High-field fate of the Kitaev quantum spin liquid in $\alpha$-RuCl$_3$

Abstract

Kitaev quantum spin liquids (KQSLs) host fractionalized excitations described by itinerant Majorana quasiparticles and gapped $Z_2$ fluxes (visons), providing a platform for emergent topological matter. Whether such a state survives under strong magnetic fields, however, remains an open question. The layered honeycomb magnet $\alpha$-RuCl$_3$ is a leading candidate material: an in-plane field of $\sim$ 7 T suppresses antiferromagnetic order and induces a quantum-disordered phase exhibiting signatures consistent with Majorana excitations, including an anomalous thermal Hall effect and field-angle-dependent specific heat. At higher fields, the magnetization approaches saturation, suggesting a transition to a spin-polarized state, yet the microscopic evolution between these limits remains unresolved. Here we report high-field specific heat measurements up to 24 T that reveal a distinct crossover at $\mu_0H^*\approx$15 T, beyond which the perturbative Kitaev description breaks down. Above $H^*$, the characteristic six-fold angular modulation of the specific heat collapses and the excitation gap deviates from the predicted $H^3$ scaling. Meanwhile, the gap decreases with increasing field and the in-plane magnetization anisotropy persists up to $\sim$ 24 T, both in sharp contrast to a trivial spin-polarized state, indicating that KQSL signatures are preserved even at $\sim$ 90 % of magnetization saturation. These results reveal that the KQSL in $\alpha$-RuCl$_3$ extends well beyond the perturbative window, persisting as a nonperturbative regime in which the Majorana and vison energy scales merge, before eventually giving way to spin polarization. This thermodynamic roadmap provides a basis for understanding how fractionalized phases evolve under strong magnetic fields.