标题： 在外加磁场和各向异性下的螺旋磁体中磁霍普夫子晶格的控制 显示英文标题

标题： Control of the magnetic hopfion lattice in helimagnet with the external field and anisotropy

摘要： 一个考虑了具有二维（允许径向和方位角依赖性）的螺旋磁体中Hopfion的广义微观磁模型被考虑。 计算证实了Hopfion的椭圆稳定性以及之前得到的它们晶格的上临界场的解析表达式。 得到了Hopfion晶格周期与施加的外部磁场大小和材料的单轴各向异性常数之间的依赖关系。 结果显示，在各向异性螺旋磁体中，Hopfion晶格沿各向异性轴方向扩展，且这种扩展可以通过外部场和单轴各向异性常数进行控制。 显示英文摘要

摘要： A generalized micromagnetic model of hopfions in a helimagnet with a two-dimensional (allowing both radial and azimuthal dependence) profile function is considered. Calculations confirm the elliptical stability of hopfions and the previously obtained analytical expression for the upper critical field of their lattice. Dependencies of the hopfion lattice periods on the magnitude of the applied external magnetic field and the uniaxial anisotropy constant of the material are obtained. It is shown that in an anisotropic helimagnet, the hopfion lattice expands in the direction of the anisotropy axis, and the expansion can be controlled by the external field and the uniaxial anisotropy constant.