Wilson ratio of a Tomonaga-Luttinger liquid in a spin-1/2 Heisenberg ladder

TL;DR

This study measures the magnetization and susceptibility of a spin-1/2 Heisenberg ladder at very low temperatures, confirming theoretical predictions about the Wilson ratio and Tomonaga-Luttinger-liquid behavior.

Contribution

First experimental verification of the Wilson ratio relation in a spin-1/2 Heisenberg ladder using micromechanical force magnetometry.

Findings

Magnetization exhibits a maximum near the critical field H_c.

A minimum in magnetization appears above H_c as temperature varies.

The Wilson ratio supports the relation R_W=4K, consistent with Tomonaga-Luttinger-liquid theory.

Abstract

Using micromechanical force magnetometry, we have measured the magnetization of the strong-leg spin-1/2 ladder compound (C$_7$H$_{10}$N)$_2$CuBr$_2$ at temperatures down to 45 mK. Low-temperature magnetic susceptibility as a function of field exhibits a maximum near the critical field H_c at which the magnon gap vanishes, as expected for a gapped one-dimensional antiferromagnet. Above H_c a clear minimum appears in the magnetization as a function of temperature as predicted by theory. In this field region, the susceptibility in conjunction with our specific heat data yields the Wilson ratio R_W. The result supports the relation R_W=4K, where K is the Tomonaga-Luttinger-liquid parameter.