We study the existence of intrinsic localized one-spin excitation in the Heisenberg one-dimensional ferromagnetic spin chain in the presence of perpendicular and parallel external magnetic fields and current with spin-transfer torque and field-like torque. The Landau-Lifshitz-Gilbert-Slonczewski(LLGS) equation is exactly solved for the one spin excitation in the absence of onsite anisotropy for the excitations of spin with fields perpendicular and parallel to the chain. We show the removal of damping in the spin excitations by appropriately introducing current and also the enhancement of angular frequency of the oscillations due to field-like torque in the case of both perpendicular and parallel field. The exactness of the analytical results is verified by matching with numerical counterparts. Further, we numerically confirm the existence of in-phase and anti-phase stable synchronized oscillations for two spin-excitations in the presence of current with perpendicular field and field-like torque.
Momentum-space topology of electrons under strong spin-orbit coupling contributes to the electrically induced torques exerting on magnetic textures insensitively to disorder or thermal fluctuation. We present a direct connection between band topology and the torques by classifying the whole torques phenomenologically. As well as the intrinsic anomalous Hall effect, the torques also emerge intrinsically from the anomalous velocity of electrons regardless of a nonequilibrium transport current. We especially point out the intrinsic contribution arising exclusively in magnetic textures, which we c…
We derive an intrinsic contribution to the non-adiabatic spin torque for non-uniform magnetic textures. It differs from previously considered contributions in several ways and can be the dominant contribution in some models. It does not depend on the change in occupation of the electron states due to the current flow but rather is due to the perturbation of the electronic states when an electric field is applied. Therefore it should be viewed as electric-field-induced rather than current-induced. Unlike previously reported non-adiabatic spin torques, it does not originate from extrinsic relaxa…
We propose that topological spin currents flowing in topologically non-trivial magnetic textures, such as magnetic skyrmions and vortices, produce an intrinsic non-adiabatic torque of the form ${\bf T}_t\sim [(\partial_x{\bf m}\times\partial_y{\bf m})\cdot{\bf m}]\partial_y{\bf m}$. We show that this torque, which is absent in one-dimensional domain walls and/or non-topological textures, is responsible for the enhanced non-adiabaticity parameter observed in magnetic vortices compared to one-dimensional textures. The impact of this torque on the motion of magnetic skyrmions is expected to be cr…
An antiferromagnet is a promising material for spin-orbit torque generation. Earlier studies of the spin-orbit torque in an antiferromagnet are limited to collinear spin configurations. We calculate the spin-orbit torque in an antiferromagnet whose spin ordering is weakly noncollinear. Such noncollinearity may be induced spontaneously during the magnetization dynamics even when the equilibrium spin configuration is perfectly collinear. It is shown that deviation from perfect collinearity can modify properties of the spin-orbit torque since noncollinearity generates extra Berry phase contributi…
We demonstrate a high-quality spin orbit torque nano-oscillator comprised of spin wave modes confined by the magnetic field by the strongly inhomogeneous dipole field of a nearby micromagnet. This approach enables variable spatial confinement and systematic tuning of magnon spectrum and spectral separations for studying the impact of multi-mode interactions on auto-oscillations. We find these dipole field-localized spin wave modes exhibit good characteristic properties as auto-oscillators--narrow linewidth and large amplitude--while persisting up to room temperature. We find that the linewidth…
Integrated power and linewidth of a propagating and a self-localized spin wave modes excited by spin-polarized current in an obliquely magnetized magnetic nanocontact are studied experimentally as functions of the angle $θ_e$ between the external bias magnetic field and the nanocontact plane. It is found that the power of the propagating mode monotonically increases with $θ_e$, while the power of the self-localized mode has a broad maximum near $θ_e = 40$ deg, and exponentially vanishes near the critical angle $θ_e = 58$ deg, at which the localized mode disappears. The linewidth of the propaga…
Spin torque and spin Hall effect nanooscillators generate high intensity spin wave auto oscillations on the nanoscale enabling novel microwave applications in spintronics, magnonics, and neuromorphic computing. For their operation, these devices require externally generated spin currents either from an additional ferromagnetic layer or a material with a high spin Hall angle. Here we demonstrate highly coherent field and current tunable microwave signals from nanoconstrictions in single 15 and 20 nm thick permalloy layers. Using a combination of spin torque ferromagnetic resonance measurements,…
