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FIG 2 - Microscopic theory of electric polarization induced by skyrmionic order in GaV$_{4}$S$_{8}

FIG. 2. a) Spin patterns as obtained in Monte-Carlo calculations for the model (4) with an applied magnetic field h z at temperature T = 0.1J for the supercell of 72?72?3 spins with periodic boundary conditions. In these notations, a "skyrmion lattice" means the lattice of well distinguished skyrmionic tubes of the same size, while a "cycloidal phase" includes large interconnected regions with the same direction of spins. The corresponding h-dependence of (b) the magnetization and (c) electric polarization: total and partial contributions, calculated from Eq. (7) relative to the FM state.
a) Spin patterns as obtained in Monte-Carlo calculations for the model (4) with an applied magnetic field h z at temperature T = 0.1J for the supercell of 72?72?3 spins with periodic boundary conditions. In these notations, a "skyrmion lattice" means the lattice of well distinguished skyrmionic tubes of the same size, while a "cycloidal phase" includes large interconnected regions with the same direction of spins. The corresponding h-dependence of (b) the magnetization and (c) electric polarization: total and partial contributions, calculated from Eq. (7) relative to the FM state.
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