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Magnetoelectric nature of skyrmions in a chiral magnetic insulator Cu<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow /><mml:mn>2</mml:mn></mml:msub></mml:math>OSeO<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow /><mml:mn>3</mml:mn></mml:msub></mml:math>
Dielectric properties were investigated under various magnitudes and directions of magnetic field ($H$) for a chiral magnetic insulator Cu${}_{2}$OSeO${}_{3}$. We found that the skyrmion crystal induces electric polarization ($P$) along either in-plane or out-of-plane direction of the spin vortices depending on the applied $H$ direction. The observed $H$ dependence of …