The spin-transfer-torque-driven (STT-driven) dynamics of a domain wall in an easy-axis rare-earth transition-metal ferrimagnet is investigated theoretically and numerically in the vicinity of the angular momentum compensation point $T_A$, where the net spin density vanishes. The particular focus is given on the unusual interaction of the antiferromagnetic dynamics of a ferrimagnetic domain wall and the adiabatic component of STT, which is absent in antiferromagnets but exists in the ferrimagnets due to the dominant coupling of conduction electrons to transition-metal spins. Specifically, we first show that the STT-induced domain-wall velocity changes its sign across $T_A$ due to the sign change of the net spin density, giving rise to a phenomenon unique to ferrimagnets that can be used to characterize $T_A$ electrically. It is also shown that the frequency of the STT-induced domain-wall precession exhibits its maximum at $T_A$ and it can approach the spin-wave gap at sufficiently high currents. Lastly, we report a numerical observation that, as the current density increases, the domain-wall velocity starts to deviate from the linear-response result, calling for a more comprehensive theory for the domain-wall dynamics in ferrimagnets driven by a strong current.
We discuss the current induced magnetization dynamics of spin valves F0|N|SyF where the free layer is a synthetic ferrimagnet SyF made of two ferromagnetic layers F1 and F2 coupled by RKKY exchange coupling. In the interesting situation where the magnetic moment of the outer layer F2 dominates the magnetization of the ferrimagnet, we find that the sign of the effective spin torque exerted on the free middle layer F1 is controlled by the strength of the RKKY coupling: for weak coupling one recovers the usual situation where spin torque tends to, say, anti-align the magnetization of F1 with resp…
Magnetic skyrmionium is a skyrmion-like spin texture with nanoscale size and high mobility. It is a topologically trivial but dynamically stable structure, which can be used as a non-volatile information carrier for next-generation spintronic storage and computing devices. Here, we study the dynamics of a skyrmionium driven by the spin torque in a ferrimagnetic nanotrack. It is found that the direction of motion is jointly determined by the internal configuration of a skyrmionium and the spin polarization vector. Besides, the deformation of a skyrmionium induced by the intrinsic skyrmion Hall …
The spin-orbit torque switching of ferrimagnetic Gd$_x$(Fe$_{90}$Co$_{10}$)$_{100-x}$ films was studied for both transition metal (TM)-rich and rare earth (RE)-rich configurations. The spin-orbit torque driven magnetization switching follows the same handedness in TM-rich and RE-rich samples with respect to the total magnetization, but the handedness of the switching is reversed with respect to the TM magnetization. This indicates that the sign of the spin-orbit-torque-driven magnetic switching follows the total magnetization, although transport based techniques such as anomalous Hall effect a…
We use micro-focus Brillouin light scattering spectroscopy to study the effects of spin-orbit torque on thermal spin waves in almost angular-momentum compensated ferrimagnetic CoGd alloy films. The spin-orbit torque is produced by the electric current flowing in the Pt layer adjacent to CoGd. Both the ferromagnetic and the exchange modes are detected in our measurements. The intensity and the linewidth of the ferromagnetic mode are modified by the spin-orbit torque. In contrast, the properties of the exchange mode are unaffected by the spin-orbit torque. We also find that the frequencies and t…
A theory of magnetization dynamics in ferrimagnetic materials with antiparallel aligned spin sub-lattices under action of spin-transfer torques (STT) is developed. We consider magnetization dynamics in GdFeCo layers in two cases of magnetic anisotropy: easy plane and easy axis. We demonstrate that, (i) for the easy plane anisotropy the precession of the Néel vector is conical and the cone angle depends on the STT strength and the value of spin non-compensation, while the frequency of precession can reach sub-THz frequencies; (ii) for the easy axis anisotropy two regimes are possible: determini…
So far, studies of spin-orbit torques (SOT) in ferromagnets with perpendicular magnetic anisotropy (PMA) have been restricted to ultra thin samples, while a systematic study of its thickness dependence is still lacking in literature. In this article we discuss the thickness dependence of SOT in GdFeCo samples with bulk PMA. We show that the effective SOT fields are decreasing inversely as a function of thickness while the spin-Hall angle stays constant, as expected from angular momentum conservation. Further we show that even 30nm thick GdFeCo samples can be switched with SOT. This has importa…
The fascinating high-speed field-driven domain wall (DW) motion along ferrimagnetic nanowires near the angular momentum compensation point (AMCP) is solved based on the generic ferrimagnetic dynamics. The physics of the absences of precessional torque and infinite high Walker breakdown field at the AMCP is proved under general conditions. Based on the energy conservation principle, an almost exact DW velocity formula, valid beyond the Walker breakdown field, is obtained. Our results agree with all existing experiments and simulations. This theory provides useful guidances to DW manipulation.
