Calculating linear-response functions for finite temperatures on the basis of the alloy analogy model

Abstract

A scheme is presented that is based on the alloy analogy model and allows one to account for thermal lattice vibrations as well as spin fluctuations when calculating response quantities in solids. Various models to deal with spin fluctuations are discussed concerning their impact on the resulting temperature-dependent magnetic moment, longitudinal conductivity, and Gilbert damping parameter. It is demonstrated that, by using the Monte Carlo (MC) spin configuration as input, the alloy analogy model is capable of reproducing the results of MC simulations on the average magnetic moment within all spin fluctuation models under discussion. On the other hand, the response quantities are much more sensitive to the spin fluctuation model. Separate calculations accounting for the thermal effect due to either lattice vibrations or spin fluctuations show that they give comparable contributions to the electrical conductivity and Gilbert damping. However, comparison to results accounting for both thermal effects demonstrates violation of Matthiessen's rule, showing the nonadditive effect of lattice vibrations and spin fluctuations. The results obtained for bcc Fe and fcc Ni are compared with the experimental data, showing rather good agreement for the temperature-dependent electrical conductivity and the Gilbert damping parameter.

Nonlocal torque operators inab initiotheory of the Gilbert damping in random ferromagnetic alloys

“…23 Future studies should clarify the applicability of the introduced nonlocal torques to a full quantitative description of the finite-temperature behavior as well as to other torque-related phenomena, such as the spin-orbit torques due to applied electric fields. 58,59 …”

“…This trend is in a qualitative agreement with trends reported previously by other authors, who employed phenomenological models of the electron lifetime 11,12 as well as models for phonons and magnons. 21,23 The origin of the nonmonotonic dependence α(δ) has been identified on the basis of the band structure of the ferromagnetic system as an interplay between the intraband contributions to α, dominating for small values of δ, and the interband contributions, dominating for large values of δ. 7,11,12 Since the present CPAbased approach does not use any bands, we cannot perform a similar analysis.…”

“…However, a more accurate description of the temperature dependence of the Gilbert damping parameter cannot be obtained, mainly due to the neglected true atomic displacements and the noncollinearity of magnetic moments (magnons). 23 …”

“…11,12,21,23 In this study, we have simulated the effect of finite temperatures by intro- ducing static fluctuations of the one-particle potential. The adopted model of atomic-level disorder assumes that random spin-independent shifts ±δ, constant inside each atomic sphere and occurring with probabilities 50% of both signs, are added to the nonrandom selfconsistent potential obtained at zero temperature.…”

“…Further improvements of the model, including static temperature-induced random orientations of local magnetic moments, have appeared recently. 23 The ab initio studies have also been successful in reproduction and interpretation of values and concentration trends of the Gilbert damping in random ferromagnetic alloys, such as the NiFe alloy with the face-centered cubic (fcc) structure (Permalloy) 17,22 and Fe-based alloys with the body-centered cubic (bcc) structure (FeCo, FeV, FeSi). 19,22,24 Other studies addressed also the effects of doping the Permalloy and bcc iron by 5d transitionmetal elements 19,20,22 and of the degree of atomic longrange order in equiconcentration FeNi and FePt alloys with the L1 0 -type structures.…”