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Vortex rings are remarkably stable structures occurring in numerous systems: for example in turbulent gases, where they are at the origin of weather phenomena [1]; in fluids with implications for biology [2]; in electromagnetic discharges [3]; and in plasmas [4]. While 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 loops in a bulk micromagnet, each composed of a vortex-antivortex pair. Based on the magnetic vorticity, a quantity analogous to hydrodynamic vorticity, we identify these configurations as magnetic vortex rings. While such structures have been predicted to exist as transient states in exchange ferromagnets [5], the vortex rings we observe exist as stable, static configurations, whose stability we attribute to the dipolar interaction. In addition, we observe stable vortex loops intersected by magnetic singularities [7], at which the magnetisation within the vortex and antivortex cores reverses. We gain insight into the stability of these states through field and thermal equilibration protocols. These measurements pave the way for the observation of complex three-dimensional solitons in bulk magnets, as well as for the development of applications based on three-dimensional magnetic structures.
In the past decades, topological concepts have emerged to classify matter states beyond the Ginzburg-Landau symmetry breaking paradigm. The underlying global invariants are usually characterized by integers, such as Chern or winding numbers. Very rec
The degree of contact between a system and the external environment can alter dramatically its proclivity to quantum mechanical modes of relaxation. We show that controlling the thermal coupling of cubic centimeter-sized crystals of the Ising magnet
We present a simple Hamiltonian description of the dynamics of a quantized vortex ring in a trapped superfluid, compare this description with dynamical simulations, and characterize the dependence of the dynamics of the shape of the trap.
Weyl points are the simplest topologically-protected degeneracy in a three-dimensional dispersion relation. The realization of Weyl semimetals in photonic crystals has allowed these singularities and their consequences to be explored with electromagn
The study of the laws of nature has traditionally been pursued in the limit of isolated systems, where energy is conserved. This is not always a valid approximation, however, as the inclusion of features like gain and loss, or periodic driving, quali