Antiferromagnets and compensated ferrimagnets offer opportunities to investigate spin dynamics in the 'terahertz gap' because their resonance modes lie in the 0.3 THz to 3 THz range. Despite some inherent advantages when compared to ferromagnets, these materials have not been extensively studied due to difficulties in exciting and detecting the high-frequency spin dynamics, especially in thin films. Here we show that spin-obit torque in a single layer of the highly spin-polarized compensated ferrimagnet Mn2RuxGa is remarkably efficient at generating spin-orbit fields μ_0H_eff, which approach 0…
We theoretically study a ferrimagnetic domain-wall motion driven by a rotating magnetic field. We find that, depending on the magnitude and the frequency of the rotating field, the dynamics of a ferrimagnetic domain wall can be classified into two regimes. First, when the frequency is lower than a certain critical frequency set by the field magnitude, there is a stationary solution for the domain-wall dynamics, where a domain-wall in-plane magnetization rotates in-phase with the external field. The field-induced precession of the domain wall gives rise to the translational motion of the domain…
The switching speed and the write current required for spin-transfer-torque reversal of spintronic devices such as magnetic tunnel junctions (MTJ) currently hinder their wide implementation into memory and logic devices. This problem is further exacerbated as the dimensions of MTJ nanostructures are scaled down to tens of nanometers in diameter, as higher magnetic anisotropy materials are required to meet thermal stability requirements that demand higher switching current densities. Here, we propose a simple solution to these issues based on synthetic ferrimagnet (SFM) structures. It is common…
Current-induced spin-orbit torques (SOTs) are of interest for fast and energy-efficient manipulation of magnetic order in spintronic devices. To be deterministic, however, switching of perpendicularly magnetized materials by SOT requires a mechanism for in-plane symmetry breaking. Existing methods to do so involve the application of an in-plane bias magnetic field, or incorporation of in-plane structural asymmetry in the device, both of which can be difficult to implement in practical applications. Here, we reported bias-field-free SOT switching in a single perpendicular CoTb layer with an eng…
Spintronics provides an efficient platform for realizing non-volatile memory and logic devices. In these systems, data is stored in the magnetization of magnetic materials, and magnetization is switched in the writing process. In conventional spintronic devices, ferromagnetic materials are used which have a magnetization dynamics timescale of around the nanoseconds, setting a limit for the switching speed. Increasing the magnetization switching speed has been one of the challenges in spintronic research. In this work we take advantage of the ultrafast magnetization dynamics in ferrimagnetic ma…
Spintronics is showing promising results in the search for new materials and effects to reduce energy consumption in information technology. Among these materials, ferrimagnets are of special interest, since they can produce large spin currents that trigger the magnetization dynamics of adjacent layers or even their own magnetization. Here, we present a study of the generation of spin current by GdFeCo in a GdFeCo/Cu/NiFe trilayer where the FeCo sublattice magnetization is dominant at room temperature. Magnetic properties such as the saturation magnetization are deduced from magnetometry measu…
Ferrimagnets (FIMs) can function as high-frequency antiferromagnets while being easy to detect as ferromagnets, offering unique opportunities for ultrafast device applications. While the physical behavior of FIMs near the compensation point has been widely studied, there lacks a generic understanding of FIMs where the ratio of sublattice spins can vary freely between the ferromagnetic and antiferromagnetic limits. Here we investigate the physical properties of a model two-sublattice FIM manipulated by static magnetic fields and current-induced torques. By continuously varying the ratio of subl…
We investigate ferrimagnetic domain wall dynamics induced by circularly polarized spin waves theoretically and numerically. We find that the direction of domain wall motion depends on both the circular polarization of spin waves and the sign of net spin density of ferrimagnet. Below the angular momentum compensation point, left- (right-) circularly polarized spin waves push a domain wall towards (away from) the spin-wave source. Above the angular momentum compensation point, on the other hand, the direction of domain wall motion is reversed. This bidirectional motion originates from the fact t…
