Laser-induced nucleation of magnetic hopfions

Hopfions are three-dimensional topological solitons formed by closed loops of vortex strings, often taking the shape of rings. In magnetic crystals, hopfions have so far been observed only in unusual configurations in which hopfion rings are linked to skyrmion strings. Although theory predicts the existence of stable, isolated hopfions, their experimental realization has remained challenging. Here we demonstrate the laser-induced nucleation and direct observation of isolated magnetic hopfions in a cubic chiral magnet, FeGe, using transmission electron microscopy. The nucleation conditions are determined as a function of laser fluence and external magnetic field. Quantitative agreement between experimental data and micromagnetic simulations provides evidence for the emergence of isolated hopfions. We derive the topological invariant for hopfions under realistic rather than idealized boundary conditions and calculate its integer values for the observed objects. We also reveal that hopfions can coexist and interact with other topological spin textures over a broad field range. These findings demonstrate a contact-free approach for nucleating complex three-dimensional magnetic textures, thus providing a basis for further fundamental and applied research on magnetic hopfions.