Reorientation of skyrmion crystal (SkX) with respect to crystallographic axes is believed to be insensitive to anisotropies of fourth order in spin-orbit coupling, for which sixth order terms are considered for explanation. Here, we show that this is wrong due to an oversimplified assumption that SkX possesses hexagonal symmetry. When the deformation of SkX is taken into account, fourth order anisotropies such as exchange anisotropy and magnetocrystalline anisotropy have pinning \textcolor{red}{(in this work, the word ‘pinning’ refers to the reorientation effects of intrinsic anisotropy terms)} effects on SkX. In particular, we reproduce some experiments of MnSi and Fe$_{1-x}$Co$_{x}$Si by considering the effect of fourth order magnetocrystalline anisotropy alone. We reproduce the $30^\circ$ rotation of SkX in Cu$_2$OSeO$_3$ by considering the combined effects of the exchange and magnetocrystalline anisotropies. And we use the exchange anisotropy to explain the reorientation of SkX in VOSe$_2$O$_5$.

中文翻译：

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交换和磁晶各向异性对天rm子晶格的钉扎效应

认为天旋子晶体（SkX）相对于晶体学轴的重新取向对自旋-轨道耦合中的四阶各向异性不敏感，考虑使用六阶项进行解释。在这里，我们证明这是错误的，因为过度简化了SkX具有六边形对称性的假设。考虑到SkX的变形，交换各向异性和磁晶各向异性等四阶各向异性具有钉扎\ textcolor {red} {（在本文中，“钉扎”一词是指固有各向异性项的重新定向效应）}效应在SkX上。特别是，我们仅考虑了四阶磁晶各向异性的影响，就对MnSi和Fe $ _ {1-x} $ Co $ _ {x} $ Si进行了一些实验。通过考虑交换和磁晶各向异性的综合作用，我们在Cu $ _2 $ OSeO $ _3 $中重现了SkX的$ 30 ^ \ circ $旋转。并且我们使用交换各向异性来解释Sk在VOSe $ _2 $ O $ _5 $中的重新定向。