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

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 has a layered (graphite-like) layout, which can be controlled by the external field and the uniaxial anisotropy.