Divergence of the orbital nuclear magnetic relaxation rate in metals

TL;DR

This paper investigates how the orbital contribution to nuclear magnetic relaxation in metals diverges due to long-range current fluctuations and how impurity scattering regularizes this divergence, highlighting differences from spin-dipolar effects.

Contribution

It provides a detailed analysis of the divergence in the orbital nuclear relaxation rate and how impurity scattering influences this behavior in metals.

Findings

Orbital relaxation rate diverges in clean metals due to long-range current fluctuations.

Impurity scattering introduces a cutoff, controlling the divergence magnitude.

Spin-dipolar coupling does not lead to divergence in relaxation rate.

Abstract

We analyze the nuclear magnetic relaxation rate $(1/T_1)_{orb}$ due to the coupling of nuclear spin to the orbital moment of itinerant electrons in metals. In the clean non--interacting case, contributions from large--distance current fluctuations add up to cause a divergence of $(1/T_1)_{orb}$. When impurity scattering is present, the elastic mean free time $\tau$ cuts off the divergence, and the magnitude of the effect at low temperatures is controlled by the parameter $\ln(\mu \tau)$, where $\mu$ is the chemical potential. The spin--dipolar hyperfine coupling, while has the same spatial variation $1/r^3$ as the orbital hyperfine coupling, does not produce a divergence in the nuclear magnetic relaxation rate.