Gr\"{u}neisen Parameter and Thermal Expansion by the Self-Consistent Renormalization Theory of Spin Fluctuations

TL;DR

This paper derives expressions for thermal expansion and Grüneisen parameter near magnetic quantum critical points using the self-consistent renormalization theory of spin fluctuations, revealing their divergence and temperature dependence in different magnetic and dimensional contexts.

Contribution

It provides a novel theoretical framework connecting spin fluctuation dynamics with thermal properties at quantum criticality, including explicit formulas and critical behavior analysis.

Findings

The Grüneisen parameter diverges at the QCP for ferromagnetic and antiferromagnetic cases.

Temperature dependence of thermal expansion and Grüneisen parameter is derived near the QCP.

The theory explains enhanced Grüneisen parameter in heavy electron systems.

Abstract

The thermal expansion coefficient $\alpha$ and the Gr\"{u}neisen parameter $\Gamma$ near the magnetic quantum critical point (QCP) are derived on the basis of the self-consistent renormalization (SCR) theory of spin fluctuation. From the SCR entropy, the specific heat $C_{V}$, $\alpha$, and $\Gamma$ are shown to be expressed in a simple form as $C_{V}=C_{\rm a}-C_{\rm b}$, $\alpha=\alpha_{\rm a}+\alpha_{\rm b}$, and $\Gamma=\Gamma_{\rm a}+\Gamma_{\rm b}$, respectively, where $C_{\rm i}$, $\alpha_{\rm i}$, and $\Gamma_{\rm i}$ $({\rm i}={\rm a}, {\rm b})$ are related with each other. As the temperature $T$ decreases, $C_{\rm a}$, $\alpha_{\rm b}$, and $\Gamma_{\rm b}$ become dominant in $C_{V}$, $\alpha$, and $\Gamma$, respectively. The inverse susceptibility of spin fluctuation coupled to the volume $V$ in $\Gamma_{\rm b}$ is found to give rise to the divergence of $\Gamma$ at the QCP for each class of ferromagnetism and antiferromagnetism (AFM) in spatial dimensions $d=3$ and $2$. This $V$-dependent inverse susceptibility in $\alpha_{b}$ and $\Gamma_{\rm b}$ contributes to the $T$ dependences of $\alpha$ and $\Gamma$, and even affects their criticality in the case of the AFM QCP in $d=2$. $\Gamma_{\rm a}$ is expressed as $\Gamma_{\rm a}(T=0)=-\frac{V}{T_0}\left(\frac{\partial T_0}{\partial V}\right)_{T=0}$ with $T_0$ being the characteristic temperature of spin fluctuation, which has an enhanced value in heavy electron systems.