Spin-torque oscillators are strong candidates as nano-scale microwave generators and detectors. However, because of large amplitude-phase coupling (non-linearity), phase noise is enhanced over other linear auto-oscillators. One way to reduce nonlinearity is to use ferromagnetic layers as a resonator and excite them at localized spots, making a resonator-excitor pair. We investigated the excitation of oscillations in dipole-coupled ferromagnetic layers, driven by localized current at ferromagnetic nano-contacts. Oscillations possessed properties of optical-mode spin-waves and at low field ($\ap…
The spin-orbit torque induced by a topological insulator (TI) is theoretically examined for spin wave generation in a neighboring antiferromagnetic thin film. The investigation is based on the micromagnetic simulation of Néel vector dynamics and the analysis of transport properties in the TI. The results clearly illustrate that propagating spin waves can be achieved in the antiferromagnetic thin-film strip through localized excitation, traveling over a long distance. The oscillation amplitude gradually decays due to the non-zero damping as the Néel vector precesses around the magnetic easy axi…
We report the observation of the intrinsic damping-like spin-orbit torque (SOT) arising from the Berry curvature in metallic-magnet/CuO$_x$ heterostructures. We show that a robust damping-like SOT, an order of magnitude larger than a field-like SOT, is generated in the heterostructure despite the absence of the bulk spin-orbit effect in the CuO$_x$ layer. Furthermore, by tuning the interface oxidation level, we demonstrate that the field-like SOT changes drastically and even switches its sign, which originates from oxygen modulated spin-dependent disorder. These results provide an important in…
We study, both experimentally and by numerical modeling, the magnetic dynamics that can be excited in a magnetic thin-film nanopillar device using the spin torque from a spatially localized current injected via a 10s-of-nm-diameter aperture. The current-driven magnetic dynamics can produce large amplitude microwave emission at zero magnetic field, with a frequency well below that of the uniform ferromagnetic resonance mode. Micromagnetic simulations indicate that the physical origin of this efficient microwave nano-oscillator is the nucleation and subsequent steady-state rotational dynamics of…
We present theoretical studies of the intrinsic spin orbit torque (SOT) in a single domain ferromagnetic layer with Rashba spin-orbit coupling (SOC) using the non-equilibrium Green's function formalism for a model Hamiltonian. We find that, to the first order in SOC, the intrinsic SOT has only the field-like torque symmetry and can be interpreted as the longitudinal spin current induced by the charge current and Rashba field. We analyze the results in terms of the material related parameters of the electronic structure, such as band filling, band width, exchange splitting, as well as the Rashb…
We investigated temperature dependent current driven spin-orbit torques in magnetron sputtered Ru2Sn3 (4 and 10 nm) /Co20Fe60B20 (5 nm) layered structures with in-plane magnetic anisotropy. The room temperature damping-like and field-like spin torque efficiencies of the amorphous Ru2Sn3 films were measured to be 0.14 +- 0.008 (0.07 +- 0.012) and -0.03 +- 0.006 (-0.20 +- 0.009), for the 4 (10 nm) films respectively, by utilizing the second harmonic Hall technique. The large field-like torque in the relatively thicker Ru2Sn3 (10 nm) thin film is unique compared to the traditional spin Hall mater…
The establishment of chiral coupling in thin magnetic films with inhomogeneous anisotropy has led to the development of artificial systems of fundamental and technological interest. The chiral coupling itself is enabled by the Dzyaloshinskii-Moriya interaction (DMI) enforced by the patterned noncollinear magnetization. Here, we create a domain wall track with out-of-plane magnetization coupled on each side to a narrow parallel strip with in-plane magnetization. With this we show that the chiral torques emerging from the DMI at the boundary between the regions of noncollinear magnetization in a…
Magnetic domain wall (DW) motion induced by a localized Gaussian temperature profile is studied in a Permalloy nanostrip within the framework of the stochastic Landau-Lifshitz-Bloch equation. The different contributions to thermally induced DW motion, entropic torque and magnonic spin transfer torque, are isolated and compared. The analysis of magnonic spin transfer torque includes a description of thermally excited magnons in the sample. A third driving force due to a thermally induced dipolar field is found and described. Finally, thermally induced DW motion is studied under realistic condit…
We obtain the exact one-spin intrinsic localized excitation in an anisotropic Heisenberg ferromagnetic spin chain in a constant/variable external magnetic field with Gilbert damping included. We also point out how an appropriate magnitude spin current term in a spin transfer nano-oscillator (STNO) can stabilize the tendency towards damping. Further, we show how this excitation can be sustained in a recently suggested PT-symmetric magnetic nanostructure. We also briefly consider more general spin excitations.
