Effect of spin-flip scattering on magnetic properties of metals

Abstract

The itinerant-electron model is used to derive magnetic properties of paramagnetic and ferromagnetic metals in which nonmagnetic impurities are embedded. The results are valid for various relative strengths of the spin-flip and spin-independent scattering caused by the impurities. Essentially $s$-wave scattering by impurities is considered in the second-order Born approximation. Starting from a Hamiltonian the kinetic equations for the density-matrix elements are derived in the presence of an external magnetic field, and in the random-phase approximation. The kinetic equations are transformed to the equations of motion for the magnetization components. The longitudinal and transverse components of the rf susceptibility tensor are calculated. For the case of very small spin-flip scattering known results are obtained, whereas for other cases of spin-flip scattering the results obtained here are new. Conditions are found to obtain Bloch-like equations. Explicit expressions for the parameters of the Bloch-like equations are obtained, such as the relaxation "destination" of the longitudinal and transverse components of the magnetization and their spin-lattice relaxation times. Measurable shifts in the $g$ factor of the itinerant electrons caused by the spin-flip scattering of the impurities are obtained. Expressions for the static shifts in the magnetic excitations, paramagnons, and magnons are calculated.