Abstract
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.
Highlights
To realise skyrmion-based applications1–5, research into the creation, control and stabilisation of skyrmions is in an active phase1,6–13
We show how an applied E field causes a relatively small shift of the skyrmion lattice (SkL) free energy that is commensurate with the mean-field free energy difference between the competing skyrmion and conical phases, and dramatically controls the SkL phase stability
Measurements of Cu2OSeO323, it was suggested that skyrmions may be “created” or “annihilated” by applying a dc E-field in suitable parts of the temperature–magnetic field (T,H) phase diagram
Summary
To realise skyrmion-based applications (skyrmionics), research into the creation, control and stabilisation of skyrmions is in an active phase1,6–13 In this context, it could seem problematic that in bulk materials the skyrmion phase is stable only for a narrow interval at finite temperature (T) just below the magnetic ordering temperature TC, and under an applied magnetic field (H). A new approach for treating the fluctuative part of the free energy contributed by quasiparticle modes around TC The inclusion of these modes proves pivotal for the correct evaluation of the free energy difference between the competing skyrmion and conical phases, both with and without E field, and represents an improved approach more generally for the calculation of the skyrmion phase diagram
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