Using bilayer films of $β$-Ta/Ni$_{0.8}$Fe$_{0.2}$, we fabricate structures consisting of two, three and four crossing ellipses which exhibit shape-induced bi-axial, tri-axial and quadro-axial magnetic anisotropy in the crossing area, respectively. Structures consisting of N crossing ellipses can be stabilized in 2N remanent states by applying (and removing) an external magnetic field. However, we show that with field-free spin-orbit torques induced by flowing currents in individual ellipses, the number of remanent states grows to 2$^\text{N}$. Furthermore, when the current flows between the e…
This paper micromagnetically studies the magnetization dynamics driven by the spin-Hall effect in a Platinum/Permalloy bi-layer. For a certain field and current range, the excitation of a uniform mode, characterized by a power with a spatial distribution in the whole ferromagnetic cross section, is observed. We suggest to use the ferromagnet of the bi-layer as basis for the realization of an array of spin-torque oscillators (STOs): the Permalloy ferromagnet will act as shared free layer, whereas the spacers and the polarizers are built on top of it. Following this strategy, the frequency of th…
We introduce time-dependent density matrix renormalization group (tDMRG) as a solution to long standing problem in spintronics -- how to describe spin-transfer torque (STT) between flowing spins of conduction electrons and localized spins within a magnetic material by treating the dynamics of both spin species fully quantum-mechanically. In contrast to conventional Slonczewski-Berger STT, where the localized spins are viewed as classical vectors obeying the Landau-Lifshitz-Gilbert equation and where their STT-driven dynamics is initiated only when the spin-polarization of flowing electrons and…
We report a comprehensive study of the maximization of the spin Hall ratio (θSH) in Pt thin films by the insertion of sub-monolayer layers of Ti to decrease carrier lifetime while minimizing the concurrent reduction in the spin Hall conductivity. We establish that the intrinsic spin Hall conductivity of Pt, while robust against the strain and the moderate interruption of crystal order caused by these insertions, begins to decrease rapidly at high resistivity level because of the shortening carrier lifetime. The unavoidable trade-off between the intrinsic spin Hall conductivity and carrier life…
Current-induced spin-transfer torques (STTs) have been studied in Fe, Co and Ni domain walls (DWs) by the method based on the first-principles noncollinear calculations of scattering wave functions expanded in the tight-binding linearized muffin-tin orbital (TB-LMTO) basis. The results show that the out-of-plane component of nonadiabatic STT in Fe DW has localized form, which is in contrast to the typical nonlocal oscillating nonadiabatic torques obtained in Co and Ni DWs. Meanwhile, the degree of nonadiabaticity in STT is also much greater for Fe DW. Further, our results demonstrate that comp…
Spin torque oscillators (STOs) are emerging microwave devices that can potentially be used in spin-logic devices and the next-generation high-speed computing architecture. Thanks to their non-linear nature, STOs are easily tunable by the magnetic field and the dc current. Spin Hall nano-oscillators (SHNOs) are promising types of STOs and most of the current studies focus on localized modes that can be easily excited. Here, we study using micromagnetic simulations, the nature of the spin-torque-induced excitations in nanowire devices made of perpendicular magnetic anisotropy (PMA) material. Our…
The standard model of spin-transfer torque (STT) in antiferromagnetic spintronics considers exchange of angular momentum between quantum spins of flowing electrons and noncollinear-to-them localized spins treated as classical vectors. These vectors are assumed to realize Néel order in equilibrium, $\uparrow \downarrow \ldots \uparrow \downarrow$, and their STT-driven dynamics is described by the Landau-Lifshitz-Gilbert (LLG) equation. However, many experimentally employed materials (such as archetypal NiO) are strongly electron-correlated antiferromagnetic Mott insulators (AFMI) where localize…
