Dynamic magnetic textures may transfer the angular moment from the varying in time antiferromagnetic order to spins of conduction electrons. Due to the spin orbit coupling (SOC) these spin excitations can induce the electric current of conduction electrons. We calculated the electric current and the electromotive force (EMF) which are produced by a domain wall (DW) moving parallel to the magnetically compensated interface between an antiferromagnetic insulator (AFMI) and a two-dimensional spin orbit coupled metal. Spins of conduction electrons interact with localized spins of a collinear AFMI through the interface exchange interaction. The Keldysh formalism of nonequilibrium Green functions was applied for the analysis of this system. It is shown that a Bloch DW generates the current perpendicular to the DW motion direction. At the same time a Néel DW creates the electric potential which builds up across the wall. The total charge which is pumped by a Bloch DW can be expressed in terms of a topologically invariant charge quantum. The latter does not depend on variations of DW's velocity and shape. These effects increase dramatically when the Fermi energy approaches the van Hove singularity of the Fermi surface. The obtained results are important for the electrical detection and control of dynamic magnetic textures in antiferromagnets.
Recently it has been recognized that the electromotive force (emf) can be induced just by the spin precession where the generation of the electromotive force has been considered as a real-space topological pumping effect. It has been shown that the amount of the electromotive force is independent of the functionality of the localized moments. It was also demonstrated that the rigid domain wall (DW) motion cannot generate electromotive force in the system. Based on real-space topological pumping approach in the current study we show that the electromotive force can be induced by rigid motion of…
We formulate a theory on the dynamics of conduction electrons in the presence of moving magnetic textures in ferromagnetic materials. We show that the variation of local magnetization in both space and time gives rise to topological fields, which induce electromotive forces on the electrons. Universal results are obtained for the emf induced by both transverse and vortex domain walls traveling in a magnetic film strip, and their measurement may provide clear characterization on the motion of such walls.
The antiferromagnetic domain wall dynamics is currently a hot topic in mesoscopic magnetic systems. In this work, it is found that, based on the Thiele approach, the motion of an antiferromagnetic domain wall is described by the Duffing equation. Numerical simulations demonstrate that the antiferromagnetic domain wall can be used as a Duffing oscillator, and the transition between the periodic and chaotic motion can be used to detect the periodic signal in the presence of the white noise. Furthermore, we calculate the bifurcation diagram and Lyapunov exponents to study the chaotic behavior of …
Spin waves in antiferromagnets are linearly or circularly polarized. Depending on the polarization, traversing spin waves alter the staggered field in a qualitatively different way. We calculate the drift velocity of a moving domain wall as a result of spin wave mediated forces, and show that the domain wall moves in opposite directions for linearly and circularly polarized waves. The analytical results agree with a micromagnetics simulation of an antiferromagnetic domain wall driven by a localized and alternating magnetic field.
We theoretically study the antiferromagnetic domain wall motion actuated by an inhomogeneous external magnetic field. The Lagrangian and the equations of motion of antiferromagnetic spins under an inhomogeneous magnetic field are derived, first in terms of the Néel vector, and then using collective coordinates of the domain wall. A solution is found that describes the actuation of a domain wall by an inhomogeneous field, in which the motion is initiated by a paramagnetic response of wall magnetization, which is then driven by a Stern-Gerlach like force. The effects of pinning potential are als…
An antiferromagnetic domain wall in a thermal gradient is found to experience a force towards colder regions upon the application of a uniform magnetic field along the easy axis. This force increases with the strength of the applied field and, for sufficiently high values, it overcomes the entropic force the that pushes wall towards the hotter regions. The force is proportional to the thermal gradient and it shows a linear dependence with the net magnetic moment of the domain wall induced by the field. The origin of this force lies on the increase of the domain wall reflectivity due the field-…
