Scattering theory of charge-current–induced magnetization dynamics

Abstract

In ferromagnets, charge currents can excite magnons via the spin-orbit coupling. We develop a novel and general scattering theory of charge current induced macrospin magnetization torques in normal metal|ferromagnet|normal metal layers. We apply the formalism to a dirty GaAs|(Ga,Mn)As|GaAs system. By computing the charge current induced magnetization torques and solving the Landau-Lifshitz-Gilbert equation, we find magnetization switching for current densities as low as 5 × 10 6 A/cm 2 . Our results are in agreement with a recent experimental observation of charge-current induced magnetization switching in (Ga,Mn)As.Magnetic random access memories are read using the principle of the giant magnetoresistance effect. Information is written by non-local magnetic fields, and this limits the density of the memory cells. In small systems, a promising direct and local writing technique is to utilize spin-transfer torques from spin-polarized currents in noncollinear magnetic structures [1]. The interplay between out-of-equilibrium quasi-particle spin-polarized currents and collective magnetization dynamics exhibits a rich variety of phenomena, and receives currently much attention from the scientific community. When a spin polarized current enters a ferromagnet, the itinerant flow of angular momentum normal to the magnetization direction is absorbed. The absorbed angular momentum is transferred to the ferromagnetic order parameter as a torque on the magnetization [1]. Magnetization switching has been seen in several experiments at current densities of the order 10. Most theories of spin-transfer torques in layered systems disregard spin-orbit interaction in the band structure and impurity potentials. Interestingly, the spinorbit interaction, which is responsible for spin memory loss, also enables transfer of orbital angular momentum to the collective magnetization. Thus, an unpolarized current can induce a torque on the magnetization even in magnetic homogeneous systems. This has recently been demonstrated theoretically for a simplified magnetic 2DEG Rashba Hamiltonian [2] and experimentally seen in (Ga,Mn)As [3]. The experimental results call for 1) an extension of current induced torque theories to include spin-orbit interaction which is valid for general band-structures and disorder as well as a 2) quantitative computation of the current induced magnetization dynamics.We consider a ferromagnet in electric contact with normal metals. The torque on a macrospin ferromagnet characterized by a spatially independent unit vector m can be written aṡwhere γ is the gyromagnetic ratio and H eff is the effective magnetic field arising from the ferromagnet's equilibrium energy. H s and H c are induced by non-equilibrium quasiparticle transport. H s ∝ µ s describes the spin-transfer torque induced by a spin accumulation µ s in the normal metals adjacent to the ferromagnet. Our main focus is the charge-current induced torque, represented by H c ∝ V , induced by a voltage bias V across the ferromagnet without any spin bias. When the ...

Charge pumping by magnetization dynamics in magnetic and semimagnetic tunnel junctions with interfacial Rashba or bulk extrinsic spin-orbit coupling

“…For example, a generalized scattering theory of adiabatic charge pumping by a single precessing F layer within N|F|N junctions containing SOCs has been formulated in Ref. 9. Also, the pumping of current of magnetic monopoles and the associated (via Ampère law) charge current flowing in the plane of the Rashba SO-coupled interface (rather than perpendicular to it as is the focus of our study) between the precessing F layer and a nonmagnetic layer has been predicted in Ref.…”

“…However, SOC renders all components of pumped spin or charge current time-dependent so that one has to compute the scattering matrix at all times within one period τ = 2π/ω of the pumping cycle and then find the time-averaged value of pumped currents. 9,55 This is prohibitively expensive for 3D system composed of large number of atomic orbitals [such as the device in Fig. 1(a) whose Hamiltonian matrix is of the size 84000 × 84000], especially in the presence of disorder where additional averaging over impurity configurations is required.…”

“…That is, observation of one of these two effects implies, by Onsager reciprocal relations, the existence of the other effect. 9 …”

Self-consistent calculation of spin transport and magnetization dynamics

“…Obata and Tatara [143], and Manchon and Zhang [144] independently predicted the existence of field-like spin transfer torque induced by in-plane current in Rashba ferromagnets. A number of experimental [145][146][147][148][149][150] and theoretical [151][152][153][154][155][156][157][158][159] studies have followed this work. Miron et al reported that an in-plane current-induced field-like spin torque is present for Pt|Co|AlO x structures where the inversion symmetry is broken [145].…”

New Boundary-Driven Twist States in Systems with Broken Spatial Inversion Symmetry

“…Important examples of the SOC effects include current-driven spin-orbit torques [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], charge-pumping via magnetization precession [8,[22][23][24][25][26], and the formation of topologically nontrivial skyrmion textures [27][28][29][30][31][32][33][34][35][36][37][38] and chiral domain walls [15,16,[39][40][41], as well as the multiferroic behaviour of chiral magnets [42,43] and the ferroelectricity of magnetic textures [41,44].…”