Field-direction-dependent skyrmion crystals in noncentrosymmetric cubic magnets: A comparison between point groups $(O,T)$ and $T_{\mathrm{d}}$

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 $T_{\mathrm{d}}$. 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 $T_{\mathrm{d}}$ 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 $T_{\mathrm{d}}$ leads to the SkX instability by considering an additional effect of the uniaxial strain, which lowers the symmetry to $D_{2\mathrm{d}}$. 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 three-dimensional 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.