Degeneracies and fluctuations of Néel skyrmions in confined geometries

Abstract

The recent discovery of tunable Dzyaloshinskii-Moriya interactions in layered magnetic materials with perpendicular magnetic anisotropy makes them promising candidates for stabilization and manipulation of skyrmions at elevated temperatures. In this article, we use Monte Carlo simulations to investigate the robustness of skyrmions in these materials against thermal fluctuations and finite-size effects. We find that in confined geometries and at finite temperatures skyrmions are present in a large part of the phase diagram. Moreover, we find that the confined geometry favors the skyrmion over the spiral phase when compared to infinitely large systems. Upon tuning the magnetic field through the skyrmion phase, the system undergoes a cascade of transitions in the magnetic structure through states of different number of skyrmions, elongated and half-skyrmions, and spiral states. We consider how quantum and thermal fluctuations lift the degeneracies that occur at these transitions, and find that states with more skyrmions are typically favored by fluctuations over states with less skyrmions. Finally, we comment on electrical detection of the various phases through the topological and anomalous Hall effects.

Minimal radius of magnetic skyrmions: statics and dynamics

“…In both cases the phase diagram is colored using the density order parameter ρ, but two different scaling schemes have been found to separate the corresponding phases. While in [20,28] no distinction between the Skx and the isolated skyrmions has been made, in our calculations at finite temperatures the isolated skyrmions survive up to the boundary indicated by the stars. The transition from the skyrmion lattice to the spin-spiral state appears to be diffuse: a rather broad region exists in which skyrmions and elongated spiral-like textures coexist as can also be observed in figure 1(a).…”

Complex magnetic phase diagram and skyrmion lifetime in an ultrathin film from atomistic simulations

“…The topological charge is also no longer an integer for free boundaries, which complicates the determination of the skyrmion lifetime at finite temperature. Therefore, we conclude that the periodic boundary conditions are probably more appropriate for the simulation of a homogeneous system considered in this paper, while free boundary conditions are preferable in constrained geometries [74,75]. siderations given in Appendix C. Even if such structures with opposite topological charge would form in the system, we expect that the energy barrier between the fieldpolarized state and the skyrmion will mainly depend on the isotropic exchange interactions in the system [22,52], which makes no difference between skyrmions and antiskyrmions with opposite topological charges.…”

“…Ref. [74]. The topological charge is also no longer an integer for free boundaries, which complicates the determination of the skyrmion lifetime at finite temperature.…”

Spintronics via non-axisymmetric chiral skyrmions

“…Importantly, magnetic saturation is never fully reached in confined nanosystems as surface modulations occur near the sample edges (so called chiral surface twists) 13 with a penetration depth estimated as 0.1 p (p is the helix period at zero field) 14 . In the case of a narrow strip, the edge states manifest themselves as remnants of the helical spiral [14][15][16] with a smooth deviation of the magnetization from being co-aligned with the field in the middle of the sample ( Fig. 1 (a), (b)) to composing some (field-and anisotropy-dependent) angle θ 0 at the edge.…”

“…In the saturated state, isolated skyrmions are axisymmetric and translationally invariant along z 1,2 . Chiral surface twists for H > H D have been investigated in a number of earlier contributions [14][15][16] . Below H D , the incompatibility with the longitudially modulated conical phase imposes a complex, three-dimensional character on the magnetic modulations of the skyrmions and edge states (Figs.…”