Stabilization mechanisms of magnetic skyrmion crystal and multiple-$Q$ states based on momentum-resolved spin interactions

TL;DR

This paper reviews how microscopic momentum-resolved spin interactions stabilize various multiple-Q magnetic states, including skyrmion crystals, and how effective models can predict experimental phase diagrams.

Contribution

It introduces an effective momentum-resolved spin model as a unifying framework for understanding and exploring multiple-Q states with topological properties.

Findings

Effective spin model reproduces experimental phase diagrams.

Key ingredients identified for stabilizing various multiple-Q states.

Momentum-resolved interactions are crucial for understanding topological magnetic states.

Abstract

Multiple-$Q$ states as represented by a magnetic skyrmion crystal and hedgehog crystal have been extensively studied in recent years owing to their unconventional physical properties. The materials hosting multiple-$Q$ states have been so far observed in a variety of lattice structures and chemical compositions, which indicates rich stabilization mechanisms inducing the multiple-$Q$ states. We review recent developments in the research of the stabilization mechanisms of such multiple-$Q$ states with an emphasis on the microscopic spin interactions in momentum space. We show that an effective momentum-resolved spin model is a canonical model for not only understanding the microscopic origin of various multiple-$Q$ states but also exploring further exotic multiple-$Q$ states with topological properties. We introduce several key ingredients to realize the magnetic skyrmion crystal with the skyrmion numbers of one and two, hedgehog crystal, meron-antimeron crystal, bubble crystal, and other multiple-$Q$ states. We also review that the effective spin model can be used to reproduce the magnetic phase diagram in experiments efficiently.