insets in Fig. 1(a)) and density currents (J). Our full μm model treats spin dynamics in each sublattice separately, which yields results close to ‘realistic’ FiM. Results show that strips with low width and high curvature give high DW velocities (VDW &gt; 1000 m/s), with ultra-short response times (τ &lt;&lt;0.1 ns, see Fig.1 (b)). This is optimal for developing compact and high-speed tracks for domains since opposite DWs travel at lower but similar speeds, leading to negligible domain distortion. Our results will help to understand curvature effects to develop efficient and reliable DW-based devices.

![](https://assets.underline.io/uploads/markdown_image/1/image/8036e1ee8c0a9ee895bd4c2baa9dc144.jpg)

Fig.1. (a) DW velocity as a function of J from sub-lattice i = 1 in a FiM strip of width w = 256 nm and different effective radius re (nm) at the angular momentum compensation temperature TA = 260 K. (b) Instantaneous DW velocities for three values of J and for a curved strip of re = 384 nm and w = 256 nm at T = TA. Relaxation times (τ) are extracted from the equation (solid curve) fitted to the data (symbols).

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