A new spinmotive force is predicted in ferromagnets with spin-orbit coupling. By extending the theory of spinmotive force, we show that a time-varying electric field can induce a spinmotive force with static and uniform magnetization. This spinmotive has two advantages; it can be detected free from the inductive voltage owing to the absence of dynamical magnetization and it can be tuned by electric fields. To observe the effect, we propose two experimental setups: electric voltage measurement in a single ferromagnet and spin injection from a ferromagnet into an attached nonmagnetic conductor.
Interaction between local magnetization and conduction electrons is responsible for a variety of phenomena in magnetic materials. It has been recently shown that spin current and associated electric voltage can be induced by magnetization that depends on both time and space. This effect, called spinmotive force, provides for a powerful tool for exploring the dynamics and the nature of magnetic textures, as well as a new source for electromotive force. Here we theoretically demonstrate the generation of electric voltages in magnetic bubble array systems subjected to a magnetic field gradient. I…
We theoretically show that a temporally oscillating spin-driven electromotive force or voltage with a large DC component can be generated by exciting microwave-active spin-wave modes of a skyrmion crystal confined in a quasi two-dimensional magnet under a tilted magnetic field. The DC component and the AC amplitude of the oscillating electric voltage is significantly enhanced when the microwave frequency is tuned to an eigenfrequency of the peculiar spin-wave modes of the skyrmion crystal called ``rotation modes" and ``breathing mode", whereas the sign of the DC component depends on the microw…
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…
Established forms of electromagnetic coupling are usually conservative (in insulators) or dissipative (in metals and semiconductors). Here we point out the possibility of nondissipative electric driving of magnetization dynamics, if the valence electronic states have nontrivial topology in the combined space of crystal momentum and magnetization configuration. We provide a hybrid insulator system to demonstrate that the topology-based nonconservative electrical generalized force is capable of supporting sustained magnetization motion in the presence of Gilbert damping, with quantized and stead…
We have investigated the effect of electric field control on the magnetization and the transport properties in La0.7Ca0.3MnO3 (LCMO) ultrathin film (~10 nm) by using it as the semiconductor channel material of a prototypical field effect device and SiO2 as dielectric gate. A large electroresistance (ER) of ~78% at Vg = -8 V is found in LCMO at 200 K. The direct magnetization measurements confirm the formation of a large ferromagnetic phase with the increase in the applied gate voltage at 200 K.
Manipulation of magnetization by electric field is a central goal of spintronics because it enables energy-efficient operation of spin-based devices. Spin wave devices are promising candidates for low-power information processing but a method for energy-efficient excitation of short-wavelength spin waves has been lacking. Here we show that spin waves in nanoscale magnetic tunnel junctions can be generated via parametric resonance induced by electric field. Parametric excitation of magnetization is a versatile method of short-wavelength spin wave generation, and thus our results pave the way to…
Electric-field induced magnetization switching in multiferroic magnetoelectric devices is promising for beyond Moore's law computing. We show here that interface-coupled multiferroic heterostructures, i.e., a ferroelectric layer coupled with a ferromagnetic layer, are particularly suitable for highly-dense, non-volatile, and ultra-low-energy computing. By solving stochastic Landau-Lifshitz-Gilbert equation of magnetization dynamics in the presence of room-temperature thermal fluctuations, we demonstrate that error-resilient switching of magnetization is possible in sub-nanosecond delay while e…
The authors show that it is possible to rotate the magnetization of a multiferroic (strain-coupled two-layer magnetostrictive-piezoelectric) nanomagnet by a large angle with a small electrostatic potential. This can implement Bennett clocking in nanomagnetic logic arrays resulting in unidirectional propagation of logic bits from one stage to another. This method of Bennett clocking is superior to using spin-transfer torque or local magnetic fields for magnetization rotation. For realistic parameters, it is shown that a potential of ~ 0.2 V applied to a multiferroic nanomagnet can rotate its ma…
