Topological order is important in many aspects of condensed matter physics and has been extended to bosonic systems. In this Letter we report on the nontrivial topology of the magnon bands in two distinct quantum skyrmion crystals appearing in zero external magnetic field. This is revealed by nonzero Chern numbers for some of the bands. As a bosonic analog of the quantum anomalous Hall effect, we show that topological magnons can appear in skyrmion crystals without explicitly breaking time-reversal symmetry with an external magnetic field. By tuning the value of the easy-axis anisotropy at zero temperature, we find eight quantum topological phase transitions signaled by discontinuous jumps in certain Chern numbers. We connect these quantum topological phase transitions to gaps closing and reopening between magnon bands.

• Received 23 May 2022
• Accepted 29 June 2022

DOI:https://doi.org/10.1103/PhysRevResearch.4.L032025

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society