Vector vorticity of skyrmionic texture: An internal degree of freedom tunable by magnetic field

Abstract

Different from the skyrmion driven by the Dzyaloshinskii-Moriya interaction in non-centrosymmetric materials, the skyrmionic texture in centrosymmetric magnet may possess the extra internal degrees of freedom, which greatly enrich its morphologies, imply the continuous deformation allowed by topological protection, and enable flexible tunability and potential functionality. To describe the internal degree of freedom to full extent, the conventional integer-valued scalar vorticity is extended into a vector vorticity with continuous rotation allowed. The further simplified vorticity angle, together with helicity angle, represents the whole rotation freedom of spin space. The centrosymmetric magnet with frustration provides a perfect platform for realizing a controllable manipulation on these internal degrees of freedom, where the magnetic field can be applied to tune vorticity continuously in both crystal and isolated forms of skyrmionic texture, and the helicity can be further controlled by electric field. Moreover, the simulation reveals the distinctive dynamic effects related to the vorticity modulation, namely, a straight motion can be generated by rotating magnetic field to tune vorticity, and the vorticity can also be controlled to modulate the dynamics induced by the spin polarized current.

Modulation of skyrmionic magnetic textures in two-dimensional vdW materials and their heterostructures

“…The calculation predicted that for the frustration-induced SMT in centrosymmetric magnet, its internal degrees of freedom can be manipulated by applying magnetic field and electric field with appropriate orientation and magnitude. 79 , 80 The very recent experimental observation reported unconventional helicity polarization of skyrmions in vdW Fe 5−δ GeTe 2 , 81 where the skyrmion helicity is controlled by both the dipolar interaction and DMI. The helicity polarization can be attributed to the localized DMI originating from non-uniform regions or deficiencies.…”

“…The tunable internal degree of freedom implies the continuous deformation allowed by topological protection, and enables potential functionality by external stimuli with invariant topological property. The calculation predicted that for the frustration-induced SMT in centrosymmetric magnet, its internal degrees of freedom can be manipulated by applying magnetic field and electric field with appropriate orientation and magnitude 79,80 . The very recent experimental observation reported unconventional helicity polarization of skyrmions in vdW Fe 5−δ GeTe 2…”

Multifarious skyrmion phases on a trilayer triangular lattice

“…Similarly, the studies have revealed that the SkX in itienrant magnets is stabilized by considering thermal fluctuations [93][94][95], single-ion anisotropy [96], spin-charge coupling including the biquadratic interaction [97][98][99][100][101][102][103], and circularly polarized microwave field [104] in addition to the RKKY interaction. In these cases, the helicity and vorticity of the SkX are arbitrary, which results in peculiar symmetry breaking states [84,94,105] and transport properties [86,[106][107][108][109][110][111]. In centrosymmetric magnets, the degeneracy in the SkXs is (partly) lifted in the presence of the symmetric anisotropic exchange interaction and dipolar interaction, the former of which arises from the discrete lattice symmetry [112][113][114][115][116][117].…”

Stability of Skyrmion Crystal Phase in Centrosymmetric Distorted Triangular-Lattice Antiferromagnets

“…59,60) Another feature of the frustrationbased mechanisms is to keep degeneracy for the spin texture due to the presence of the global spin rotation symmetry, which leads to a coexisting state of skyrmions and anti-skyrmions, 8) a replica-symmetry-breaking SkX state, 61) and their dynamics. 11,12,[62][63][64] With such situations in mind, we aim at illuminating the stability of the SkX in centrosymmetric low-symmetry lattice systems without n-fold rotation axis (n = 3, 4, 6) in order to further stimulate an exploration of multiple-Q states in both theoretical and experimental studies. For that purpose, we consider a uniaxially distorted triangular lattice belonging to the orthorhombic point group with twofold rotation symmetry, which has often been studied in noncentrosymmetric systems where the modulated Dzyaloshinskii-Moriya interaction becomes important.…”