Grüneisen Parameter and Thermal Expansion by the Self-Consistent Renormalization Theory of Spin Fluctuations

Abstract

The thermal expansion coefficient $\alpha$ and the Grüneisen 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 $C_V=C_{\mathrm{a}}-C_{\mathrm{b}}$, $\alpha ={\alpha }_{\mathrm{a}}+{\alpha }_{\mathrm{b}}$, and $\Gamma ={\Gamma }_{\mathrm{a}}+{\Gamma }_{\mathrm{b}}$, respectively, where $C_{\mathrm{i}}$, ${\alpha }_{\mathrm{i}}$, and ${\Gamma }_{\mathrm{i}}$ $(\mathrm{i}=\mathrm{a},\mathrm{b})$ are related with each other. As the temperature $T$ decreases, $C_{\mathrm{a}}$, ${\alpha }_{\mathrm{b}}$, and ${\Gamma }_{\mathrm{b}}$ become dominant in $C_V$, $\alpha$, and $\Gamma$, respectively. The inverse susceptibility of spin fluctuation coupled to the volume $V$ in ${\Gamma }_{\mathrm{b}}$ 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 ${\Gamma }_{\mathrm{b}}$ contributes to the $T$ dependences of $\alpha$ and $\Gamma$, and even affects their criticality in the case of the AFM QCP in $d=2$. ${\Gamma }_{\mathrm{a}}$ is expressed as ${\Gamma }_{\mathrm{a}}(T=0)=-\frac{V}{T_0}{\left(\frac{\partial T_0}{\partial V}\right)}_{T=0}$ with $T_0$ being the characteristic temperature of spin fluctuation, which has an enhanced value in heavy electron systems.

arXiv comment7 pages, 2 figures

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Cited by in corpus (1)

• Grüneisen Parameters: origin, identity and quantum refrigeration