Theory of Spin Resonance of Localized Moments in Dilute Alloys

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We develop a dynamical theory of localized magnetic moments in a normal metal pertinent to describing the "bottle-neck effects" in the spin resonance, extending Caroli, Caroli and Fredkin's calculation to include conduction electron spin-lattice relaxation effects. We deal with the Anderson Hamiltonian plus additional perturbations of potential scattering using the Hartree-Fock approximation for the ground state and the RPA for the rf susceptibility so as to keep proper rotational invariance. When the amplitude of the ordinary potential scattering is much larger than that of spin-orbit scattering, the resulting rf susceptibility χ(ω) can be written in such a form that the s-spin Zeeman frequency ω_s is just replaced by ω_s-i/τ_1 everywhere in the formula given by Caroli et al., where 2τ_1 is the life time due to spin-orbit scattering. The χ(ω) is shown to satisfy the two basic requirements of rotational invariance; (i) the total spin conservation rule, and (ii) the isotropy condition (the equality between the transverse and longitudinal susceptibilities in the static limit). A simplified resonance condition is obtained which reflects the bottle-neck feature as a function of the s-spin lattice relaxation rate 1/τ_1. When this dominates over the s-d cross-relaxation rate, the s-spin system is shown to behave as if it were static, yielding a full external torque on d-spins, but at the same time as if it were unaffected by s-d coupling. It is proved that the low-frequency form of the present χ(ω) in the case of the equal g factors for s- and d-spins is precisely equal to what may be obtained from a coupled set of temporal equations M^^・_s=γM_s×(H_<ext>+λM_d)-(M_s)/(T_<ds>)+(M_d)/(T_<ds>)-1/(T_<sL>)(m_s-M^^-_s), M^^・_d=γM_d×(H_<ext>+λM_s)+(M_s)/(T_<ds>)-(M_d)/(T_<ds>)-1/(T_<dL>)(m_d-M^^-_d), with parameters properly renormalized, in particular, with the "destination" values of M^^-_s and M^^-_d; M^^-_s=χ_sH_<ext>, M^^-_d=χ_<d´>H_<ext>. here χ_s and χ_<d´> are the static susceptibilities for the free s-spins and for the "clothed" d-spins, respectively, and H_<ext> includes every external field, static and rf, but excludes the internal fields λM_<s,d>.
理論物理学刊行会の論文
1971-04-25

Theory of Spin Resonance of Localized Moments in Dilute Alloys

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