In this paper we show that the spin transfer torque can be described by a pseudo magnetic field, proportional to the magnetic moment of the itinerant electrons that enters the Landau-Lifshitz-Gilbert equation in the same way as other external or internal magnetic fields. However, unlike an ordinary magnetic field, which is always conservative in nature, the spin torque induced pseudo field may have both conservative and non-conservative components. We further show that the magnetic moment of itinerant electrons develops an out-of-plane component only at non-equilibrium and this component is responsible for the Slonczewski type switching that acts against the damping and is always non-conservative. On the other hand, the in-plane components of the pseudo field exist both at equilibrium and out-of-equilibrium, and are responsible for the field like term. For tunnel based devices, this term results in lower switching current for anti-parallel (AP) to parallel (P) switching compared to P to AP, even when the torque magnitudes are completely symmetric with voltage.
In contrast to recent description [Phys. Rev. Lett. 106 (2011)116803], we show that pseudo spin in graphene is not completely a real angular momentum. The pseudo spin only in the direction perpendicular to graphene sheet is real angular momentum, while the pseudo spin parallel to graphene plane is still not real angular momentum. Interestingly, it is also shown that the Newtonian-like force and pseudo spin torque of massive Dirac electrons in graphene under strain field mimic gravitomagnetic force and gravitomagnetic spin torque, respectively. This is due to the equivalence of pseudo spin and …
We use self-consistent quantum transport theory to investigate the influence of electron-electron interactions on interlayer transport in semiconductor electron bilayers in the absence of an external magnetic field. We conclude that, even though spontaneous pseudospin order does not occur at zero field, interaction-enhanced quasiparticle tunneling amplitudes and pseudospin transfer torques do alter tunneling I-V characteristics, and can lead to time-dependent response to a dc bias voltage.
In this manuscript the general concepts of spin wave theory are adapted to the dynamics of a self-polarized system based on two layers coupled via interlayer exchange (conservative coupling) and mutual spin torque (dissipative coupling). An analytical description of the non-linear dynamics is proposed and validated through numerical simulations. In contrast to the single layer model, the phase equation of the coupled system has a contribution coming from the dissipative part of the LLGS equation. It is shown that this is a major contribution to the frequency mandatory to describe well the most…
At total filling factor $ν=1$ quantum Hall bilayers can have an ordered ground state with spontaneous interlayer phase coherence. The ordered state is signaled experimentally by dramatically enhanced interlayer tunnel conductances at low bias voltages; at larger bias voltages inter-layer currents are similar to those of the disordered state. We associate this change in behavior with the existence of a critical current beyond which static inter-layer phase differences cannot be maintained, and examine the dependence of this critical current on sample geometry, phase stiffness, and the coherent …
We consider a reversal of the magnetic moment of a nano-magnet by the fluctuating spin-torque induced by a non-equilibrium current of electron spins. This is an example of the problem of the escape of a particle from a metastable state subjected to a fluctuating non-conservative force. The spin-torque is the non-conservative force and its fluctuations are beyond the description of the fluctuation-dissipation theorem. We estimate the joint probability distribution of work done by the spin torque and the Joule heat generated by the current, which satisfies the fluctuation theorem for a small eng…
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…
Open-dissipative systems obeying parity-time ($\mathcal{PT}$) symmetry are capable of demonstrating oscillatory dynamics akin to the conservative systems. In contrast to limit cycle solutions characteristic of nonlinear systems, the $\mathcal{PT}$-symmetric oscillations form a continuum of non-isolated orbits. However, precise sculpturing of the real potential and the gain-loss spatial profiles required for establishing of the $\mathcal{PT}$-symmetry is practically challenging. The optical devices, such as lasers, exhibit relaxation dynamics and do not operate as the $\mathcal{PT}$-symmetric s…
A novel type of solitary wave is predicted to form in spin torque oscillators when the free layer has a sufficiently large perpendicular anisotropy. In this structure, which is a dissipative version of the conservative droplet soliton originally studied in 1977 by Ivanov and Kosevich, spin torque counteracts the damping that would otherwise destroy the mode. Asymptotic methods are used to derive conditions on perpendicular anisotropy strength and applied current under which a dissipative droplet can be nucleated and sustained. Numerical methods are used to confirm the stability of the droplet …
We derive a unified theory of spin and charge degrees of freedom in a ferromagnet. The spin-transfer torque and spin electromotive force are examined from the coarse-grained perspective of collective coordinates. The resulting equations of motion reflect a balance of conservative, gyroscopic (Berry-phase), and dissipative forces. We then expand the space of collective coordinates by adding the electric charge. The adiabatic spin-transfer torque and spin emf turn out to be a gyroscopic force; their nonadiabatic counterparts are a dissipative force.
