We investigate the stability of the skyrmion crystal phase in a tetragonal polar system with the Dzyaloshinskii-Moriya interaction by focusing on the symmetry of ordering wave vectors forming the skyrmion crystal. Our analysis is based on numerical simulations for an effective spin model, which is derived from the weak-coupling regime in the Kondo lattice model on a polar square lattice. We show that a hybrid square skyrmion crystal consisting of Bloch and Néel spin textures emerges even under polar C4v symmetries when the ordering wave vectors correspond to low-symmetric wave vectors in momentum space, which is in contrast to the expectation from the Lifshitz invariants. We also show the instability toward the anti-skyrmion crystal and rhombic skyrmion crystal depending on the direction of the Dzyaloshinskii-Moriya vector in momentum space. Furthermore, we show that the regions of the skyrmion crystal phases are affected by taking into account the symmetric anisotropic exchange interaction. Our results open the potential direction of engineering the hybrid skyrmion crystal and anti-skyrmion crystal phases in polar magnets.

We theoretically investigate a new stabilization mechanism of a skyrmion crystal (SkX) in centrosymmetric itinerant magnets with magnetic anisotropy. By considering a trigonal crystal system without the horizontal mirror plane, we derive an effective spin model with an anisotropic Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction for a multi-band periodic Anderson model. We find that the anisotropic RKKY interaction gives rise to two distinct SkXs with different skyrmion numbers of one and two depending on a magnetic field. We also clarify that a phase arising from the multiple-Q spin density waves becomes a control parameter for a field-induced topological phase transition between the SkXs. The mechanism will be useful not only for understanding the SkXs, such as that in Gd$$_2$$ 2 PdSi$$_3$$ 3 , but also for exploring further skyrmion-hosting materials in trigonal itinerant magnets.

We investigate the instability toward a skyrmion crystal (SkX) in noncentrosymmetric cubic magnets with an emphasis on a comparison between point groups (O, T ) and T d . By constructing low-temperature magnetic phase diagrams under an external magnetic field for three directions based on numerically simulated annealing, we find that the system under the point group (O, T ) exhibits different two types of SkXs depending on the field direction, while that under T d does not show such an instability. The difference between them is understood from the difference in the momentum-dependent Dzyaloshinskii-Moriya interaction under each point group. Meanwhile, we show that the system under T d leads to the SkX instability by considering an additional effect of the uniaxial strain, which lowers the symmetry to D 2d . We obtain two different SkXs: Néel-type and anti-type SkXs, the former of which is stabilized in the presence of the interactions at the threedimensional ordering wave vectors. The present results provide rich topological spin textures in the three-dimensional systems, which are sensitive to the magnetic-field direction and point-group symmetry.

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