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Angle-dependent thermodynamics of $α$-RuCl$_3$

Thermodynamics of the Kitaev honeycomb magnet $α$-RuCl$_3$ is studied for different directions of in-plane magnetic field using measurements of the magnetic Grüneisen parameter $Γ_B$ and specific heat $C$. We identify two critical fields $B_c^{\rm AF1}$ and $B_c^{\rm AF2}$ corresponding, respectively, to a transition between two magnetically ordered states and the loss of magnetic order toward a quantum paramagnetic state. The $B_c^{AF2}$ phase boundary reveals a narrow region of magnetic fields where inverse melting of the ordered phase may occur. No additional transitions are detected above $B_c^{\rm AF2}$ for any direction of the in-plane field, although a shoulder anomaly in $Γ_B$ is observed systematically at $8-10$ T. Large field-induced entropy effects imply additional low-energy excitations at low fields and/or strongly field-dependent phonon entropies. Our results establish universal features of $α$-RuCl$_3$ in high magnetic fields and challenge the presence of a field-induced Kitaev spin liquid in this material.