We theoretically study the scattering of spin waves from a sharp domain wall in an antiferromagnetic spin chain. While the continuum model for an antiferromagnetic material yields the well-known result that spin waves can pass through a wide domain wall with no reflection, here we show that, based on the discrete spin Hamiltonian, spin waves are generally reflected by a domain wall with a reflection coefficient that increases as the domain-wall width decreases. Remarkably, we find that, in the interesting case of an atomically sharp domain wall, the reflection of spin waves exhibits strong dep…
We investigate magnetic domain walls in a single fcc Mn layer on Re(0001) employing spin-polarized STM, atom manipulation, and spin dynamics simulations. The low symmetry of the row-wise antiferromagnetic (1Q) state leads to a new type of domain wall which connects rotational 1Q domains by a transient 2Q state with characteristic 90$^\circ$ angles between neighboring magnetic moments. The domain wall properties depend on their orientation and their width of about 2 nm essentially results from a balance of Heisenberg and higher-order exchange interactions. Atom manipulation allows domain wall i…
While spin textures in materials exhibiting zero net magnetization, such as antiferromagnetic domain walls (DWs), have attracted much interest lately due to their robustness against external magnetic noise, their generic detection via conventional magnetometry remains a challenging task. Here, we propose quantum relaxometry as a new route to image spin textures by probing the collective spin modes harbored by them. We investigate the Goldstone modes hosted by an antiferromagnetic domain wall and assess the relaxation rate of a quantum-spin sensor interacting with them. We show that such modes …
Soliton-based computing is relied on their unique properties for transporting energy and emerging intact from head-on collisions. Magnetic domain walls are often referred to as solitons disregarding the strict mathematical definition requiring the above scattering property. Here we demonstrate the conditions of elastic and inelastic scattering for spin-orbit torque-induced dynamics of antiferromagnetic domain walls on the example of a technologically relevant Mn$_2$Au material. We show that even domain walls with opposite winding numbers can experience elastic scattering and we present a corre…
We present the theory of the spin motive force in antiferromagnets. We consider a one-dimensional antiferromagnetic domain wall strongly coupled with conduction electrons via an exchange interaction. We carry out a unitary transformation that rotates the spin coordinate system of the conduction electron locally, so that the quantization axis is in the direction of the localized spin. By numerically solving the time-dependent Schr$ö$dinger equation, we clearly demonstrate that the spin motive force acts on the conduction electron. The result suggests that there is no distinction between antifer…
We theoretically examine a cross effect of magnetic field and charge current on antiferromagnetic domain wall dynamics. Since antiferromagnetic materials are largely insensitive to external magnetic fields in general, charge current has been shown recently as an alternative and efficient way to manipulate antiferromagnets. We find a new role of the magnetic field in the antiferromagnetic dynamics that appears when it is combined with charge current, demonstrating a domain wall motion in the presence of both field and current. We show that a spatially-varying magnetic field can shift the curren…
We propose a Hamiltonian dynamics formalism for the current and magnetic field driven dynamics of ferromagnetic and antiferromagnetic domain walls in one dimensional systems. To demonstrate the power of this formalism, we derive Hamilton equations of motion via Poisson brackets based on the Landau-Lifshitz-Gilbert phenomenology, and add dissipative dynamics via the evolution of the energy. We use this approach to study current induced domain wall motion and compute the drift velocity. For the antiferromagnetic case, we show that a nonzero magnetic moment is induced in the domain wall, which in…
We consider a domain wall in the mesoscopic quasi-one-dimensional sample (wire or stripe) of weakly anisotropic two-sublattice antiferromagnet, and estimate the probability of tunneling between two domain wall states with different chirality. Topological effects forbid tunneling for the systems with half-integer spin S of magnetic atoms which consist of odd number of chains N. External magnetic field yields an additional contribution to the Berry phase, resulting in the appearance of two different tunnel splittings in any experimental setup involving a mixture of odd and even N, and in oscilla…
The theory of special relativity is one of the most significant achievements in modern physics, with several important predictions such as time dilation, size contraction for a moving object and mass-energy equivalence. Recent studies have demonstrated size contraction for an antiferromagnetic (AFM) domain wall (DW). Here, we show the mass-energy equivalence by numerically investigating the excitation of terahertz (THz) magnons from a moving AFM DW under the magnetic anisotropy energy gradient. The energy of magnons comes from the loss of DW mass, accompanied with a DW width broadening, overco…
