Mutual conversion between a magnetic Neel hopfion and a Neel toron

Three-dimensional (3D) magnetic textures attract much attention from researchers due to their fascinating structures and dynamic behaviors. The magnetic hopfion is a prominent example of a 3D magnetic texture. Here, we numerically study the mutual conversion between a Neel-type hopfion and a Neel-type toron under an external magnetic field. We also investigate the excitation modes of hopfions and torons in a film with strong perpendicular magnetic anisotropy. It is found that the Neel-type hopfion could be a stable state in the absence of the external magnetic field, and its diameter varies with the out-of-plane magnetic field. The Neel-type hopfion may transform into a Neel-type toron at an out-of-plane magnetic field of about 20 mT, where the cross-section structure is a Neel-type skyrmion. The hopfion and toron show different excitation modes in the presence of an in-plane microwave magnetic field. Our results provide a method to realize the conversion between a Neel-type hopfion and a Neel-type toron, which also opens a path to distinguish between a Neel-type hopfion and a Neel-type toron based on their excitation modes.