Spin-transfer torque in disordered weak ferromagnets

Abstract

We study theoretically the spin transfer effect on a domain wall in disordered weak ferromagnets. We have identified the adiabatic condition for the disordered case as $\lambda \gg \lambda_{\rm D}\equiv \sqrt{{\hbar D}/{\spol}}$, where $D$ and $\spol$ are the diffusion constant and the spin splitting energy due to the $s$-$d$ type exchange interaction, respectively, and found out that perfect spin-transfer effect occurs even in weak ferromagnets as long as this condition is satisfied. The effective $\beta$ term arising from the force turns out to govern the wall dynamics, and therefore, the wall motion can be as efficient as in strong ferromagnets even if $\spol$ is small

Domain wall motion in a diffusive weak ferromagnet

“…The full numerical solutions of the dynamic equations of domain wall motion in Eq. (21) and Eq. (22) are shown in Fig.…”

Theory of spin relaxation torque in metallic ferromagnets

“…[21] carried out in the context of quantum correction (the diffusion without the spin-orbit interaction was considered in Ref. [22]). The equation is obtained as…”

Spin and charge transport induced by magnetization dynamics in diffusive ferromagnetic metals

“…1,2 Conversely, domain-wall motion can transfer the spin angular momentum of magnetization to conduction electrons through the flow of an induced spin current. [3][4][5][6][7] Among other consequences, these induced spin currents lead to ͑1͒ an electric voltage across a moving domain wall, known as the spin electromotive force ͑emf͒, [8][9][10][11] and ͑2͒ the electronic dissipation ͑e.g., Joule heating͒ of the spin current which provides a mechanism for the loss of the angular momenta of a processing ferromagnet, i.e., damping. 5,[12][13][14] A simple description of the above phenomena can be made as follows.…”