Dynamic properties of magnetic hopfions

We present an investigation of two important aspects of hopfions dynamics: spatial distribution of spin waves against the hopfion background and motion of hopfion in a nonuniform electric field. It is shown here by computer simulations that the hopfion confined to the discs has a rich spectra of spin-wave excitations, and that the velocity of hopfion moving in a gradient of electrical field in the ferromagnetic stripe is constant, which actualizes the still unsolved problem of determining the mass of localized magnetic textures. The knowledge of such peculiarities of hopfion dynamics is necessary for their spintronic and magnonic applications.