Skyrmion clusters and conical droplets in bulk helimagnets with cubic anisotropy

Abstract

Recent experimental findings in the bulk cubic helimagnet and Mott insulator Cu 2 OSeO 3 highlight the paramount role of cubic anisotropy in stabilizing novel chiral and skyrmion phases. It was indeed found that if a magnetic field is applied along the easy 001 crystallographic direction, competing cubic and exchange anisotropies tilt the wave vector of the conical spiral away from the magnetic field [Qian et al., Sci. Adv. 4, eaat7323 (2018)]. Furthermore, in this configuration skyrmions have been observed in a broad range of temperatures and magnetic fields [Chacon et al., Nat. Phys. 14, 936 (2018)]. Starting from these experimental observations and on the basis of a phenomenological Dzyaloshinskii theory, we investigate additional implications of the cubic anisotropy for this specified field direction. By including cubic anisotropy we show that the phase transition between the conical and field-polarized or homogeneous states becomes first order. Furthermore, we show that this transition is accompanied by the formation of conical droplets-domains of the conical phase in the homogeneous state. We investigate the internal structure of these droplets, which at their boundaries encompass alternating regions of positive and negative energy densities with respect to the homogeneous state. We thus deduce that these droplets may be zipped and unzipped in phase during the first-order phase transition that occurs by either increasing or decreasing the magnetic field. On the other hand, we show that in the conical phase skyrmions may form clusters due to their attractive mutual interaction. However, in the homogeneous state, the skyrmion-skyrmion interaction becomes repulsive, and the skyrmion clusters expand and disperse isolated skyrmions. This mutual skyrmion repulsion prevents the stabilization of skyrmion clusters even if the energy of isolated skyrmions is lower than that of the homogeneous state. Yet this skyrmion dispersal may be prevented if skyrmions are surrounded by the circular spiral state and form skyrmion bags. Such a scenario could explain the existence of skyrmions in the field-polarized state reported experimentally.

Vital role of magnetocrystalline anisotropy in cubic chiral skyrmion hosts

“…In FeGe (, another cubic chiral compound hosting Bloch SkL nearly up to room temperature [13], the change of the cubic anisotropy on cooling was proposed to drive a reorientation of the helical q-vectors from 100 -to 111 -type directions [22,23]. In spite of these early observations and the increasing number of theoretical works [24][25][26][27][28][29][30][31][32][33][34], implying a clear impact of cubic anisotropy on helical spin states the effect of anisotropy on SkLs has only been recognized recently [34][35][36].…”

Toggle-switch-like crossover between two types of isolated skyrmions within the conical phase of cubic helimagnets

“…In particular, uniaxial anisotropy of the easy-axis type 65 , which does not affect the ideal single-harmonic type of the magnetization rotation in the conical spiral but just leads to the gradual closing of the cone, grants the thermodynamical stability of the V-SkL in a broad region of theoretical and experimental phase diagrams [66][67][68] . Cubic anisotropy also stabilizes V-SkLs but for specific directions of the applied magnetic field 38,[69][70][71] . This anisotropy deforms the ideal conical configuration as the magnetization tends to deviate from the ideal conical surface trying to embrace the easy axes and to avoid the hard directions.…”

Field and anisotropy driven transformations of spin spirals in cubic skyrmion hosts

“…Skyrmion nucleation may occur via different mechanisms specified by the stable and metastable spiral states 14,15 . In particular, the low-temperature stable SkL in the bulk-insulating cubic helimagnet Cu2OSeO3 for H||[001] may appear via rupture formation of spiral states with wave vectors perpendicular to the field 14 , along [100] and [010].…”

“…Recent experimental findings, however, revealed a vast area of low-temperature skyrmion stability in the bulk insulating cubic helimagnet Cu 2 OSeO 3 , when the magnetic field is applied along the easy 001 crystallographic axis 11,13 . Remarkably, the theoretical explanation of this phenomenon is mainly based on the effect of single-ion cubic anisotropy on one-dimensional spiral states 14,15 . In fact, the ideal magnetization rotation in the conical phase, the main competitor of skyrmions, can be impaired by the easy and hard anisotropy axes for specific directions of the magnetic field.…”