Recently, the magnetic domain walls have been experimentally observed in antiferromagnetic topological insulators MnBi$_2$Te$_4$, where we find that the topological zero-line modes (ZLMs) appear along the domain walls. Here, we theoretically demonstrate that these ZLMs are layer-dependent in MnBi$_2$Te$_4$ multilayers. For domain walls with out-of-plane ferromagnetism, we find that ZLMs are equally distributed in the odd-number layers. When domain walls possess in-plane magnetization, the ZLMs can also exist in even-number layers due to in-plane mirror-symmetry breaking. Moreover, the conducti…
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…
Theory of staggered damping-like spin-orbit torque on synthetic antiferromagnetic domain walls
Frontier Research Institute for Interdisciplinary Sciences, Tohoku University（东北大学前沿跨学科研究院）；Research Institute of Electrical Communication, Tohoku University（东北大学电气通信研究所）；Institute for Materials Research, Tohoku University（东北大学材料科学研究所）；Center for Science and Innovation in Spintronics, Tohoku University（东北大学自旋电子学科学与创新中心）；International Center for Synchrotron Radiation Innovation Smart, Tohoku University（东北大学同步辐射创新智能国际中心）
Antiferromagnetic topological insulators harbor topological in-gap surface states protected by an anti-unitary $S$ symmetry, which is broken by the inevitable presence of domain walls. Whether an antiferromagnetic topological insulator with domain walls is gapless and metallic on its topological surfaces remains to be elucidated. We show that a single non-statistical index characterizing the magnetic order of domain wall-decorated antiferromagnetic topological insulator, referred to as the Ising moment, determines the topological surface gap, which can be zero even when the $S$ symmetry is man…
Polarization, denoting the precession direction with respect to the background magnetization, is an intrinsic degree of freedom of spin wave. Using magnetic textures to control the spin wave polarization is fundamental and indispensable toward reprogrammable polarization-based magnonics. Here, we show that due to the intrinsic cubic anisotropy, a $90^\circ$ antiferromagnetic domain wall naturally acts as a spin wave retarder (wave-plate). Moreover, for a $90^\circ$ domain wall pair developed by introducing a second domain in a homogenous antiferromagnetic wire, the sign of retarding effect can…
We have engineered an antiferromagnetic domain wall by utilizing a magnetic frustration effect of a thin iron cap layer deposited on a chromium film. Through lithography and wet etching we selectively remove areas of the Fe cap layer to form a patterned ferromagnetic mask over the Cr film. Removing the Fe locally removes magnetic frustration in user-defined regions of the Cr film. We present x-ray microdiffraction microscopy results confirming the formation of a 90° spin-density wave propagation domain wall in Cr. This domain wall nucleates at the boundary defined by our Fe mask.
In this work, we study the microwave field driven antiferromagnetic domain wall motion in an antiferromagnetic nanowire, using the numerical calculations based on a classical Heisenberg spin model. We show that a proper combination of a static magnetic field plus an oscillating field perpendicular to the nanowire axis is sufficient to drive the domain wall propagation along the nanowire with the axial magnetic anisotropy. More importantly, the drift velocity at the resonance frequency is comparable to that induced by temperature gradients, suggesting that microwave field can be a very promisin…
Spin thermo-electric phenomena have attracted wide attention recently, e.g. the Spin Peltier effect (SPE) heat generation by magnonic spin currents. Here we find that the Spin Peltier ef-fect also manifests as a heat wave accompanying fast moving magnetic textures. High speed andextreme magnetic excitation localisation are paramount for efficient transfer of energy from thespin-degrees of freedom to electrons and lattice. While satisfying both conditions is subject to se-vere restrictions in ferromagnets, we find that domain walls in antiferomagnets can overcome theselimitations due to their p…
We present a theoretical formalism to address the dynamics of textured, noncolliear antiferromagnets subject to spin current injection. We derive sine-Gordon type equations of motion for the antiferromagnets, which are applicable to technologically important antiferromagnets such as Mn3Ir and Mn3Sn, and enables an analytical approach to domain wall dynamics in those materials. We obtain the expression for domain wall velocity, which is estimated to reach around 1 km/s in Mn3Ir by exploiting spin Hall effect with electric current density around 10^11A/m^2.
