Topological phase transitions driven by polarity change and next-nearest-neighbor hopping in skyrmion crystals

TL;DR

This paper investigates how topological phase transitions in skyrmion crystals are driven by changes in polarity and next-nearest-neighbor hopping, revealing robustness of phases and new topological effects.

Contribution

It demonstrates the influence of polarity and next-nearest-neighbor hopping on topological phases and Hall effects in skyrmion crystals, highlighting phase transitions and robustness.

Findings

Polarity increase from 1 to 2 spans wide topological phases.

Next-nearest-neighbor hopping reshapes the emergent magnetic flux pattern.

Chern numbers change from unity to indefinite values with increasing $t'$.

Abstract

By considering the bulk-edge correspondence of the skyrmion crystal this work focused on the relation of the topological properties to the polarity ($Q_{\rm{sk}}$), next-nearest-neighbor hopping ($t'$), and exchange coupling ($J$). We found that by continually increasing polarity of the skyrmions from 1 to 2, the monopole-lattice phase and the dipole-lattice phase both span a wide range in the parameter space demonstrating topological robustness. While the next-nearest-neighbor-hopping of the electrons coexists with the nearest-neighbor hopping the flux pattern of the emergent magnetic field traversing the two-dimensional SkX is reshaped giving rise to different topological Hall effect. By increasing $t'$ from 0 to $t$ with the polarity fixed to be 1, we found Chern numbers of the electronic bands change from unity to indefinite values demonstrating a phase transition. We also considered the effect of finite $J$ and found the results obtained in the adiabatic limit hold to around $J=t$.