Skyrmion crystal under <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mn>3</mml:mn><mml:mi>h</mml:mi></mml:mrow></mml:msub></mml:math> point group: Role of out-of-plane Dzyaloshinskii-Moriya interaction

The Dzyaloshinskii-Moriya (DM) interaction that originates from relativistic spin-orbit coupling in noncentrosymmetric magnets is a source of topological spin textures. We theoretically investigate the possibility skyrmion crystal (SkX) by focusing on role out-of-plane DM different polar- and chiral-type interaction. By performing simulated annealing for model triangular lattice belonging to ${D}_{3h}$ point group, we construct low-temperature magnetic phase diagrams an applied field. As result, find instability toward crystals under in-plane fields, where key ingredients stabilize SkX are according field direction; stabilized field, while it additionally introducing easy-axis anisotropy also discuss possible multiple-$Q$ states other than presence Our result indicates materials with potential candidates host crystals.