  Magnetic hopfions are localized magnetic solitons with non-zero 3D
topological charge (Hopf index). Here I present an analytical calculation of
the toroidal magnetic hopfion vector potential, emergent magnetic field, the
Hopf index, and the magnetization configuration. The calculation method is
based on the concept of the spinor representation of the Hopf mapping. The
hopfions with arbitrary values of the azimuthal and poloidal vorticities are
considered. The special role of the toroidal coordinates and their connection
with the emergent vector po tential gauge are demonstrated. The hopfion
magnetization field is found explicitly for the arbitrary Hopf indices. It is
shown that the Hopf charge density can be represented as a Jacobian of the
transformation from the toroidal to the cylindrical coordinates.
