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 $\ensuremath{\lambda}⪢{\ensuremath{\lambda}}_{D}\ensuremath{\equiv}\sqrt{\ensuremath{\hbar}D/{\ensuremath{\Delta}}_{sd}}$, where $D$ and ${\ensuremath{\Delta}}_{sd}$ are the diffusion constant and the spin splitting energy due to the $sd$ 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 $\ensuremath{\beta}$ 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 ${\ensuremath{\Delta}}_{sd}$ is small.