A skyrmion crystal has internal degrees of freedom in terms of vorticity and helicity, which gives rise to fascinating types of skyrmion phases (Neel, Bloch, and anti-skyrmion). We show how the degeneracy lifting in tetragonal skyrmion crystals occurs in centrosymmetric itinerant magnets by focusing on microscopic interactions through the Fermi surface instability. We demonstrate that four types of skyrmion crystals can be realized according to the signs of the anisotropic Ruderman-Kittel-Kasuya-Yosida interaction, which are sensitive to band structures, electron fillings, atomic orbitals, and sublattice positions. Our findings might provide a possibility of controlling the types of the skyrmion crystals by electron doping and external pressure rather than relying on the noncentrosymmetric lattice structures.

中文翻译：

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中心对称四方系统中 Néel、Bloch 和 Anti-Skyrmion 晶体的简并提升

斯格明子晶体在涡度和螺旋度方面具有内部自由度，这产生了迷人的斯格明子相（尼尔、布洛赫和反斯格明子）。我们通过关注通过费米表面不稳定性的微观相互作用，展示了四方斯格明子晶体的简并提升如何在中心对称流动磁铁中发生。我们证明了根据各向异性 Ruderman-Kittel-Kasuya-Yosida 相互作用的迹象可以实现四种类型的斯格明子晶体，它们对能带结构、电子填充、原子轨道和亚晶格位置敏感。我们的发现可能提供通过电子掺杂和外部压力而不是依赖非中心对称晶格结构来控制斯格明子晶体类型的可能性。