Universality of annihilation barriers of large magnetic skyrmions in chiral and frustrated magnets

Abstract

Magnetic skyrmions are whirls in the magnetization whose topological winding number promises stability against thermal fluctuations and defects. They can only decay via singular spin configurations. We analyze the corresponding energy barriers of skyrmions in a magnetic monolayer for two distinct stabilization mechanisms, i.e., Dzyaloshinskii-Moriya interaction (DMI) and competing interactions. Based on our numerically calculated collapse paths on an atomic lattice, we derive analytic expressions for the saddle point textures and energy barriers of large skyrmions. The sign of the spin stiffness and the sign of 4th-order derivative terms in the classical field theory determines the nature of the saddle point and thus the height of the energy barrier. In the most common case for DMI-stabilized skyrmions, positive stiffness and negative 4th-order term, the saddle point energy approaches a universal upper limit described by an effective continuum theory. For skyrmions stabilized by frustrating interactions, the stiffness is negative and the energy barrier arises mainly from the core of a singular vortex configuration. arXiv:1907.12174v1 [cond-mat.str-el]

Role of higher-order exchange interactions for skyrmion stability

“…22 occurs. The chimera skyrmion collapse and the radial antiskyrmion collapse are similar to that found in simulations neglecting HOI 16,22,50 .…”

“…3j, k which show the spin structures in the vicinity of the saddle point of the two types of annihilation mechanisms). Interestingly, the chimera collapse mechanism has been previously discussed in ultrathin films with very strong exchange frustration 16,50,51 , which suggests that HOI act in a similar way. The energy decomposition shows that the DMI contribution is of similar magnitude at the saddle point of the path with and without HOI (Fig.…”

“…On an average, we notice an increase in barrier height of nearly 100 meV for skyrmions upon including the HOI. At low fields up to B − B c = 1.36 T, there is a transition from the normal radial collapse mechanism 22,34 without HOI to a chimera collapse mechanism 16,50 with HOI. Above B − B c = 1.36 T, the skyrmions merge into the FM background through the normal radial collapse without HOI, which remains unchanged after including HOI.…”

Instability of skyrmions in magnetic fields

“…In that respect, even at the saddle point, we confirm numerically that in soft ferromagnets a finite radius skyrmion solution exists as predicted in Ref. 27.…”

“…Recently, the saddle point configurations were explored theoretically, and it was found that even when the magnetic interactions are described in the continuum limit, a skyrmion of finite size could be expected as the saddle point configuration. 27 Here, we study the skyrmion collapse field B c of isolated skyrmions in Co islands of single atomic thickness on Ru(0001). In a previous work, 26 we have combined spin-polarized STM measurements and DFT calculations to explore the ground state properties of Co/Ru(0001) and showed that skyrmions were stabilized by a vanishing effective anisotropy in combination with a small DMI.…”