Divergence of the Magnetic Gr\"{u}neisen Ratio at the Field-Induced Quantum Critical Point in YbRh$_2$Si$_2$

TL;DR

This study investigates the divergence of the magnetic Grüneisen ratio near the quantum critical point in YbRh₂Si₂, revealing critical behavior and entropy inflection points through magnetization and specific heat measurements.

Contribution

It provides the first detailed analysis of the divergence of the magnetic Grüneisen ratio at the quantum critical point in YbRh₂Si₂, linking it to scaling behavior and entropy changes.

Findings

Magnetic Grüneisen ratio diverges at the quantum critical point.

Field dependence of dM/dT shows an entropy inflection point.

Scaling behavior of the specific-heat coefficient is confirmed.

Abstract

The heavy fermion compound YbRh$_2$Si$_2$ is studied by low-temperature magnetization $M(T)$ and specific-heat $C(T)$ measurements at magnetic fields close to the quantum critical point ($H_c=0.06$ T, $H\perp c$). Upon approaching the instability, $dM/dT$ is more singular than $C(T)$, leading to a divergence of the magnetic Gr\"uneisen ratio $\Gamma_{\rm mag}=-(dM/dT)/C$. Within the Fermi liquid regime, $\Gamma_{\rm mag}=-G_r(H-H_c^{fit})$ with $G_r=-0.30\pm 0.01$ and $H_c^{fit}=(0.065\pm 0.005)$ T which is consistent with scaling behavior of the specific-heat coefficient in YbRh$_2$(Si$_{0.95}$Ge$_{0.05}$)$_2$. The field-dependence of $dM/dT$ indicates an inflection point of the entropy as a function of magnetic field upon passing the line $T^\star(H)$ previously observed in Hall- and thermodynamic measurements.