Direct electric field control of the skyrmion phase in a magnetoelectric insulator

Magnetic skyrmions are topologically protected spin-whirls currently considered as promising for use in ultra-dense memory devices. Towards achieving this goal, exploration of the skyrmion phase response and under external stimuli is urgently required. Here we show experimentally, and explain theoretically, that in the magnetoelectric insulator Cu₂OSeO₃ the skyrmion phase can expand and shrink significantly depending on the polarity of a moderate applied electric field (few V/μm). The theory we develop incorporates fluctuations around the mean-field that clarifies precisely how the electric field provides direct control over the free energy difference between the skyrmion and the surrounding conical phase. The quantitative agreement between theory and experiment provides a solid foundation for the development of skyrmionic applications based on magnetoelectric coupling.