Direct observation of the exchange anisotropy in the helimagnetic insulator Cu${}_2$OSeO${}_3$

Abstract

The helical magnetic structures of cubic chiral systems are well-explained by the competition among Heisenberg exchange, Dzyaloshinskii-Moriya interaction, cubic anisotropy, and anisotropic exchange interaction (AEI). Recently, the role of the latter has been argued theoretically to be crucial for the low-temperature phase diagram of the cubic chiral magnet Cu${}_2$OSeO${}_3$, which features tilted conical and disordered skyrmion states for a specific orientation of the applied magnetic field ($\hat{I}{¼}_0\vec{\mathrm{H}}\parallel [001]$). In this study, we exploit transmission resonant x-ray scattering ($t-$REXS) in vector magnetic fields to directly quantify the strength of the AEI in Cu${}_2$OSeO${}_3$, and measure its temperature dependence. We find that the AEI continuously increases below 50\,K, resulting in a conical spiral pitch variation of $10\%$ in the (001) plane. Our results contribute to establishing the interaction space that supports tilted cone and low-temperature skyrmion state formation, facilitating the goals for both a quantitative description and eventual design of the diverse spiral states existing amongst chiral magnets.