The current-driven domain wall dynamics along ferrimagnetic systems are here theoretically analyzed as a function of the temperature by means of micromagnetic simulations and a one dimensional model. Contrarily to conventional effective approaches, our model takes into account the two coupled ferromagnetic sublattices forming the ferrimagnetic system. Although the model is suitable for systems with asymmetric exchange interaction and spin-orbit coupling effects due to adjacent heavy metal layers, we here focus our attention on the case of single-layer ferrimagnetic strips where domain walls ad…
Antiferromagnetic materials are outstanding candidates for next generation spintronic applications, because their ultrafast spin dynamics makes it possible to realize several orders of magnitude higher-speed devices than conventional ferromagnetic materials1. Though spin-transfer torque (STT) is a key for electrical control of spins as successfully demonstrated in ferromagnetic spintronics, experimental understanding of STT in antiferromagnets has been still lacking despite a number of pertinent theoretical studies2-5. Here, we report experimental results on the effects of STT on domain-wall (…
Domain walls in ferromagnetic nanowires are potential building-blocks of future technologies such as racetrack memories, in which data encoded in the domain walls are transported using spin-polarised currents. However, the development of energy-efficient devices has been hampered by the high current densities needed to initiate domain wall motion. We show here that a remarkable reduction in the critical current density can be achieved for in-plane magnetised coupled domain walls in CoFe/Ru/CoFe synthetic ferrimagnet tracks. The antiferromagnetic exchange coupling between the layers leads to si…
One fundamental obstacle to efficient ferromagnetic spintronics is magnetic precession, which intrinsically limits the dynamics of magnetic textures, We demonstrate that the domain wall precession fully vanishes with a record mobility when the net angular momentum is compensated (TAC) in DWs driven by spin-orbit torque in a ferrimagnetic GdFeCo/Pt track. We use transverse in-plane fields to reveal the internal structure of DWs and provide a robust and parameter-free measurement of TAC. Our results highlight the mechanism of faster and more efficient dynamics in materials with multiple spin lat…
Use of a spin polarized current for the manipulation of magnetic domain walls in ferromagnetic nanowires has been the subject of intensive research for many years. Recently, due to technological advancements, creating nano-contacts with special characteristics is becoming more and more prevalent. We now present a full quantum investigation of the magnetoresistance and the spin transfer torque in a domain wall, which is embedded in a nano-contact of Ni$_{80}$Fe$_ {20}$, where the size of the domain wall becomes a relevant tunable parameter. The dependence on the domain wall width as well as the…
Current-induced spin torques in layered magnetic heterostructures have many commonalities across broad classes of magnetic materials. These include not only collinear ferromagnets, ferrimagnets, and antiferromagnets, but also more complex noncollinear spin systems. We develop a general Lagrangian-Rayleigh approach for studying the role of dissipative torques, which can pump energy into long-wavelength magnetic dynamics, causing dynamic instabilities. While the Rayleigh structure of such torques is similar for different magnetic materials, their consequences depend sensitively on the nature of …
The ferrimagnets, such as GdxFeCo(1-x), can produce ultrafast magnetic switching and oscillation due to the strong exchange field. The two-sublattices macrospin model has been widely used to explain the experimental results. However, it fails in describing the spatial nonuniform magnetic dynamics which gives rises to many important phenomenons such as the domain walls and skyrmions. Here we develop the two-dimensional atomistic model and provide a torque analysis method to study the ferrimagnetic oscillation. Under the spin-transfer torque, the magnetization oscillates in the exchange mode or …
We show that it is possible to engineer magnetic multi-domain configurations without domain walls in a prototypical rare earth/transition metal ferrimagnet using keV He+ ion bombardment. We additionally shown that these patterns display a particularly stable magnetic configuration due to a deep minimum in the free energy of the system which is caused by flux closure and the corresponding reduction of the magnetostatic part of the total free energy. This is possible because light-ion bombardment differently affects an elements relative contribution to the effective properties of the ferrimagnet…
Recently, magnetic skyrmion has emerged as an active topic of fundamental study and applications in magnetic materials research. Magnetic skyrmions are vortex-like spin excitations with topological protection and therefore are more robust to pinning compared with magnetic domain walls. We employ atomistic simulations to create room-temperature ultra-small Neel skyrmions in amorphous ferrimagnet. The fast propagation and low-dissipation dynamics of ultra-small ferrimagnetic skyrmions make them attractive for utilization as an alternative to domain walls in spin-based memory and logic devices.
