Spin-orbit-coupling induced torque in ballistic domain walls: equivalence of charge-pumping and nonequilibrium magnetization formalisms

Abstract

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 $\beta$ 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 that gives rise to an intrinsic DW resistance in the presence of SOC leads to a linear dependence of $\beta$ on the DW length. To understand this counterintuitive divergence of $\beta$ in the long DW limit, we use the "nonequilibrium magnetization" formalism to examine the spatially resolved spin-transfer torque. The SOC-induced out-of-plane torque in ballistic DWs is found to be quantitatively consistent with the values obtained using the charge-pumping calculations indicating the equivalence of the two theoretical methods.

11+pages, 10 figures

References in corpus (14)

• Microscopic Calculation of Spin Torques in Disordered Ferromagnets
• Ab initio studies of the spin-transfer torque in tunnel junctions
• Theory of current-driven magnetization dynamics in inhomogeneous ferromagnets
• Direct and inverse spin-orbit torques
• Direct Method for Calculating Temperature-Dependent Transport Properties
• Current-Induced Torques in Magnetic Metals: Beyond Spin Transfer
• Current Induced Order Parameter Dynamics: Microscopic Theory Applied to Co/Cu/Co spin valves
• Effects of non-adiabaticity on the voltage generated by a moving domain wall
• Implementation of a non-equilibrium Green's function method to calculate spin transfer torque
• Gilbert damping in noncollinear ferromagnets
• Intrinsic Coupling between Current and Domain Wall Motion in (Ga,Mn)As
• Spin-Orbit Torques and Anisotropic Magnetization Damping in Skyrmion Crystals
• Influence of band structure effects on domain-wall resistance in diluted ferromagnetic semiconductors
• Spin-orbit-coupling induced domain-wall resistance in diffusive ferromagnets

Cited by in corpus (10)

• Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems
• Intrinsic mechanism for anisotropic magnetoresistance and experimental confirmation in Co${}_x$Fe${}_{1-x}$ single-crystal films
• Calculating the transport properties of magnetic materials from first-principles including thermal and alloy disorder, non-collinearity and spin-orbit coupling
• Topological Hall and Spin Hall Effects in Disordered Skyrmionic Textures
• Spin and charge pumping by steady or pulse current-driven magnetic domain wall: A self-consistent multiscale time-dependent-quantum/time-dependent-classical approach
• Fourfold anisotropic magnetoresistance of L1${}_0$ FePt due to relaxation time anisotropy
• Spin correlation function theory of spin-charge conversion effects
• Chiral damping, chiral gyromagnetism and current-induced torques in textured one-dimensional Rashba ferromagnets
• Algebraic decay of the nonadiabaticity arising through chiral spin transfer torque in magnetic domain walls with Rashba spin-orbit interaction
• Spin and Orbital Rashba response in ferroelectric polarized PtSe${}_2$/MoSe${}_2$/LiNbO${}_3$ heterostructures