Topological spin crystals by itinerant frustration

TL;DR

This paper reviews how itinerant frustration, arising from competing electron-mediated interactions, stabilizes various unconventional topological spin textures such as skyrmion, meron, and hedgehog crystals in itinerant magnets.

Contribution

It introduces a unified framework based on bilinear and biquadratic interactions in momentum space to understand the stabilization of topological spin crystals in itinerant systems.

Findings

Itinerant frustration stabilizes diverse topological spin textures.

Charge-spin interplay is crucial for topological spin crystal formation.

Unconventional skyrmion crystals with high skyrmion number are identified.

Abstract

Spin textures with nontrivial topology, such as vortices and skyrmions, have attracted attention as a source of unconventional magnetic, transport, and optical phenomena. Recently, a new generation of topological spin textures has been extensively studied in itinerant magnets; in contrast to the conventional ones induced, e.g., by the Dzyaloshinskii-Moriya interaction in noncentrosymmetric systems, they are characterized by extremely short magnetic periods and stable even in centrosymmetric systems. Here we review such new types of topological spin textures with particular emphasis on their stabilization mechanism. Focusing on the interplay between charge and spin degrees of freedom in itinerant electron systems, we show that itinerant frustration, which is the competition among electron-mediated interactions, plays a central role in stabilizing a variety of topological spin crystals including a skyrmion crystal with unconventional high skyrmion number, meron crystals, and hedgehog crystals. We also show that the essential ingredients in the itinerant frustration are represented by bilinear and biquadratic spin interactions in momentum space. This perspective not only provides a unified understanding of the unconventional topological spin crystals but also stimulates further exploration of exotic topological phenomena in itinerant magnets.