A Consideration on the Temperature Dependence of Damping Behavior in FMR of Itinerant Electron Ferromagnets

We discuss the temperature dependence of the damping behavior in intrinsic origin of itinerant-electron ferromagnetic systems, including the region near T C . It is known from the theory of spin dynamics that the relaxation rate Γ of FMR is inversely proportional to the transverse magnetic susceptibility, χ −+ (T). We consider the spin–orbit interaction (SOI) as an intrinsic origin of the magnetic damping and also focus on its role in giving rise to the magnetic anisotropy energy expressed by K(T). Assuming, for instance, a uniaxial anisotropy with K(T) > 0, we can expect Γ ∝ 1/χ −+ (T) ∼ H K (T)/M(T) = 2K(T)/M(T) 2 below T C where M(T) and H K (T) are the magnetization and magnetic anisotropy field, respectively. Since it was theoretically predicted that K(T) is proportional to M(T) a (2 < a < 3) in metallic ferromagnets, we suggest Γ ∝ M(T) a −2 for T < T C . When the resonance frequency is ω = γH K , the Gilbert damping constant α = Γ/ω is found to be proportional to 1/M(T) which equals to the form given by Kamberský. In realistic experimental situation, we further discuss how α remains finite even near T C . In addition, we examined, based on a simple scaling analysis, the effects of SOI on the critical nature of the FMR linewidth in the region of critical slowing down near T C .