Tunable skyrmion-skyrmion interactions on the surface of a three dimensional topological insulator

The surface of a three-dimensional topological insulator is characterized by a gapless two-dimensional Dirac cone dispersion. In a magnetic topological insulator, this surface dispersion is gapped by a Zeeman term proportional to the local magnetization. Magnetic skyrmions—stable, low energy excitations in chiral planar magnetic systems—lead to sign changes in this Zeemen term and, consequently, topologically protected bound states. It has been shown previously [1] that magnetic skyrmions on the surface of a topological insulator may result in a discrete set of localized orbitals—skyrmion bound states. We study the skyrmion-skyrmion interaction mediated by the hybridization of these orbitals. In particular, we consider the effective interaction between a pair of skyrmions in the presence of their hybridized orbitals. We show that the skyrmions form a bound state for high chemical potential. For low chemical potential their interaction is strictly repulsive. For intermediate chemical potential, both the bound and the unbound configurations locally minimize the free energy. We support our phenomenological theory with numerical calculations.

[1] H. M. Hurst, D. K. Efimkin, J. Zang, and V. Galitski, Phys. Rev. B, 91, 060401 (2015)