Spin-orbitronics and single pulse all-optical switching (AOS) of magnetization are two major successes of the rapidly advancing field of nanomagnetism in recent years, with high potential for enabling novel, fast and energy-efficient memory and logic platforms. Fast current-induced domain wall motion (CIDWM) and single shot AOS have been individually demonstrated in different ferrimagnetic alloys. However, the stringent requirement for their composition control makes these alloys challenging materials for wafer-scale production. Here, we simultaneously demonstrate fast CIDWM and energy efficie…
A consistent theory to describe the correlated dynamics of quantum mechanical itinerant spins and semiclassical local magnetization is given. We consider the itinerant spins as quantum mechanical operators, whereas local moments are considered within classical Lagrangian formalism. By appropriately treating fluctuation space spanned by basis functions, including a zero-mode wave function, we construct coupled equations of motion for the collective coordinate of the center-of-mass motion and the localized zero-mode coordinate perpendicular to the domain wall plane. By solving them, we demonstra…
We report on first-principles calculations of spin-transfer torque (STT) in epitaxial magnetic tunnel junctions (MTJs) based on ferrimagnetic tetragonal Mn$_3$Ga electrodes, both as analyzer in an Fe/MgO stack, and also in an analogous stack with a second Mn$_3$Ga electrode (instead of Fe) as polarizer. Solving the ballistic transport problem (NEGF + DFT) for the nonequilibrium spin density in a scattering region extended to over 7.6 nm into the Mn$_3$Ga electrode, we find long-range spatial oscillations of the STT decaying on a length scale of a few tens of angstroms, both in the linear respo…
The magnetization dynamics equation predicts that a domain wall that changes structure should undergo a displacement by itself - automotion - due to the relaxation of the linear momentum that is associated with the wall structure. We experimentally demonstrate this effect in soft nanostrips,transforming under spin transfer torque a metastable asymmetric transverse wall into a vortex wall. Displacements more than three times as large as under spin transfer torque only are measured for 1~ns pulses. The results are explained by analytical and numerical micromagnetics. Their relevance to domain wa…
Theoretical studies dealing with current-driven domain wall dynamics in ferrimagnetic alloys and, by extension, other antiferromagnetically coupled systems as some multilayers, are here presented. The analysis has been made by means of micromagnetic simulations that consider these systems as constituted by two subsystems coupled in terms of an additional exchange interlacing them. Both subsystems differ in their respective gyromagnetic ratios and temperature dependence. Other interactions, as for example anisotropic exchange or spin-orbit torques, can be accounted for differently within each s…
We study spin accumulation and spin transfer torque in a domain wall by solving the Boltzmann equation with a diffusion approximation. We obtained the analytical expressions of spin accumulation and spin transfer torque. Both the adiabatic and the non-adiabatic components of the spin transfer torque oscillate with the thickness of the domain wall. We show that the oscillation plays a dominant role in the non-adiabatic torque when the domain wall thickness is less than the spin-flip length, which is defined by the product of the Fermi velocity and the spin-flip scattering time.
The manipulation of magnetism with a gate voltage is expected to lead the way towards the realization of energy-efficient spintronics devices and high-performance magnetic memories. Exploiting magneto-ionic effects under micro-patterned electrodes in solid-state devices adds the possibility to modify magnetic properties locally, in a non-volatile and reversible way. Tuning magnetic anisotropy, magnetization and Dzyaloshinskii-Moriya interaction allows modifying at will the dynamics of non trivial magnetic textures such as skyrmions and chiral domain walls in magnetic race tracks. In this work,…
Spin-orbit torque in magnetic domain walls was investigated by solving the Pauli-Schrödinger equation for the itinerant electrons. The Rashba interaction considered is derived from the violation of inversion symmetry at interfaces between ferromagnets and heavy metals. In equilibrium, the Rashba spin-orbit interaction gives rise to a torque corresponding to the Dzyaloshinskii-Moriya interaction. When there is a current flowing, the spin-orbit torque experienced by the itinerant electrons in short domain walls has both field-like and damping-like components. However, when the domain wall width …
The manipulation of mesoscale domain wall phenomena has emerged as a powerful strategy for designing ferroelectric responses in functional devices, but its full potential has not yet been realized in the field of magnetism. We show that mechanically strained samples of Mn$_3$O$_4$ and MnV$_2$O$_4$ exhibit a stripe-like patterning of the bulk magnetization below known magnetostructural transitions, similar to the structural domains reported in ferroelectric materials. Building off our previous magnetic force microscopy data, we use small angle neutron scattering to show that these patterns exte…
The spin transfer torque generated by a spin-polarized current can induce the shift of the magnetic domain-wall position. In this work, we study theoretically the current-induced domain-wall motion by using the collective coordinate approach [Gen Tatara and Hiroshi Kohno, Phys. Rev. Lett. 92, 86601 (2004)]. The approach is extended to include not only the domain-wall position and the polarization angle changes but also the domain-wall width variation. It is demonstrated that the width variation affects the critical current.
