Quantum criticality, a phenomenon driven by quantum fluctuations near absolute zero, plays a pivotal role in understanding exotic states in condensed matter systems. In this study [1], we introduce a novel thermodynamic quantity, the rotational Grüneisen ratio ${\mathrm{\Gamma }}_{\varphi }$, as a highly sensitive probe for detecting quantum critical behavior in anisotropic systems.

The rotational Grüneisen ratio ${\mathrm{\Gamma }}_{\varphi }$ is defined as ${\mathrm{\Gamma }}_{\varphi }=(1''/''T)(\partial T''/''\partial \varphi {)}_S$ , where $\varphi$ is the angle of the external field. In contrast to conventional Grüneisen parameters, which employ the magnitude of the magnetic field or pressure as control parameters, the rotational Grüneisen ratio utilizes the angle $\varphi$ of the external field as a tuning parameter. This method enables the detection of quantum phase transitions with higher angular resolution by measuring the rotational magnetocaloric effect, $(\partial T''/''\partial \varphi {)}_S$ [2].

We applied this method to two highly anisotropic paramagnets, CeRhSn and CeIrSn, both of which possess a quasikagome lattice and exhibit strong geometrical frustration and Kondo effect. By measuring the rotational magnetocaloric effect under varying a magnetic field angle within the ac plane, we investigated ${\mathrm{\Gamma }}_{\varphi }$ over a wide range of temperatures, magnetic fields, and field orientations.

Remarkably, for both compounds, the $(\varphi -{\varphi }_{\mathrm{c}\mathrm{r}}){\mathrm{\Gamma }}_{\varphi }$ data at each magnetic field collapse onto a universal scaling function $f\left(T/{(\varphi -{\varphi }_{\mathrm{c}\mathrm{r}})}^n\right)$, with identical critical exponents $n=4$/$5$ and a critical field angle ${\varphi }_{\mathrm{c}\mathrm{r}}=\pi /2$, as exemplified in Fig. 1 for CeRhSn. These results indicate the existence of a quantum critical line along the hard-magnetization axis (the $a$ axis), where the $c''-''$axis component of the magnetic field, $H_{\parallel }$, governs the critical behavior. The scaling behavior of the rotational magnetic Grüneisen ratio, ${\tilde{\mathrm{\Gamma }}}_{\varphi }=-{\mathrm{\Gamma }}_{\varphi }''/''H_{⟂}$, further supports the universality of the quantum criticality, where $H_{⟂}$ denotes the $a''-''$axis component of the magnetic field. The constant $H_{\parallel }{\tilde{\mathrm{\Gamma }}}_{\varphi }$ supports the presence of a quantum critical point at $H_{\parallel }=0$. The small value of the critical exponent implies relatively long correlation length and time, potentially reflecting a characteristic feature of quantum criticality driven by geometrical frustration in these compounds.

These findings highlight that the rotational Grüneisen ratio as a powerful and versatile tool for investigating quantum criticality in strongly anisotropic systems, such as Ising magnets. This method enables high-resolution, field-angle-resolved measurements, providing a novel approach to exploring quantum phase transitions in anisotropic materials.

References

• [1] S. Yuasa et al., Phys. Rev. B 111, 045123 (2025).
• [2] S. Kittaka et al., J. Phys. Soc. Jpn. 87, 073601 (2018).

Authors

• S. Yuasa^a, Y. Kono^a, Y. Ozaki^a, M. Yamashita, Y. Shimura^b, T. Takabatake^b, and S. Kittaka^a,c
• ^aChuo University
• ^bHiroshima University
• ^cDepartment of Basic Science, The University of Tokyo