Generalized spin-orbit torques in two-dimensional ferromagnets with spin-orbit coupling

Abstract

Based on the spinor Boltzmann equation, we obtain the continuity equations of charge and spin accumulation in two-dimensional ferromagnets with Rashba or Dresselhaus spin-orbit coupling, in which the spin diffusion equation (the continuity equation of spin accumulation) gives the spin-orbit torques that have an extra term of charge density gradient that is paid little attention in previous studies. Numerical results indicate this term plays an important role in inhomogeneous systems. In order to study the magnetization dynamics of ferromagnets, we solve the Landau-Lifshitz-Gilbert equation together with the spin diffusion equation. Our results indicate that the magnetization in systems with Rashba SOI is easier to be switched by an external electric field than the system with Dresselhaus SOI, and for anisotropic ferromagnets, we study the critical external electric field that manipulate the reversal of magnetization.

Transport Property and Spin–Orbit Torque in 2D Rashba Ferromagnetic Electron Gas

“…The spin–orbit torque is the result of s–d interaction between the local magnetic moment and spin accumulation of conduction electrons, and it is always expressed as [ 23 , 24 ]: where is the spin accumulation and can be calculated by definition [ 4 , 15 ]: According to the distribution function above, the spin accumulation along the y axis is Compared to Equation ( 9 ), is directly proportional to . , and this specific value is a constant which has no connection with the band structure and temperature.…”

“…Thus, the current and spin–orbit torque are both manifestations of the non-equilibrium transport properties of the SOC system, there must be some relations between them. Literature have showed that the magnitude of spin–orbit torque is often proportional to the current density [ 12 , 13 , 14 , 15 ]. Because the spin accumulation and charge current are proportional to the external electric field under linear transport conditions, the ratio depends on the band structure of the system [ 4 , 5 ].…”

Magnetization Reversal of Single-Molecular Magnets by a Spin-Polarized Current*

“…From the above Hamiltonian, we can derive the spinor Boltzmann equation, [22,23] based on the NEGF formalism, as…”

“…[21] Furthermore, the spin-polarized transport with spinorbit interactions was also studied by the spinor Boltzmann equation. [22,23] In this letter, we study the magnetization reversal of SMMs by spin-polarized current. The system is schematically depicted in Fig.…”

Spin-resolved transport properties in molybdenum disulfide superlattice

“…When the inversion symmetry and spin-orbit coupling break together it leads to coupled spin and valley physics in ML-MoS 2 [22]. Yang demonstrates that spin-orbit interaction provides an alternative and efficient way to handle the magnetization via spin-orbit torques [23]. It can be obtained that the transmission probability for transport is an oscillating function and depends on incident angle, barrier height, and the incident energy of electrons and that, the quasi-bound states in the well regions (outside the barriers) are responsible for the oscillating behavior.…”