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

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.