We study spin torques induced by Rashba spin-orbit coupling in two-dimensional ferromagnets under the good-metal condition $ε_{F}τ/\hbar\gg1$ ($ε_{F}$ the Fermi energy, $τ$ the electron lifetime) by employing the Kubo formula. We find that, in the presence of spin-dependent disorder the Rashba torque changes greatly as the system evolves out of the weak disorder limit where $\hbar/τ$ is much smaller than any intrinsic energy scale characterizing the multiband structure. The antidamping-like component of Rashba torque can be comparable to and larger than the field-like one out of the weak disor…
We study spin-orbit torques (SOT) in non-degenerate multiband electron systems in the weak disorder limit. In order to have better physical transparency a semiclassical Boltzmann approach equivalent to the Kubo diagrammatic approach in the non-crossing approximation is formulated. This semiclassical framework accounts for the interband- coherence effects induced by both the electric field and static impurity scattering. Using the two-dimensional Rashba ferromagnet as a model system, we show that the antidamping-like SOT arising from disorder-induced interband-coherence effects is very sensitiv…
Control of magnetic domain wall movement by the spin-polarized current looks promising for creation of a new generation of magnetic memory devices. A necessary condition for this is the domain wall shift by a low-density current. Here I show that a strongly anisotropic exchange interaction between mobile heavy holes and localized magnetic moments enormously increases the current-induced torque on the domain wall as compared to systems with isotropic exchange. This enables one to control the domain wall motion by current density 10^4 A/cm^2 in ferromagnet/semiconductor hybrids. The experimental…
Current induced spin wave excitations in spin transfer torque nano-contacts are known as a promising way to generate exchange-dominated spin waves at the nano-scale. It has been shown that when these systems are magnetized in the film plane, broken spatial symmetry of the field around the nano-contact induced by the Oersted field opens the possibility for spin wave mode co-existence including a non-linear self-localized spin-wave bullet and a propagating mode. By means of micromagnetic simulations, here we show that in systems with strong perpendicular magnetic anisotropy (PMA) in the free lay…
Effects of conduction electrons on magnetization dynamics, represented by spin torques, are calculated microscopically in the first order in spatial gradient and time derivative of magnetization. Special attention is paid to the so-called $β$-term and the Gilbert damping, $α$, in the presence of electrons' spin-relaxation processes, which are modeled by quenched magnetic (and spin-orbit) impurities. The obtained results such as $α\ne β$ hold for localized as well as itinerant ferromagnetism.
We predict that a temperature gradient can induce a magnon-mediated intrinsic torque and a transverse spin current in systems with non-trivial magnon Berry curvature. With the help of a microscopic linear response theory of nonequilibrium magnon-mediated torques and spin currents we identify the interband and intraband components that manifest in ferromagnets with Dzyaloshinskii-Moriya interactions and magnetic textures. To illustrate and assess the importance of such effects, we apply our theory to the magnon-mediated spin Nernst and torque responses in a kagome lattice ferromagnet.
In this paper, by considering the Hubbard model on a honeycomb lattice, we developed a theory for the intrinsic magnetic impurities (MIs) with the quasi-localized spin moments induced by the vacancies in graphene. Because the intrinsic MIs are characterized by the zero modes that are rthotropic to the itinerant electrons, their properties are much different from those of Anderson MIs with the well-localized spin moments.
