Field-induced transitions in the Kitaev material <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mi>RuCl</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math> probed by thermal expansion and magnetostriction

Abstract

High-resolution thermal expansion and magnetostriction measurements were performed on single crystals of $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$ 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 ${\ensuremath{\mu}}_{0}{H}_{\mathrm{c}1}=7.8(2)\phantom{\rule{0.16em}{0ex}}\mathrm{T}$ where the antiferromagnetic zigzag order is suppressed. At higher fields, a kink in the magnetostriction coefficient signals an additional transition or crossover around ${\ensuremath{\mu}}_{0}{H}_{\mathrm{c}2}\ensuremath{\approx}11\phantom{\rule{0.16em}{0ex}}\mathrm{T}$. The extracted Gr\"uneisen ratio shows typical hallmarks for quantum criticality near ${H}_{\mathrm{c}1}$ but also displays anomalous behavior above ${H}_{\mathrm{c}1}$. We compare our experimental data with 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 region above ${H}_{\mathrm{c}1}$ cannot be accounted for in our semiclassical modeling and hence suggest a genuine quantum nature. We construct a phase diagram for $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$ in a magnetic field along the Ru-Ru bonds, displaying a zigzag ordered state below ${H}_{\mathrm{c}1}$, a quantum paramagnetic regime between ${H}_{\mathrm{c}1}$ and ${H}_{\mathrm{c}2}$, and a semiclassical partially polarized state above ${H}_{\mathrm{c}2}$.

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