Higher-order modulations in the skyrmion-lattice phase of Cu$_2$OSeO$_3$

TL;DR

This study investigates higher-order peaks in the skyrmion-lattice phase of Cu$_2$OSeO$_3$ using neutron scattering, revealing intrinsic modulations and their field-dependent behavior, supported by Monte Carlo simulations.

Contribution

It provides the first detailed analysis of higher-order modulations in the skyrmion lattice of Cu$_2$OSeO$_3$, demonstrating their intrinsic nature and field-dependent switching.

Findings

Higher-order peaks observed at (110) and (200) positions.

Intrinsic higher-order modulations confirmed, not double scattering.

Field-dependent switching of dominant modulation from (110) to (200).

Abstract

Using small angle neutron scattering, we have investigated higher-order peaks in the skyrmion-lattice phase of Cu$_2$OSeO$_3$, in which two different skyrmion lattices, SkX1 and SkX2, are known to form. For each skyrmion-lattice phase, we observed two sets of symmetrically inequivalent peaks at the higher-order-reflection positions with the indices $(110)$ and $(200)$. Under the condition where the SkX1 and SkX2 coexist, we confirmed the absence of the scattering at $\mathbf{Q}$ positions combining reflections from the two phases, indicating a significantly weak double-scattering component. Detailed analysis of the peak profile, as well as the temperature and magnetic-field dependence of the peak intensity, also supports the intrinsic higher-order modulation rather than the parasitic double scattering. The two higher-order modulations show contrasting magnetic-field dependence; the former $(110)$ increases as the field is increased, whereas the latter $(200)$ decreases. This indicates that, in Cu$_2$OSeO$_3$, skyrmions are weakly distorted, and the distortion is field-dependent in a way that the dominant higher-order modulation switches from $(110)$ to $(200)$ under field. Monte Carlo simulations under sweeping external magnetic field qualitatively reproduce the observed magnetic-field dependence, and suggests that the higher-order modulations correspond to the superlattices of weak swirlings appearing in the middle of the original triangular-latticed skyrmions.