Experimental observation of vortex rings in a bulk magnet

Vortex rings are remarkably stable structures that occur in a large variety of systems, such as in turbulent gases (where they are at the origin of weather phenomena) 1 , fluids (with implications for biology) 2 , electromagnetic discharges 3 and plasmas 4 . Although vortex rings have also been predicted to exist in ferromagnets 5 , they have not yet been observed. Using X-ray magnetic nanotomography 6 , we imaged three-dimensional structures forming closed vortex loops in a bulk micromagnet. The cross-section of these loops consists of a vortex–antivortex pair and, on the basis of magnetic vorticity (a quantity analogous to hydrodynamic vorticity), we identify these configurations as magnetic vortex rings. Although such structures have been predicted to exist as transient states in exchange ferromagnets 5 , the vortex rings we observe exist as static configurations, and we attribute their stability to the dipolar interaction. In addition, we observe stable vortex loops intersected by point singularities 7 at which the magnetization within the vortex and antivortex cores reverses. We gain insight into the stability of these states through field and thermal equilibration protocols. The observation of stable magnetic vortex rings opens up possibilities for further studies of complex three-dimensional solitons in bulk magnets, enabling the development of applications based on three-dimensional magnetic structures. Three-dimensional structures of vortex loops in a bulk micromagnet GdCo 2 have been observed using X-ray magnetic nanotomography. The cross-section of these loops consists of a vortex–antivortex pair stabilized by the dipolar interaction.