Effect of exchange-correlation spin\u2013torque on spin dynamics

Abstract

A recently proposed exchange-correlation functional within density functional theory, which ensures that the exchange-correlation magnetic field is source-free, is shown to give non-zero internal spin–torque. This spin–torque is identically zero for all conventional local and semi-local functionals. Extension of this source-free functional to the time domain is used to study the effect of the internal spin–torque on the laser induced spin-dynamics in bulk Co, Ni and interfaces of these metals with Pt. It is shown that the internal spin–torque contributes significantly to spin-dynamics only when the magneto crystalline anisotropy energy is small, as in the case of cubic bulk materials. For surfaces or interfaces, where the anisotropy energy is large, these torques are too small to cause any significant precession of spins in early times (<100 fs). Furthermore, it is shown that the spin-dynamics caused by the internal spin–torque is slow compared to the inter-site spin transfer and spin–orbit mediated spin-flips.