  Hopfions are an intriguing class of string-like solitons, named according to
a classical topological concept classifying three-dimensional direction fields.
The search of hopfions in real physical systems is going on for nearly half a
century, starting with the seminal work of Faddeev. But so far realizations in
solids are missing. Here, we present a theory that identifies magnetic
materials featuring hopfions as stable states without the assistance of
confinement or external fields. Our results are based on an advanced
micromagnetic energy functional derived from a spin-lattice Hamiltonian.
Hopfions appear as emergent particles of the classical Heisenberg model.
Magnetic hopfions represent three-dimensional particle-like objects of
nanometre-size dimensions opening the gate to a new generation of spintronic
devices in the framework of a truly three-dimensional architecture. Our
approach goes beyond the conventional phenomenological models. We derive
material-realistic parameters that serve as concrete guidance in the search of
magnetic hopfions bridging computational physics with materials science.
