Field-angle anisotropy of proximate Kitaev systems under an in-plane magnetic field: Magnon contribution in the polarized phase

α-RuCl₃ is a proximate Kitaev system, in which dominant bond-directional Ising interaction (Kitaev interaction) is allowed among nearest neighboring sites in the honeycomb lattice. Its magnetic phase transition under the magnetic field has recently drawn much attention because of putative intermediate spin liquid phase. In the presence of the magnetic field, the antiferromagnetic zigzag order of α-RuCl₃ is transferred into the polarized phase through the intermediate phase (IP). The non-Abelian spin liquid (NASL) phase has been proposed as the IP because of observed half-integer plateau of thermal Hall conductivity and field-angle anisotropy of specific heat under the magnetic field.

In this study, we have investigated the field-angle anisotropy of magnetic excitations under an in-plane magnetic field for proximate Kitaev systems. By employing the exact diagonalization method and the linear spin wave theory, we have shown that the magnetic excitation gap in the polarized phase is determined by the magnon excitation at M points and has a strong anisotropy with respect to the field direction in the vicinity of the critical field limit. The specific heat from this magnon excitation bears qualitatively the same anisotropic behaviors as the expected one for the NASL phase in the Kitaev model and the experimentally observed one of the IPs in α-RuCl₃.