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

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