We demonstrate electrical magnetization switching and spin pumping in magnetically doped Weyl semimetals. The Weyl semimetal is a new class of topological semimetals, known to have nontrivial coupling between the charge and the magnetization due to the chiral anomaly. By solving the Landau-Lifshitz-Gilbert equation for a multilayer structure of a Weyl semimetal, an insulator and a metal whilst taking the charge-magnetization coupling into account, magnetization dynamics is analyzed. It is shown that the magnetization dynamics can be driven by the electric voltage. Consequently, switching of th…
Electric field-induced magnetization switching in multiferroics is intriguing for both fundamental studies and potential technological applications. Here, we review the recent developments on electric field-induced magnetization switching in multiferroic heterostructures. Particularly, we study the dynamics of magnetization switching between the two stable states in a shape-anisotropic single-domain nanomagnet using stochastic Landau-Lifshitz-Gilbert (LLG) equation in the presence of thermal fluctuations. For magnetostrictive nanomagnets in strain-coupled multiferroic composites, such study of…
We report theoretical investigation of the switching probability of electric field-induced precessional magnetization switching by solving the Fokker-Planck equation numerically with finite difference method. The switching probability is determined by the net magnetic field induced by the deviation of precession angle from its equilibrium position after precession process. The error rate has the lowest value under an appropriate applied external field for the voltage pulse duration $τ_{pulse}$ a little longer than the half precession period. The calculated results show that ultra-low error rat…
The combined action of a transverse spin-polarized current and the current-induced Ørsted field on long ferromagnetic nanostripes is studied numerically and analytically. The magnetization behavior is analyzed for stripes with various widths and for all range of the applied current density. It is established that Ørsted field does not destroy periodical magnetization structures induced by the spin-torque, e.g. vortex-antivortex crystal and cross-tie domain walls. However, the action of the Ørsted field disables the saturation state for the strong currents: a stationary state with a single long…
The field of spintronics involves the study of both spin and charge transport in solid state devices with a view toward increasing their functionality and efficiency. Alternatively, the field of ultrafast magnetism focuses on the use of femtosecond laser pulses to excite electrons in magnetic materials, which allows the magnetic order to be dramatically changed on unprecedented sub-picosecond time-scales. Here, we unite these two distinct research activities by using picosecond electrical pulses to rapidly excite electrons in a magnetic metal. We are able to deterministically and repetitively …
Using a multi-orbital tight-binding model, we have studied the edge states of zigzag silicene, germanene, and stanene nanoribbons (ZSiNRs, ZGeNRs and ZSnNRs, respectively) in the presence of the Coulomb interaction and a vertical electric field. The resulting edge states have non-linear energy dispersions due to multi-orbital effects, and the nanoribbons show induced magnetization at the edges. Owing to this non-linear dispersion, ZSiNRs, ZGeNRs and ZSnNRs may not provide superior performance in field effect transistors, as has been proposed from single-orbital tight-binding model calculations…
Recently, signatures of quantum anomalous Hall states with spontaneous ferromagnetism were observed in twisted bilayer graphenes (TBGs) near 3/4 filling [1, 2]. Importantly, it was demon-strated that an extremely small current can switch the direction of the magnetization. This offers the prospect of realizing low energy dissipation magnetic memories. However, the mechanism of the current-driven magnetization switching is poorly understood as the charge currents in graphene layers are generally believed to be non-magnetic. In this work, we demonstrate that, in TBGs, the twist-induced reduction…
To give a general description of the influences of electric fields or currents on magnetization dynamics, we developed a semiclassical theory for the magnetization implicitly coupled to electronic degrees of freedom. In the absence of electric fields the Bloch electron Hamiltonian changes the Berry curvature, the effective magnetic field, and the damping in the dynamical equation of the magnetization, which we classify into intrinsic and extrinsic effects. Static electric fields modify these as first-order perturbations, using which we were able to give a physically clear interpretation of the…
