Ab initio theory of Gilbert damping in random ferromagnetic alloys

Abstract: We present a recently developed ab initio theory of the Gilbert damping in substitutionally disordered ferromagnetic alloys [1]. 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 (TBLMTO) 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.
The developed theory has been applied to a broad class of itinerant ferromagnets including (i) binary (fcc NiFe, bcc FeCo) and ternary (permalloy doped by transition-metal impurities) random alloys, (ii) pure iron with a model atomic-level disorder, (iii) stoichiometric FePt and CoPt alloys with a varying degree of L10 atomic long-range order, and (iv) diluted (Ga,Mn)As magnetic semiconductor [2]. Besides a comparison of the obtained results to those of other authors and to experiment, following aspects will be discussed: concentration trends of the Gilbert damping and their relation to the density of states at the Fermi energy, to the alloy magnetization and to the strength of the alloy disorder and of the spin-orbit interaction. Moreover, the non-monotonic temperature dependence of the Gilbert damping, which is conductivity-like at low temperatures and resistivity-like at elevated temperatures, has been reproduced for pure iron in semi-quantitative agreement with experiment.

[1] I. Turek, J. Kudrnovský, V. Drchal: Nonlocal torque operators in ab initio theory of the Gilbert damping in random ferromagnetic alloys, Phys. Rev. B 92 (2015) 214407.
[2] J. Kudrnovský, V. Drchal, I. Turek: Exchange and spin-orbit induced phenomena in diluted (Ga,Mn)As from first principles, Phys. Rev. B 94 (2016) 054428.