Quantized Anomalous Hall Effects in Skyrmion Crystal

TL;DR

This paper theoretically investigates the possibility of realizing the quantized anomalous Hall effect in skyrmion crystal systems without external magnetic fields, highlighting the conditions and robustness of the effect.

Contribution

It introduces a theoretical framework for QAHE in skyrmion crystals, analyzing the effects of skyrmion size, disorder, and temperature on the phenomenon's stability.

Findings

Gigantic emergent magnetic field (~4000 T) in skyrmion crystals.

QAHE can be realized at room temperature with strong disorder.

Skyrmion crystal systems are more fragile against temperature than uniform magnetic field systems.

Abstract

We theoretically study the quantized anomalous Hall effect (QAHE) in skyrmion crystal (SkX) without external magnetic field. The emergent magnetic field in SkX could be gigantic as much as $\sim4000$T when its lattice constant is $\sim1$nm. The band structure is not flat but has a finite gap in the low electron-density regime. We also study the conditions to realize the QAHE for the skyrmion size, carrier density, disorder strength and temperature. Comparing the SkX and the system under the corresponding uniform magnetic field, the former is more fragile against the temperature compared with the latter since the gap is reduced by a factor of $\sim$ 1/5, while they are almost equally robust against the disorder. Therefore, it is expected that the QAHE of SkX system is realized even with strong disorder at room temperature when the electron density of the order of one per a skyrmion.