Theory of Electron-Spin Resonance in Gapless Superconductors

The transverse dynamic spin susceptibility for conduction electrons in dirty gapless superconductors, in particular, in the vortex state of type-II superconductors, is calculated. It is shown that in the gapless region the dynamic susceptibility consists of two terms, the regular term and the anomalous term. In the low-frequency region of experimental interest, the regular term reduces to the static spin susceptibility, which is determined, for example, by the Knight-shift measurement in superconductors, while the anomalous term has a pole, which is associated with a resonance of the spin of conduction electrons. The resonance linewidth $T_2^{-1\mathrm{}}$ is determined from the imaginary part of the resonance frequency. It is shown that $T_2^{-1\mathrm{}}$ behaves quite differently in the superconducting state depending on whether $T_2^{-1\mathrm{}}$ in the normal state is primarily due to the spin-orbit scattering or due to the exchange scattering from the magnetic impurities.