Phase shift in skyrmion crystals

Abstract

The magnetic skyrmion crystal is a periodic array of a swirling topological spin texture. Since it is regarded as an interference pattern by multiple helical spin density waves, the texture changes with the relative phase shifts among the constituent waves. Although such a phase degree of freedom is relevant to not only magnetism but also transport properties, its effect has not been elucidated thus far. We here theoretically show that a phase shift in the skyrmion crystals leads to a tetra-axial vortex crystal and a meron-antimeron crystal, both of which show a staggered pattern of the scalar spin chirality and give rise to nonreciprocal transport phenomena without the spin-orbit coupling. We demonstrate that such a phase shift can be driven by exchange interactions between the localized spins, thermal fluctuations, and long-range chirality interactions in spin-charge coupled systems. Our results provide a further diversity of topological spin textures and open a new field of emergent electromagnetism by the phase shift engineering.

Square skyrmion crystal in centrosymmetric itinerant magnets

“…Let us compare the stability between the square and triangular SkXs in centrosymmetric itinerant electron systems. The triangular SkX on a triangular lattice is stabilized by taking into account either the positive biquadratic [46], the bond-dependent anisotropic [68,69], or the easy-axis anisotropic interaction [70]. In other words, it can be stabilized by only one of the three interactions.…”

Phase degree of freedom and topology in multiple-$Q$ spin textures

“…15 and 18). It was recently pointed out that the sinusoidal 3Q state changes the phase from φ = 0 (or π) to φ = π 2 by effective six-spin interactions arising from the entropic contribution or the spin-charge coupling [65] . In general, the interactions which can modulate the sum of phases in an N Q Q spin texture are given by N Q (2N Q ) multiple-spin interactions when N Q is even (odd).…”

“…Among such parameters in spin moiré, it was recently pointed out that the phase degree of freedom in the superposed waves is an important parameter to control not only the spin textures but also their symmetry and topological properties [64,65]. The situation is illustrated for superpositions of three proper screws in Fig.…”

Magnetic field-temperature phase diagrams for multiple-$Q$ magnetic orderings: Exact steepest descent approach to long-range interacting spin systems

“…In addition, the model can be extended to include higher-order contributions. For instance, the four-spin biquadratic interactions ∝ (S Qη •S −Qη ) 2 [49,50,58,63,[72][73][74][75][76][77][78][79] and the six-spin bicubic interactions ∝ {S Q1 • (S Q2 × S Q3 )} 2 [61] have also been considered as the origin of stabilization of multiple-Q magnetic orderings.…”

“…Among them, in this paper, we focus on the long-range interactions me-diated by conduction electrons [52][53][54][55][56][57]. Such interactions are incorporated into effective spin models for magnetic metals [58][59][60], and have been shown to stabilize a variety of multiple-Q magnetic orderings, such as 2Q and 3Q VCs [58,59,61,62] , and 3Q and quadruple-Q HLs [62][63][64][65]. Usually, the models exhibit complicated phase diagrams while changing the lattice structures, the interaction parameters, temperature, and an external magnetic field.…”