Quantum fluctuations stabilize skyrmion textures

Abstract

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.

Degeneracies and fluctuations of Néel skyrmions in confined geometries

“…Moreover, they are shifted in such a way that the region where the configuration with four skyrmions is the true lowest-energy state is enlarged with respect to the classical result. This conclusion is in line with the finding of Roldán-Molina et al [43] that quantum fluctuations stabilize skyrmion textures over the collinear ferromagnetic phase. Loosely speaking this comes about because larger gradients in the spin direction lead to more quantum fluctuations.…”

“…[42] and [43]. We quantize the spins and use a Holstein-Primakoff transformation to bosonic operatorsâ r andâ † r .…”

Topological spin waves in the atomic-scale magnetic skyrmion crystal

“…We consider a two-dimensional triangular lattice of spins, inspired by the observation of a skyrmion lattice in a monolayer of Fe(111) on top of Iridium [20]. The Hamiltonian has a single ion uniaxial anisotropy term that favors the magnetization along the z axis, a first neighbor ferromagnetic exchange J, the Dzyaloshinskii-Moriya interaction (DMI) D and the Zeeman term [31,32,48,49]:…”

“…The skyrmion crystal also has spin waves, like in the case of other symmetry breaking magnetic states, such as ferromagnetic and antiferromagnetic states [31,32]. Here we describe them using a conventional quantum mechanical Holstein Primakoff (HP) boson theory [29,30,32,38,49,50] for spin waves:…”

“…As in every other broken symmetry magnetic ground state [29,30], spin waves excitations are expected to play an important role in the small energy spin dynamics of the skyrmion lattice [31,32]. More generically, the question of how the non-collinear magnetic ground states influences the dynamics of the spin waves has been explored by several authors in the past [33][34][35][36][37][38].…”