Intermediate magnetic phase of the proximate Kitaev system in the in-plane magnetic field

a-RuCl₃ is the antiferromagnetic insulator with a zigzag order which is believed to be proximate to the Kitaev spin liquid. Its magnetic continuum excitation likely resulted from fractionalized Majorana fermions has been evidently observed in recent experiments. The zigzag long-range order can be suppressed and an intermediate phase, a possible quantum spin liquid, can emerge in between the zigzag phase and parallelly polarized phase when the magnetic field is applied. A few theories have attempted to explain the origin of intermediate magnetic phase in the presence of magnetic field. However, they have failed to manifest the intermediate phase in the in-plane external field observed by some experiments.
In the study, we verify that a simple magnetic model with a ferromagnetic Kitaev interaction and antiferromanetic third nearest neighbor Heisenberg interaction (K-J₃ model) can give successfully the intermediate phase in the in-plane magnetic field. Based on both exact diagonalization and density matrix renormalization group methods, we investigate the magnetic phase diagram of K-J₃ model in the in-plane magnetic field and demonstrate that the intermediate phase can occur when the field direction is perpendicular to the displacement vector between the nearest neighboring spins.