  We have investigated the field-angle behaviors of magnetic excitations under
an in-plane magnetic field for proximate Kitaev systems. By employing the exact
diagonalization method in conjunction with the linear spin wave theory, we have
demonstrated 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 expected one for the non-Abelian spin liquid
phase in the Kitaev model and experimentally observed one of the intermediate
phases in $\alpha$-RuCl$_3$.

Strongly Correlated Electrons