Critical size limits for collinear and spin-spiral magnetism in CoCr$_2$O$_4$

The multiferroic behavior of CoCr2O4 results from the appearance of conical spin-spiral magnetic ordering, which induces electric polarization. The magnetic ground state has a complex size-dependent behavior, which collapses when reaching a critical particle size. Here the magnetic phase stability of CoCr2O4 in the size range of 3.6–14.0 nm is presented in detail using the combination of neutron diffraction with XYZ polarization analysis and macroscopic magnetization measurements. We establish critical coherent domain sizes for the formation of the spin spiral and ferrimagnetic structure and reveal the evolution of the incommensurate spin spiral vector with particle size. We further confirm the presence of ferroelectric polarization in the spin spiral phase for nanocrystalline CoCr2O4