Theoretical Study on Gilbert Damping of Nonuniform Magnetization Precession in Ferromagnetic Metals

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We study Gilbert damping in bulk metallic ferromagnets containing magnetic and nonmagnetic impurities in the presence of nonuniform magnetization precession. In this model, a microscopic expression for the Gilbert damping tensor is obtained using the linear response theory with respect to the interaction between magnetization and conduction electrons. We especially focus on a diagonal element of the tensor, which is a conventional Gilbert damping constant, and evaluate it numerically as a function of the wave vector \mbi{q} of magnetization precession. We show that the impurity scattering dominates Gilbert damping for 0<|\mbi{q}|<k_{\text{F}\uparrow}-k_{\text{F}\downarrow}, while the Stoner excitation dominates for k_{\text{F}\uparrow}-k_{\text{F}\downarrow}<|\mbi{q}|<k_{\text{F}\uparrow}+k_{\text{F}\downarrow} (k_{\text{F}\sigma} is the Fermi wave number for \sigma spin electrons).
2012-11-15