ESR and longitudinal response in metals containing localized paramagnetic centers with spinS>1/2

The theory describing electron spin resonance (ESR) and the longitudinal magnetization response of coupled spin systems in a metal containing both delocalized conduction electrons (“espins”) and localized paramagnetic centers (“s-spins”) is generalized to the case of arbitrary half-integer spin value,S>1/2, of the s-spins. The consideration is based on the Bloch-Hasegawa equations supplemented by taking into account the coupled evolution of the longitudinal magnetization components and the effect of weak ESR saturation by the microwave field. The ESR transversal susceptibility and longitudinal magnetization response are worked out in terms of normal modes related to the coupled s- and e-spin oscillators taking into account the ESR fine structure (FS) of the s-spins. These modes are characterized by effective (renormalized) frequencies and relaxation rates (decays) which differ from the partial ones. In the specific cases of a well-resolved FS (in the isothermal limit) and of the relaxational collapse of the FS due to strong exchange coupling between the s- and e-spins (in both the isothermal and bottlenecked limits), the analytical expressions are derived which are relevant to the modulation technique of measuring extremely fast spin-lattice relaxation times in metals.