Nonlocal torque operators in ab initio theory of the Gilbert damping in random ferromagnetic alloys

TL;DR

This paper develops a first-principles ab initio theory for Gilbert damping in disordered ferromagnetic alloys using nonlocal torque operators, simplifying calculations and ensuring consistency with existing methods.

Contribution

It introduces nonlocal torque operators within the ab initio framework, enabling more efficient and consistent calculations of Gilbert damping in disordered alloys.

Findings

Calculated Gilbert damping parameters for NiFe and FeCo alloys.

Demonstrated equivalence with traditional local torque approaches.

Applied method to FePt alloys with varying atomic order.

Abstract

We present an ab initio theory of the Gilbert damping in substitutionally disordered ferromagnetic alloys. The theory rests on introduced nonlocal torques which replace traditional local torque operators in the well-known torque-correlation formula and which can be formulated within the atomic-sphere approximation. The formalism is sketched in a simple tight-binding model and worked out in detail in the relativistic tight-binding linear muffin-tin orbital (TB-LMTO) method and the coherent potential approximation (CPA). The resulting nonlocal torques are represented by nonrandom, non-site-diagonal and spin-independent matrices, which simplifies the configuration averaging. The CPA-vertex corrections play a crucial role for the internal consistency of the theory and for its exact equivalence to other first-principles approaches based on the random local torques. This equivalence is also illustrated by the calculated Gilbert damping parameters for binary NiFe and FeCo random alloys, for pure iron with a model atomic-level disorder, and for stoichiometric FePt alloys with a varying degree of L10 atomic long-range order.