We theoretically show that the Kitaev interaction generates a novel class of spin texture in the excitation spectrum of the antiferromagnetic insulator found in the Kitaev-Heisenberg-$Gamma$ model. In conducting electronic systems, there is a series of vortex type of spin texture along the Fermi surface induced by Rashba and Dresselhaus spin-orbit coupling. Such spin textures are rarely found in magnetic insulators, since there had been no systematic ways to control the kinetics of its quasi-particle called magnon using a magnetic field or spacially asymmetric exchange couplings. Here, we propose a general framework to explore such spin textures in arbitrary insulating antiferromagnets. We introduce an analytical method to transform any complicated Hamiltonian to the simple representation based on pseudo-spin degrees of freedom. The direction of the pseudo-spin on a Bloch sphere describes the degree of contributions from the two magnetic sublattices to the spin moment carried by the magnon. The momentum dependent fictitious Zeeman field determines the direction of the pseudo-spin and thus becomes the control parameter of the spin texture, which is explicitly described by the original model parameters. The framework enabled us to clarify the uncovered aspect of the Kitaev interaction, and further provides a tool to easily design or explore materials with intriguing magnetic properties. Since these spin textures can be a source of a pure spin current, the Kitaev materials $A_{2}$PrO$_{3}$ ($A$ =Li, Na) shall become a potential platform of power-saving spintronics devices.
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