Spin-torque nano-oscillators (STNO) are microwave auto-oscillators based on magnetic resonances having a nonlinear response with the oscillating amplitude, which provides them with a large frequency tunability including the possibility of mutual synchronization. The magnetization dynamics in STNO are induced by spin transfer torque (STT) from spin currents and can be detected by changes in electrical resistance due to giant magnetoresistance or tunneling magnetoresistance. The STT effect is usually treated as a damping-like term that reduces magnetic dissipation and promotes excitation of magn…
The recent experiment [Y. Wang et al., Science 366, 1125 (2019)] on magnon-mediated spin-transfer torque (MSTT) was interpreted in terms of a picture where magnons are excited within an antiferromagnetic insulator (AFI), by applying nonequilibrium electronic spin density at one of its surfaces, so that their propagation across AFI deprived of conduction electrons eventually leads to reversal of magnetization of a ferromagnetic metal (FM) attached to the opposite surface of AFI. We employ a recently developed time-dependent nonequilibrium Green functions combined with the Landau-Lifshitz-Gilber…
We study the spin orbit torque arising from an intrinsic linear Dresselhaus spin-orbit coupling in a single layer III-V diluted magnetic semiconductor. We investigate the transport properties and spin torque using the linear response theory and we report here : (1) a strong correlation exists between the angular dependence of the torque and the anisotropy of the Fermi surface; (2) the spin orbit torque depends nonlinearly on the exchange coupling. Our findings suggest the possibility to tailor the spin orbit torque magnitude and angular dependence by structural design.
Spin is an intrinsically quantum property, characterized by angular momentum. A change in the spin state is equivalent to a change in the angular momentum or mechanical torque. This spin-induced torque has been invoked as the intrinsic mechanism in experiments ranging from the measurements of angular momentum of photons g-factor of metals and magnetic resonance to the magnetization reversal in magnetic multi-layers A spin-polarized current introduced into a nonmagnetic nanowire produces a torque associated with the itinerant electron spin flip. Here, we report direct measurement of this mechan…
Magnetization dynamics in single-domain ferromagnets can be triggered by charge current if spin-orbit coupling is sufficiently strong. We apply functional Keldysh theory to investigate Rashba spin-orbit torques in metallic two-dimensional ferromagnets. A reactive, anti-damping-like spin-orbit torque as well as a dissipative, field-like torque are calculated microscopically, to the leading order in the spin-orbit interaction strength. By calculating the first vertex correction we show that the intrinsic anti-damping-like torque vanishes unless the scattering rates are spin-dependent.
A microscopic calculation is presented for the spin-transfer torques (STT) and damping torques in metallic antiferromagnets (AF). It is found that the sign of the STT is opposite to that in ferromagnets because of the AF transport character, and the current-to-STT conversion factor is enhanced near the AF gap edge. The dissipative torque parameter $β_n$ and the damping parameter $α_n$ for the Néel vector arise from spin relaxation of electrons. Physical consequences are demonstrated for the AF domain wall motion using collective coordinates, and some similarities to the ferromagnetic case are …
We study spin-orbit torques and charge pumping in magnetic quasi-one dimensional zigzag nanoribbons with hexagonal lattice, in the presence of large intrinsic spin-orbit coupling. Such a system experiences topological phase transition from a trivial band insulator to a quantum spin Hall insulator either by tuning the magnetization direction or the intrinsic spin-orbit coupling. We find that spin-charge conversion efficiency (i.e. spin-orbit torque and charge pumping) is dramatically enhanced at the topological transition, displaying a substantial angular anisotropy.