The control of magnetic domain walls is essential for the magnetic-based memory and logic applications. As an elementary excitation of magnetic order, spin wave is capable of moving magnetic domain walls just as the conducting electric current. Ferromagnetic spin waves can only be right-circularly polarized. In contrast, antiferromagnetic spin waves have full polarization degree of freedom, including both left- and right-circular polarizations, as well as all possible linear or elliptical ones. Here we demonstrate that, due to the Dzyaloshinskii-Moriya interaction, the spin wave driven domain …
The pinning and depinning of antiferromagnetic (AFM) domain wall is certainly the core issue of AFM spintronics. In this work, we study theoretically the Néel-type domain wall pinning and depinning at a notch in an antiferromagnetic (AFM) nano-ribbon. The depinning field depending on the notch dimension and intrinsic physical parameters are deduced and also numerically calculated. Contrary to conventional conception, it is revealed that the depinning field is remarkably dependent of the damping constant and the time-dependent oscillation of the domain wall position in the weakly damping regime…
The scalability of quantum networks based on solid-state spin qubits is hampered by the short range of natural spin-spin interactions. Here, we propose a scheme to entangle distant spin qubits via the soft modes of an antiferromagnetic domain wall (DW). As spin qubits, we focus on quantum impurities (QI's) placed in the vicinity of an insulating antiferromagnetic thin film. The low-energy modes harbored by the DW are embedded in the antiferromagnetic bulk, whose intrinsic spin-wave dynamics have a gap that can exceed the THz range. By setting the QI frequency and the temperature well within th…
We theoretically investigate domain wall motion in an antiferromagnetic insulator layer caused by thermally generated spin currents in an adjacent spin-split superconductor layer. An uncompensated antiferromagnet interface enables the two crucial ingredients underlying the mechanism - spin splitting in the superconductor and absorption of spin currents by the antiferromagnet. Treating the superconductor using the quasiclassical theory and the antiferromagnet via Landau-Lifshitz-Gilbert description, we find domain wall propagation along the thermal gradient with relatively large velocities $\si…
Magnetic nanowires supporting field- and current-driven domain wall motion are envisioned for new methods of information storage and processing. A major obstacle for their practical use is the domainwall velocity, which is traditionally limited due to the Walker breakdown occurring when the forcing field or current reaches a critical threshold value. We show through numerical and analytical modeling that the Walker breakdown limit can be extended or completely eliminated in antiferromagnetically coupled magnetic nanowires. These coupled nanowires allow for giant domain-wall velocities driven b…
Antiferromagnets (AFMs) exhibit intrinsic magnetization when the order parameter spatially varies. This intrinsic spin is present even at equilibrium and can be interpreted as a twisting of the homogeneous AFM into a state with a finite spin. Because magnetic moments couple directly to external magnetic fields, the intrinsic magnetization can alter the dynamics of antiferromagnetic textures under such influence. Starting from the discrete Heisenberg model, we derive the continuum limit of the free energy of AFMs in the exchange approximation and explicitly rederive that the spatial variation o…
Antiferromagnets offer remarkable promise for future spintronics devices, where antiferromagnetic order is exploited to encode information. The control and understanding of antiferromagnetic domain walls (DWs) - the interfaces between domains with differing order parameter orientations - is a key ingredient for advancing such antiferromagnetic spintronics technologies. However, studies of the intrinsic mechanics of individual antiferromagnetic DWs remain elusive since they require sufficiently pure materials and suitable experimental approaches to address DWs on the nanoscale. Here we nucleate…
Searching for new methods controlling antiferromagnetic (AFM) domain wall is one of the most important issues for AFM spintronic device operation. In this work, we study theoretically the domain wall motion of an AFM nanowire, driven by the axial anisotropy gradient generated by external electric field, allowing the electro control of AFM domain wall motion in the merit of ultra-low energy loss. The domain wall velocity depending on the anisotropy gradient magnitude and intrinsic material properties is simulated based on the Landau-Lifshitz-Gilbert equation and also deduced using the energy di…
Within linear continuum theory, no magnetic texture can propagate faster than the maximum group velocity of its spin waves. Here we report a transient regime due to the appearance of additional antiferromagnetic textures that breaks the Lorentz translational invariance of the magnetic system by atomistic spin dynamics simulations. This dynamical regime is akin to domain wall Walker-breakdown in ferromagnets and involves the nucleation of an antiferromagnetic domain wall pair. Subsequently, one of the nucleated 180$^{\circ}$ domain wall creates with the original domain wall a 360$^{\circ}$ spin…
In antiferromagnetically coupled multilayers with perpendicular anisotropy unusual multidomain textures can be stabilized due to a close competition between long-range demagnetization fields and short-range interlayer exchange coupling. In particular, the formation and evolution of specific topologically stable planar defects within the antiferromagnetic ground state, i.e. wall-like structures with a ferromagnetic configuration extended over a finite width, explain configurational hysteresis phenomena recently observed in [Co/Pt(Pd)]/Ru and [Co/Pt]/NiO multilayers. Within a phenomenological th…
The dynamics of a 90$^{\circ }$ domain wall in an antiferromagnetic nanostrip driven by the current-induced spin-orbital torque are theoretically examined in the presence of random thermal fluctuations. A soliton-type equation of motion is developed on the basis of energy balance between the driving forces and dissipative processes in terms of the domain wall velocity. Comparison with micromagnetic simulations in the deterministic conditions shows good agreement in both the transient and steady-state transport. When the effects of random thermal fluctuations are included via a stochastic treat…
