Theoretical investigation on the relationship between the torque correlation and spin correlation models for the Gilbert damping constant

To gain insight into the relationship between the spin correlation (SC) and torque correlation (TC) models for the Gilbert damping constant, α, we first make a simple consideration on the physical aspect of these models and calculate α for the Fe₅₀Co₅₀ disordered alloy by the two models using the first principles technique. Electron scattering is introduced through the random arrangement of atoms and is treated with coherent potential approximation. The results indicate that in the TC model, vertex correction (VC) does not have significant contribution and the results are insensitive to the infinitesimal positive value, δ, which is used in Green's function. In the SC model, on the other hand, the VC is indispensable and the obtained values of α are found to be considerably sensitive to δ. We confirm that the value of α in the SC model approaches the value obtained in the TC model in the limit δ→+0.