Divergence of the orbital nuclear magnetic relaxation rate in metals

Abstract

We analyze the nuclear magnetic relaxation rate ${(1∕{T}_{1})}_{\mathit{orb}}$ due to the coupling of nuclear spin to the orbital moment of itinerant electrons in metals. In the clean noninteracting case, contributions from large-distance current fluctuations add up to cause a divergence of ${(1∕{T}_{1})}_{\mathit{orb}}$. When impurity scattering is present, the elastic mean free time $\ensuremath{\tau}$ cuts off the divergence, and the magnitude of the effect at low temperatures is controlled by the parameter $\mathrm{ln}(\ensuremath{\mu}\ensuremath{\tau})$, where $\ensuremath{\mu}$ is the chemical potential. The spin-dipole hyperfine coupling, while having the same spatial variation $1∕{r}^{3}$ as the orbital hyperfine coupling, does not produce a divergence in the nuclear magnetic relaxation rate.