Field-induced phase transitions of the Kitaev material $\alpha$-RuCl${}_3$ probed by thermal expansion and magnetostriction

Abstract

High-resolution thermal expansion and magnetostriction measurements were performed on single crystals of $\alpha$-RuCl${}_3$ in magnetic fields applied parallel to the Ru-Ru bonds. The length changes were measured in the direction perpendicular to the honeycomb planes. Our data show clear thermodynamic characteristics for the field-induced phase transition at the critical field ${\mu }_0{H}_{c1}=7.8(2)$ T where the antiferromagnetic zigzag order is suppressed. At higher fields, a kink in the magnetostriction coefficient signals an additional phase transition around ${\mu }_0{H}_{c2}\approx 11$ T. The extracted Grüneisen parameter shows typical hallmarks for quantum criticality near $H_{c1}$, but also displays anomalous behavior above $H_{c1}$. We compare our experimental data with linear spin-wave calculations employing a minimal Kitaev-Heisenberg model in the semiclassical limit. Most of the salient features are in agreement with each other, however, the peculiar features in the high-field region above $H_{c1}$ cannot be accounted for in our modelling and hence suggest a genuine quantum nature. We construct a phase diagram for $\alpha$-RuCl${}_3$ showing two low-temperature transitions induced by an in-plane field along the Ru-Ru bonds.

14 pages, 10 figures