Quantum fluctuations stabilize skyrmion textures

We study the quantum spin waves associated to skyrmion textures. We show that the zero-point energy associated to the quantum spin fluctuations of a noncollinear spin texture produce Casimir-like magnetic fields. We study the effect of these Casimir fields on the topologically protected noncollinear spin textures known as skyrmions. In a Heisenberg model with Dzyalonshinkii-Moriya interactions, chosen so the classical ground state displays skyrmion textures, we calculate the spin-wave spectrum, using the Holstein-Primakoff approximation, and the associated zero-point energy, to the lowest order in the spin-wave expansion. Our calculations are done both for the single-skyrmion case, for which we obtain a discrete set of skyrmion bound states, as well as for the skyrmion crystal, for which the resulting spectrum gives the spin-wave bands. In both cases, our calculations show that the Casimir magnetic field contributes up to 10% of the total Zeeman energy necessary to delete the skyrmion texture with an applied field.

The authors acknowledge funding from Fondecyt Grant No. 1150072, Grant No. ICM P10-061-F by Fondo de Innovación para la Competitividad-MINECON, and Anillo Grant No. ACT 1117. A.S.N. also acknowledges support from Financiamiento Basal para Centros Científicos y Tecnológicos de Excelencia, under Project No. FB 0807(Chile).