We demonstrate the possibility to drive an antiferromagnet domain-wall at high velocities by field-like Néel spin-orbit torques. Such torques arise from current-induced local fields that alternate their orientation on each sub-lattice of the antiferromagnet and whose orientation depend primarily on the current direction, giving them their field-like character. The domain-wall velocities that can be achieved by this mechanism are two orders of magnitude greater than the ones in ferromagnets. This arises from the efficiency of the staggered spin-orbit fields to couple to the order parameter and …
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…
Efficient manipulation of antiferromagnetic (AF) domains and domain walls has opened up new avenues of research towards ultrafast, high-density spintronic devices. AF domain structures are known to be sensitive to magnetoelastic effects, but the microscopic interplay of crystalline defects, strain and magnetic ordering remains largely unknown. Here, we reveal, using photoemission electron microscopy combined with scanning X-ray diffraction imaging and micromagnetic simulations, that the AF domain structure in CuMnAs thin films is dominated by nanoscale structural twin defects. We demonstrate t…
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 (…
A flat band in fermionic system is a dispersionless single-particle state with a diverging effective mass and nearly zero group velocity. These flat bands are expected to support exotic properties in the ground state, which might be important for a wide range of promising physical phenomena. For many applications it is highly desirable to have such states in Dirac materials, but so far they have been reported only in non-magnetic Dirac systems. In this work we propose a realization of topologically protected spin-polarized flat bands generated by domain walls in planar magnetic topological ins…
Antiferromagnetically coupled multilayers with perpendicular anisotropy, as [CoPt]/Ru, Co/Ir, Fe/Au, display ferromagnetic stripe phases as the ground states. It is theoretically shown that the antiferromagnetic interlayer exchange causes a relative shift of domains in adjacent layers. This ``exchange shift'' is responsible for several recently observed effects: an anomalous broadening of domain walls, the formation of so-called ``tiger-tail'' patterns, and a ``mixed state'' of antiferromagnetic and ferromagnetic domains in [CoPt]/Ru multilayers. The derived analitical relations between the va…
We theoretically demonstrate dc and ac electric voltage generation due to spinmotive forces originating from domain wall motion and magnetic resonance, respectively, in two-sublattice antiferromagnets. Our theory accounts for the canting between the sublattice magnetizations, the nonadiabatic electron spin dynamics, and the Rashba spin-orbit coupling, with the inter-sublattice electron dynamics treated as a perturbation. This work suggests a new way to observe and explore the dynamics of antiferromagnetic textures by electrical means, an important aspect in the emerging field of antiferromagne…
We explore the emergence of spin-polarised flat-bands at head-to-head domain walls in a recently predicted class of antiferromagnetic topological insulators hosting planar magnetisation. We show, in the framework of quantum well physics, that by tuning the width of a domain wall one can control the functional form of the bound states appearing across it. Furthermore, we demonstrate the effect that the parity of the number of layers in a multilayer sample has on the electronic dispersion. In particular, the alignment of the magnetisation vectors on the terminating surfaces of odd layer samples …
We develop the theory of magnetic domain wall motion in coupled double-layer systems where electrons can hop between the layers giving rise to an antiferromagnetic coupling. We demonstrate that the force from the interlayer coupling drives the walls and the effect of the extrinsic pinning is greatly reduced if the domain walls are initially separated. The threshold current density for metastable spin-aligned configurations is also much lower. We conclude that the interlayer coupling has a significant effect on domain wall mobility in double-layer systems.
We derive equations of motion for topological solitons in antiferromagnets under the combined action of perturbations such as an external magnetic field and torque-generating electrical current. Aside from conservative forces, such perturbations generate an effective "magnetic field" exerting a gyrotropic force on the soliton and an induced "electric field" if the perturbation is time-dependent. We apply the general formalism to the cases of a domain wall and of a vortex. An antiferromagnetic vortex can be effectively moved by combined applications of a magnetic field and an electric current.
Spin valves consisting of heterostructures of single-layer hexagonal crystal on an antiferromagnetic substrate or of bilayer hexagonal crystal intercalated between two (anti)ferromagnetic insulators, with the current-in-plane geometry, are proposed. The two-dimensional hexagonal crystals such as graphene, silicene, germanene, and stanene are modeled by the tight binding model of honeycomb lattice. The magnetization orientation of the antiferromagnetic substrate(s) controls the band gap and topological properties of bulk, which in turn control the transport of three types of spin valve geometri…
In this paper, we develop the mathematical framework to describe the physical phenomenon behind the equilibrium configuration joining two antiferromagnetic domains. We firstly define the total energy of the system and deduce the governing equations by minimizing it with respect to the field variables. Then, we solve the resulting system of nonlinear PDEs together with proper initial and boundary conditions by varying the orientation of the 90$^{\circ}$ domain wall (DW) configuration along the sample. Finally, the angular dependence of elastic and magnetoelastic energies as well as of incompati…