We explore a spin Josephson effect in a system of two ferromagnets coupled by a tunnel junction formed of 2D time-reversal invariant topological insulators. In analogy with the more commonly studied instance of the Josephson effect for charge in superconductors, we investigate properties of the phase-coherent {\it spin} current resulting from the misalignment of the in-plane magnetization angles of the two ferromagnets. We show that the topological insulating barrier offers the exciting prospect of hosting a {\it fractional} spin Josephson effect mediated by bound states at the ferromagnet-top…
A simple model of magnetization dynamics in a ferromagnet/doped semiconductor hybrid structure with Rashba spin-orbit interaction (SOI) driven by an applied pulse of the electric field is proposed. The electric current excited by the applied field is spin-polarized due to the SOI and therefore it induces the magnetization rotation in the ferromagnetic layer via s-d exchange coupling. Magnetization dynamics dependence on the electric pulse shape and magnitude is analyzed for realistic values of parameters. We show that it is similar to the dynamics of a damped nonlinear oscillator with the time…
We propose an electric-field-controlled mechanism for magnetization switching assisted solely by the interlayer-exchange coupling (IEC) between the fixed and the free magnets, which are separated by two oxide barriers sandwiching a spacer material known for exhibiting large IEC. The basic idea relies on the formation of a quantum-well (QW) within the spacer material and controlling the transmission coefficient across the structure with an electric-field via the resonant tunneling phenomena. Using non-equilibrium Green's function (NEGF) method, we show that the structure can exhibit a bias-depe…
We show that the magnetic moment of a composite multiferroic torsional oscillator can be switched by the electric field. The 180$^o$ switching arises from the spin-rotation coupling and is not prohibited by the different symmetry of the magnetic moment and the electric field as in the case of a stationary magnet. Analytical equations describing the system have been derived and investigated numerically. Phase diagrams showing the range of parameters required for the switching have been obtained.
We show that the magneto-electric coupling in 3D (strong) topological insulators is related to a second derivative of the bulk magnetization. The formula we derive is the non-linear response analog of the Streda formula for Hall conductivity (P. Streda, J. Phys. C: Solid State Physics, 15, 22 (1982)), which relates the Hall conductivity to the derivative of the magnetization with respect to chemical potential. Our finding allows one to extract the magneto-electric coefficient by measuring the magnetization, while varying the chemical potential and one more perturbing field. Such an experimenta…
A mechanism of current-induced magnetization reversal based on the parametric resonance is described. The source of the magnetization reversal is a current-induced magnetic field, which is applied perpendicularly to the easy axis of magnetic anisotropy of a ferromagnetic nanomagnet. The current-induced magnetic field was measured in a FeCoB nanomagnet to be 60 Gauss at a current density of 65 mA/um2. Two mechanisms of the magnetization reversal are described and calculated. The first mechanism is the reversal by a RF electrical current, which modulated at a frequency close to the precession fr…
Within the linear response of polycrystalline magnetic films to electric currents, a general analysis predicts three new galvanomagnetic effects originated from the two-dimensional nature of the films. These new galvanomagnetic effects, which differ from the conventional extraordinary Hall effect and anisotropic magnetoresistance, are follows. 1) The longitudinal resistivity depends linearly on the magnetization component perpendicular to a film. 2) A current parallel to the magnetization can generate an electric field in the vertical direction of a film. 3) A current perpendicular to a film c…
A valley-contrasting Berry curvature in bilayer transition metal dichalcogenides with spin-orbit coupling can generate valley magnetization when the inversion symmetry is broken, for example, by an electric field, regardless of time-reversal symmetry. A nontrivial Berry curvature can also lead to anomalous transport responses, such as the anomalous Hall effect and the anomalous Nernst effect. Applied to a bilayer WSe$_2$, an electric field can tune the Berry curvature and orbital magnetic moment, which has important consequences for the orbital magnetization and the anomalous Nernst responses.…