We numerically compute current-induced spin-transfer torques for antiferromagnetic domain walls, based on a linear response theory in a tight-binding model. We find that, unlike for ferromagnetic domain wall motion, the contribution of adiabatic spin torque to antiferromagnetic domain wall motion is negligible, consistent with previous theories. As a result, the non-adiabatic spin-transfer torque is a main driving torque for antiferromagnetic domain wall motion. Moreover, the non-adiabatic spin-transfer torque for narrower antiferromagnetic domain walls increases more rapidly than that for fer…
Charge resistance and spin torque are generated by coherent carrier transport through ferromagnetic 360 degree domain walls, although they follow qualitatively different trends than for 180 degree domain walls. The charge resistance of 360 degree domain walls reaches a maximum at an intermediate wall thickness, unlike 180 degree domain walls, whose resistance decreases monotonically with wall thickness. The peak amplitude of the spin torque and the optimal thickness of the domain wall to maximize torque for a 360 degree wall are more than twice as large as found for a 180 degree domain wall in…
Thermally assisted motion of magnetic domain wall under spin torque is studied theoretically. It is shown that the wall velocity $v$ depends exponentially on the spin current, $\Is$, below the threshold value, in the same way as in a thermally activated motion driven by a force. A novel property of the spin torque driven case at low temperature is that the linear term in spin current is universal, i.e., $\ln v \sim \frac{π\hbar}{2e}(\Is/\kB T)$. This behavior, which is independent of pinning and material constants, could be used to confirm experimentally the spin torque as the driving mechanis…
Spin transfer torque in a two dimensional electron gas system without space inversion symmetry was theoretically investigated by solving the Pauli-Schrödinger equation for the itinerant electrons inside magnetic domain walls. Due to the presence of the Rashba spin-orbit coupling induced by the broken inversion symmetry, the spin transfer torque is chiral and the nonadiabaticity, which is defined to measure the relative importance of the nonadiabatic, field-like torque to the adiabatic, damping-like torque, exhibits an inverse power law decay as the domain wall width is increased. This algebrai…
We discover that the way spin-waves exert magnetic torques in multiferroic materials can cause not only domain wall motion, but also magnetization dynamics for homogeneous magnetization textures. Interestingly, the domain wall motion can be controlled via purely electrical means with the spin-waves being generated by an ac electric field $E$ while the direction of the wall motion also is sensitive to an applied dc $E$ field. Moreover, we determine the interaction between spin-transfer torque from an electric current and a magnetic domain wall in multiferroics and show that the Walker breakdown…
We investigate the domain wall dynamics of a ferromagnetic wire under the combined influence of a spin-polarized current and magnonic spin-transfer torque generated by an external field, taking also into account Rashba spin-orbit coupling interactions. It is demonstrated that current-induced motion of the domain wall may be completely reversed in an oscillatory fashion by applying a magnonic spin-transfer torque as long as the spin-wave velocity is sufficiently high. Moreover, we show that the motion of the domain wall may be fully terminated by means of the generation of spin-waves, suggestin…
Within the s-d model description, we derive the current-driven spin torque in a ferromagnet, taking explicitly into account a spin-relaxing Caldeira-Leggett bath coupling to the s-electrons. We derive Bloch-Redfield equations of motion for the s-electron spin dynamics, and formulate a systematic gradient expansion to obtain non-adiabatic (higher-order) corrections to the well-known adiabatic (first-order) spin torque. We provide simple analytical expressions for the second-order spin torque. The theory is applied to current-driven domain wall motion. Second-order contributions imply a deformat…