Currents induce magnetization torques via spin-transfer when the spin angular momentum is conserved or via relativistic spin-orbit coupling. Beyond simple models, the relationship between material properties and spin-orbit torques is not known. Here, we present a novel phenomenology of current-induced torques that is valid for any strength of intrinsic spin-orbit coupling. In $\rm Pt|Co|AlO_x$, we demonstrate that the domain walls move in response to a novel relativistic dissipative torque that is dependent on the domain wall structure and that can be controlled via the Dzyaloshinskii-Moriya i…
We theoretically investigate the supercurrent-induced magnetization dynamics of a two-dimensional lattice of ferromagnetically ordered spins placed on a conventional superconductor with broken spatial inversion symmetry and strong spin-orbit coupling. We develop a phenomenological description of the coupled dynamics of the superconducting condensate and the spin system, and demonstrate that supercurrents produce a reactive spin-orbit torque on the magnetization. By performing a microscopic self-consistent calculation, we show that the spin-orbit torque originates from a spin-polarization of th…
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 present numerical simulation studies of the steady-state magnetization dynamics driven by a spin-polarized current in a point contact geometry for the case of a relatively large contact diameter (D = 80 nm) and small external field (H = 30 Oe). We show, that under these conditions the magnetization dynamics is qualitatively different from the dynamics observed for small contacts in large external fields. In particular, the 'bullet' mode with a homogeneous mode core, which was the dominating localized mode for small contacts, is not found here. Instead, all localized oscillation modes observ…
In cavity quantum electrodynamics, the multiple reflections of a photon between two mirrors defining a cavity is exploited to enhance the light-coupling of an intra-cavity atom. We show that this paradigm for enhancing the interaction of a flying particle with a localized object can be generalized to spintronics based on van der Waals 2D magnets. Upon tunneling through a magnetic bilayer, we find the spin transfer torques per electron incidence can become orders of magnitude larger than $\hbar/2$, made possible by electron's multi-reflection path through the ferromagnetic monolayers as an inte…
To study the effect of spin-orbit coupling (SOC) on spin-transfer torque in magnetic materials, we have implemented two theoretical formalisms that can accommodate SOC. Using the "charge-pumping" formalism, we find two contributions to the out-of-plane spin-transfer torque parameter $β$ in ballistic Ni domain walls (DWs). For short DWs, the nonadiabatic reflection of conduction electrons caused by the rapid spatial variation of the exchange potential results in an out-of-plane torque that increases rapidly with decreasing DW length. For long DWs, the Fermi level conduction channel anisotropy t…
We report measurements of the spin torque efficiencies in perpendicularly-magnetized Pt/Co bilayers where the Pt resistivity $ρ_{Pt}$ is strongly dependent on thickness $t_{Pt}$ . The damping-like spin Hall torque efficiency per unit current density, $ξ^j_{DL}$ , varies significantly with $t_{Pt}$, exhibiting a peak value $ξ^j_{DL}=0.12$ at $t_{Pt} = 2.8 - 3.9$ nm. In contrast, $ξ^j_{DL}/ρ_{Pt}$ increases monotonically with $t_{Pt}$ and saturates for $t_{Pt} > 5$ nm, consistent with an intrinsic spin Hall effect mechanism, in which $ξ^j_{DL}$ is enhanced by an increase in $ρ_{Pt}$ . Assuming t…
We study the Casimir torque between two metallic one-dimensional gratings rotated by an angle $θ$ with respect to each other. We find that, for infinitely extended gratings, the Casimir energy is anomalously discontinuous at $θ=0$, due to a critical zero-order geometric transition between a 2D- and a 1D-periodic system. This transition is a peculiarity of the grating geometry and does not exist for intrinsically anisotropic materials. As a remarkable practical consequence, for finite-size gratings, the torque per area can reach extremely large values, increasing without bounds with the size of…
We investigate the spectral characteristics of spin torque oscillator (STO) excited by the spin Hall-induced spin current. We observe that the modest spin current injection triggers the conventional single peak oscillating behavior of STO. As the spin current is further increased to enter the non-linear regime, we find the transition of the spectrum from a single peak to multipeak structure whose frequency spacing is constant. This behavior can be primarily explained by the extremely broadened peak of the STO, which is accompanied by the frequency-dependent filtering by the transmission line. …
