Rotational Gr\"{u}neisen ratio: a probe for quantum criticality in anisotropic systems

The Gr\"{u}neisen ratio $\Gamma$ and its magnetic analog, the magnetic Gr\"{u}neisen ratio $\Gamma_H$, are powerful probes to study the nature of quantum phase transitions. Here, we propose a Gr\"{u}neisen parameter, the rotational Gr\"{u}neisen ratio $\Gamma_\phi$, by introducing the orientation of the external field as a control parameter. We investigate $\Gamma_\phi$ of the highly anisotropic paramagnets CeRhSn and CeIrSn by measuring the rotational magnetocaloric effect in a wide range of temperatures and magnetic fields. We find that the $\Gamma_\phi$ data of both compounds are scaled by using the same critical exponents and the field-invariant critical field angle. Remarkably, the scaling function for the $\Gamma_\phi$ data reveals the presence of highly anisotropic quantum criticality that develops as a function of the easy-axis component of the magnetic field from the quantum critical line. This paper provides a thermodynamic approach to detect and identify magnetic quantum criticality in highly anisotropic systems.