Theory of Paramagnetic Impurity Spin Resonance in Metals

Abstract

The frequency-dependent magnetic susceptibility describing the magnetic resonance of spin impurities in a metal is investigated theoretically, using thermodynamic Green functions and the Abrikosov diagram technique for spin operators. The single-particle pseudofermion propagator is shown to lead to formulas for the impurity spin energy-level shifts and widths which are identical, to all orders in perturbation theory, to those obtained in the standard quantum-mechanical theory of decaying states. The two-particle pseudofermion propagator describing impurity magnetic-resonance experiments is discussed, and it is shown that there are corrections to the interpretation of the magnetic resonance frequency shift and linewidth in terms of the individual level shifts and widths mentioned above. A perturbative evaluation of some of the formulas obtained shows that both the $g$ shift and the linewidth of the impurity spin resonance exhibit Kondo-like corrections depending on $\ln T$ when $\mathrm{kT}>\mathrm{}\hslash {\omega }_0$, or on $\ln {\omega }_0$ when $\mathrm{kT}<\mathrm{}\hslash {\omega }_0$, ${\omega }_0$ being the impurity spin-resonance frequency. The theory as developed is valid only when the conduction-electron spin-resonance frequency ${\omega }_e$ is sufficiently different from ${\omega }_0$, and it is shown that the contribution of the conduction-electron spin-magnetic moment to the absorption becomes increasingly important when this is not the case.