Two-step gap opening across the quantum critical point in a Kitaev honeycomb magnet

Abstract: Quantum spin liquid involves fractionalized quasipariticles such as spinons and visons. They are expressed as itinerant Majorana fermions and $Z_2$ fluxes in the Kitaev model with bond-dependent exchange interactions on a honeycomb spin lattice. The observation has recently attracted attention for a candidate material $\alpha$-RuCl$_3$, showing spin liquid behaviour induced by a magnetic field. Since the observable spin excitation is inherently composed of the two quasiparticles, which further admix each other by setting in the magnetic field as well as non-Kitaev interactions, their individual identification remains challenging. Here we report an emergent low-lying spin excitation through nuclear magnetic and quadrupole resonance measurements down to $\sim 0.4$ K corresponding to $1/500$ of the exchange energy under the finely tuned magnetic field across the quantum critical point. We determined the critical behaviour of low-lying excitations and found evolution of two kinds of the spin gap at high fields. The two excitations exhibit repulsive magnetic field dependence, suggesting anti-crossing due to the hybridization between fractionalized quasiparticles.