The valleys in hexagonal two-dimensional systems with broken inversion symmetry carry an intrinsic orbital magnetic moment. Despite this, such systems possess zero net magnetization unless additional symmetries are broken, since the contributions from both valleys cancel. A nonzero net magnetization can be induced through applying both uniaxial strain to break the rotational symmetry of the lattice and an in-plane electric field to break time-reversal symmetry owing to the resulting current. This creates a magnetoelectric effect whose strength is characterized by a magnetoelectric susceptibili…
We report observation of a "non-volatile" converse magneto-electric effect in elliptical FeGa nanomagnets delineated on a piezoelectric PMN-PT substrate. The nanomagnets are initially magnetized with a magnetic field directed along their nominal major axis and subsequent application of an electric field across the substrate generates strain in the substrate, which is partially transferred to the nanomagnets and rotates the magnetizations of some of them to metastable orientations. There they remain after the field is removed, resulting in "non-volatility". In isolated nanomagnets, the angular …
The interplay of tunneling transport and carrier-mediated ferromagnetism in narrow semiconductor multi-quantum well structures containing layers of GaMnAs is investigated within a self-consistent Green's function approach, accounting for disorder in the Mn--doped regions and unwanted spin-flips at heterointerfaces on phenomenological ground. We find that the magnetization in GaMnAs layers can be controlled by an external electric bias. The underlying mechanism is identified as spin-selective hole tunneling in and out of the Mn-doped quantum wells, whereby the applied bias determines both hole …
We theoretically study electrical responses of magnetization in Weyl semimetals. The Weyl semimetal is a new class of topological semimetals, possessing hedgehog type spin textures in momentum space. Because of this peculiar spin texture, an interplay of electron transport and spin dynamics might provide new method to electrical control of magnetization. In this paper, we consider the magnetically doped Weyl semimetals, and systematically study current- and charge-induced spin torque exerted on the local magnetization in three-dimensional Dirac-Weyl metals. We determine all current-induced spi…
We show that a controllable dc magnetization is accumulated in a junction comprising a quantum dot coupled to non-magnetic reservoirs if the junction is subjected to a time-dependent spin-orbit interaction. The latter is induced by an ac electric field generated by microwave irradiation of the gated junction. The magnetization is caused by inelastic spin-flip scattering of electrons that tunnel through the junction, and depends on the polarization of the electric field: a circularly polarized field leads to the maximal effect, while there is no effect in a linearly polarized field. Furthermore…
Magnetic hysteresis loops show a moderate perpendicular anisotropy of the magnetostrictive CFO pillars, which is related to their vertical compression. The application of an electric field to the electromechanical PMN-PT substrate produced significant and reversible changes in the magnetization due to an additional strain-induced magnetic anisotropy. This demonstrates completely reversible, room-temperature electric-field-assisted control of magnetization in self-assembled vertical nanocomposites of CFO and BFO.
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…
It is well-known that the Curie temperature, and hence the magnetization, in diluted magnetic semiconductor (DMS) like Ga$_{1-x}$Mn$_x$As can be controlled by changing the equilibrium density of holes in the material. Here, we propose that even with a constant hole density, large changes in the magnetization can be obtained with a relatively small imbalance in the quasi-Fermi levels for up-spin and down-spin electrons. We show, by coupling mean field theory of diluted magnetic semiconductor ferromagnetism with master equations governing the Mn spin-dynamics, that a mere splitting of the up-spi…
Magnetic electric effects in ferromagnetic metals are discussed from the viewpoint of effective spin electromagnetic field that couples to conduction electron spin. The effective field in the adiabatic limit is the spin Berry's phase in space and time, and it leads to spin motive force (voltage generated by magnetization dynamics) and topological Hall effect due to spin chirality. Its gauge coupling to spin current describes the spin transfer effect, where magnetization structure is driven by an applied spin current. The idea of effective gauge field can be extended to include spin relaxation …
Recent advances in the studies of pure spin currents - flows of angular momentum (spin) not accompanied by the electric currents - have opened new horizons for the emerging technologies based on the electron's spin degree of freedom, such as spintronics and magnonics. The main advantage of pure spin current, as compared to the spin-polarized electric current, is the possibility to exert spin transfer torque on the magnetization in thin magnetic films without electrical current flow through the material. In addition to minimizing Joule heating and electromigration effects, this characteristic e…
