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Magnetic anisotropies often originate from the spin-orbit coupling anddetermine magnetic ordering patterns. We develop a microscopic theory for DCelectric-field controls of magnetic anisotropies in magnetic Mott insulatorsand discuss its applications to Kitaev materials and topological spin textures.Throughout this paper, we take a microscopic approach based on Hubbard-likelattice models, tight-binding models with on-site interactions. We derive alow-energy spin Hamiltonian from a fourth-order perturbation expansion of theHubbard-like model. We show in the presence of a strong intra-atomic spin-orbitcoupling that DC electric fields add non-Kitaev interactions such as aDzyaloshinskii-Moriya interaction and an off-diagonal $\Gamma'$ interaction tothe Kitaev-Heisenberg model and can induce a topological quantum phasetransition between Majorana Chern insulating phases. We also investigate theinter-atomic Rashba spin-orbit coupling and its effects on topological spintextures. DC electric fields turn out to create and annihilate magneticskyrmions, hedgehogs, and chiral solitons. We propose several methods ofcreating topological spin textures with external electromagnetic fields. Ourtheory clarifies that the strong but feasible electric field can control Kitaevspin liquids and topological spin textures.

Electric-field control of magnetic anisotropies: applications to Kitaev spin liquids and topological spin textures