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
$\mu_0H_c1 = 7.8(2)$ T where the antiferromagnetic zigzag order is
suppressed. At higher fields, a kink in the magnetostriction coefficient
signals an additional phase transition around $\mu_0H_c2 11$ 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.
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