We study experimentally the effect of electric field on the magnetization of Co/Al2O3 granular multilayers. We observe two distinct regimes: (a) low-field regime when the net magnetization of the system changes in a reversible way with the applied electric field and (b) high-field regime when the magnetization decreases irreversibly. The former is attributed to the changes in the relative 3d-orbital occupation of the minority and majority bands in the Co granules. A theoretical model has been developed to explain the electric field induced changes in the band structure of the granular system a…
Existing investigations of the anomalous Hall effect i.e. a current flowing transverse to the electric field in the absence of an external magnetic field) are concerned with the transport current. However, for many applications one needs to know the total current, including its pure magnetization part. In this paper, we employ the two-dimensional massive Dirac equation to find the exact universal total current flowing along a potential step of arbitrary shape. For a spatially slowly varying potential we find the current density $\mathbf{j}(\vec r)$ and the energy distribution of the current de…
We reveal the unexpected role of the material inhomogeneity in unifying the formulation of intrinsic thermal and thermoelectric transport as well as magnetization currents. The smooth inhomogeneity leads to the position dependent local band dispersion and phase-space Berry curvature, enabling a general and rapid access to transport and magnetization currents displaying the momentum-space Berry curvature physics. Our theory does not invoke the boundary current, the thermodynamic approach to magnetization or any mechanical counterpart of statistical forces. By introducing a fictitious inhomogene…
We report that the irreversible magnetization switching process in ferromagnetic nanoparticles is governed by the formation and dynamics of topological point-defects in the form of hedgehog-antihedgehog pairs. After nucleation, these pairs rapidly separate with speeds exceeding domain wall velocities, and they generate an emergent electric field of solenoidal character and substantial magnitude.
The Curie temperature is one of the most fundamental physical properties of ferromagnetic materials and can be described by Weiss molecular field theory with the exchange interaction of neighboring atoms. Recently, the electric-field-induced modulation of the Curie temperature has been demonstrated in transition metals. This can be interpreted as indirect evidence for the electrical modulation of exchange coupling. However, the scenario has not yet been experimentally verified. Here, we demonstrate the electrical control of exchange coupling in cobalt film from direct magnetization measurement…
Magnetization dynamics in a ferromagnet can induce a spin-dependent electric field through spin motive force. Spin current generated by the spin-dependent electric field can in turn modify the magnetization dynamics through spin-transfer torque. While this feedback effect is usually weak and thus ignored, we predict that in Rashba spin-orbit coupling systems with large Rashba parameter $α_{\rm R}$, the coupling generates the spin-dependent electric field [$\pm(α_{\rm R}m_e/e\hbar) (\vhat{z}\times \partial \vec{m}/\partial t)]$, which can be large enough to modify the magnetization dynamics sig…
Control of the magnetization vector in ferromagnetic films and heterostructures by using electric tools instead of external magnetic fields can lead to low-power memory devices. We observe the robust changes in magnetization states of a thin (about 30 nm) film of alpha-Fe covered by the naturally formed layer ( about 6 nm in thickness) of iron ohyhydroxides (FeOOH) under discharging a capacitor through the film. Strikingly, the magnetization vector is switchable by the discharge even with no any biasing field at room temperatures. In this electrically induced magnetization switching (EIMS) we …
We present the theoretical description for a class of experimental setups that measure quantum Hall coefficients in ferromagnet-topological insulator-ferromagnet (FM-TI-FM) junctions. We predict that varying the magnetization direction in ferromagnets, one can change the induced Hall voltage and transverse temperature gradient from the maximal values, corresponding to the quantized Hall coefficients, down to their complete suppression to zero. We provide detailed analysis of thermal and electrical Hall resistances as functions of the magnetization directions in ferromagnets, the spin-scatterin…
