Investigations of the size distribution and magnetic properties of nanoparticles of Cu$_2$OSeO$_3$

Skyrmions in confined geometries have been a subject of increasing interest due to the different properties that they exhibit compared to their bulk counterparts. In this study, nanoparticles of skyrmion-hosting $\text{Cu}_{2}\text{OSeO}_{3}$ have been synthesised using a precipitation method followed by thermal treatment. This enables us to produce nanoparticles whose mean size varies from tens of nanometers to a few micrometers by varying the temperature and duration of the thermal decomposition of the precursor. These sizes span the $\sim 63$~nm diameter of skyrmions in $\text{Cu}_{2}\text{OSeO}_{3}$, allowing investigations into how the magnetic state changes when the size of the geometrical confinement is similar to and smaller than the size of an isolated magnetic skyrmion. AC susceptibility measurements performed on nanoparticles with a size distribution from 15 to 250 nm show a change in the magnetic phase diagram compared to bulk $\text{Cu}_{2}\text{OSeO}_{3}$.