Divergence of the Magnetic Grüneisen Ratio at the Field-Induced Quantum Critical Point in YbRh${}_2$Si${}_2$

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 Grüneisen ratio ${\Gamma }_{\mathrm{mag}}=-(dM/dT)/C$. Within the Fermi liquid regime, ${\Gamma }_{\mathrm{mag}}=-G_r(H-H_c^{fit})$ 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.

4 pages, 3 Figures

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• Fermi-liquid instabilities at magnetic quantum phase transitions
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• Weak magnetism and non-Fermi liquids near heavy-fermion critical points
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• Multiple energy scales at a quantum critical point
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