Abstract
Magnetic hopfions are topologically protected three-dimensional solitons that are constituted by a tube which exhibits a topologically nontrivial spin texture in the cross-section profile and is closed to a torus. Here we show that the hopfion's locally uncompensated emergent field leads to a topological Hall signature, although the topological Hall effect vanishes on the global level. The topological Hall signature is switchable by magnetic fields or electric currents and occurs independently of the anomalous and conventional Hall effects. It can therefore be exploited to electrically detect hopfions in experiments and even to distinguish them from other textures like skyrmion tubes. Furthermore, it can potentially be utilized in spintronic devices. Exemplarily, we propose a hopfion-based racetrack data storage device and simulate the electrical detection of the hopfions as carriers of information.
Highlights
In recent years, noncollinear spin textures have attracted an enormous amount of research interest
We find that hopfions exhibit a local topological Hall signature due to a locally uncompensated emergent field, which cancels only on a global level
We have shown that magnetic hopfions exhibit a local topological Hall signature which is compensated on a global level
Summary
Noncollinear spin textures have attracted an enormous amount of research interest. The quasi-two-dimensional skyrmions elongate as strings or tubes along the magnetic field direction For these textures, the occurrence of an additional contribution to the Hall effect of electrons [4,5] has been observed. A related object is the magnetic hopfion [9,10,11,12,13,14] It can be understood as a skyrmion tube that is closed to a torus [Fig. 1(a)]; this brings about another layer of topological protection, since a torus cannot be transformed to a string continuously. We find that hopfions exhibit a local topological Hall signature due to a locally uncompensated emergent field, which cancels only on a global level Based on these findings, we discuss consequences for the electrical detection and for the spintronic applicability of magnetic hopfions
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