Vertex Corrections and the Korringa Ratio in Strongly Correlated Electron Materials

TL;DR

This paper demonstrates that in strongly correlated electron materials, the Korringa ratio equals one and exhibits specific temperature behaviors when vertex corrections are negligible and hyperfine coupling is momentum independent, regardless of system dimensionality.

Contribution

It provides a theoretical analysis linking vertex corrections and the Korringa ratio, clarifying conditions for Korringa behavior in correlated electron systems.

Findings

Korringa ratio equals one under certain conditions.

T1 relaxation rate is proportional to temperature.

Knight shift remains temperature independent.

Abstract

We show that the Korringa ratio, associated with nuclear magnetic resonance in metals, is unity if vertex corrections for the dynamic spin susceptibility are negligible and the hyperfine coupling is momentum independent. In the absence of vertex corrections we also find a Korringa behaviour for $T_1$, the nuclear spin relaxation rate, i.e., $1/T_1\propto T$, and a temperature independent Knight shift. These results are independent of the form and magnitude of the self-energy (so far as is consistent with neglecting vertex corrections) and of the dimensionality of the system.