DC current induced magnetization reversal and magnetization oscillation was observed in 500 nm large size Co90Fe10/Cu/Ni80Fe20 pillars. A perpendicular external field enhanced the coercive field separation between the reference layer (Co90Fe10) and free layer (Ni80Fe20) in the pseudo spin valve, allowing a large window of external magnetic field for exploring the free-layer reversal. The magnetization precession was manifested in terms of the multiple peaks on the differential resistance curves. Depending on the bias current and applied field, the regions of magnetic switching and magnetizatio…
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.
A strategy to drive skyrmion motion by a combination of an anisotropy gradient and spin Hall effect has recently been demonstrated. Here, we study the fundamental properties of this type of motion by combining micromagnetic simulations and a generalized Thiele equation. We find that the anisotropy gradient drives the skyrmion mainly along the direction perpendicular to the gradient, due to the conservative part of the torque. There is some slower motion along the direction parallel to the anisotropy gradient due to damping torque. When an appropriate spin Hall torque is added, the skyrmion vel…
We present an experimental study of vortex dynamics in magnetic nanocontacts based on pseudo spin valves comprising the Co$_2$MnGe Heusler compound. The films were grown by molecular beam epitaxy, where precise stoichiometry control and tailored stacking order allowed us to define the bottom ferromagnetic layer as the reference layer, with minimal coupling between the free and reference layers. 20-nm diameter nanocontacts were fabricated using a nano-indentation technique, leading to self-sustained gyration of the vortex generated by spin-transfer torques above a certain current threshold. By …
Application of Bardeen's tunneling theory to magnetic tunnel junctions having a general degree of atomic disorder reveals the close relationship between magneto-conduction and voltage-driven pseudo-torque, as well as the thickness dependence of tunnel-polarization factors. Among the results: 1) The torque generally varies as sin theta at constant applied voltage. 2) Whenever polarization factors are well defined, the voltage-driven torque on each moment is uniquely proportional to the polarization factor of the other magnet. 3) At finite applied voltage, this relation predicts significant volt…
Non-conservative physical systems admit a special kind of spectral degeneracy, known as exceptional point (EP), at which eigenvalues and eigenvectors of the corresponding non-Hermitian Hamiltonian coalesce. Dynamical parametric encircling of the EP can lead to non-adiabatic evolution associated with a state flip, a sharp transition between the resonant modes. Physical consequences of the dynamical encircling of EPs in open dissipative systems have been explored in optics and photonics. Building on the recent progress in understanding the parity-time (PT)-symmetric dynamics in spin systems, we …
Establishing the conditions under which orbital, spin and lattice-pseudospin degrees of freedom are mutually coupled in realistic nonequilibrium conditions is a major goal in the emergent field of graphene spintronics. Here, we use linear-response theory to obtain a unified microscopic description of spin dynamics and coupled spin-charge transport in graphene with an interface-induced Bychkov-Rashba effect. Our method makes use of an SO(5) extension of the familiar inverse-diffuson approach to obtain a quantum kinetic equation for the single-particle density matrix that treats spin and pseudos…
