Hopfions in chiral magnets

A magnetic Hopfion is a three-dimensional topological soliton that consists of a closed loop of a twisted magnetic Skyrmion string. The results of numerical simulations are presented that demonstrate the existence of a stable Hopfion in a nanocylinder of a chiral magnet and an explicit analytic expression is shown to provide a reasonable approximation to the numerically computed Hopfion. A mechanism is suggested to create the Hopfion from a target Skyrmion by introducing an interfacial perpendicular magnetic anisotropy.