We adapt the tight-binding linear muffin-tin orbital (TB-LMTO) method to the torque-correlation model for the Gilbert damping constant α and perform the first-principles calculation for disordered transition metal alloys, Fe-Ni and Fe-Pt systems, within the framework of the CPA. Quantitatively, the calculated α values are about one-half of the experimental values, whereas the variations in the Fermi level dependence of α are much larger than these discrepancies. As expected, we confirm in the (Fe-Ni) 1-XPt X and FePt systems that Pt atoms certainly enhance owing to their large spin-orbit coupling. For the disordered alloys, we find that decreases with increasing chemical degree of order in a wide range.
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