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

TL;DR

This study investigates how the magnetic and ferroelectric properties of CoCr$_2$O$_4$ change with particle size, identifying critical sizes for spin spiral and ferrimagnetic phases and confirming ferroelectricity at the nanoscale.

Contribution

It provides detailed size-dependent magnetic phase stability data for CoCr$_2$O$_4$, including critical domain sizes and evolution of spin structures, using neutron diffraction and magnetization measurements.

Findings

Critical domain sizes for spin spiral and ferrimagnetic phases identified.

Evolution of incommensurate spin spiral vector with particle size documented.

Ferroelectric polarization confirmed in nanocrystalline CoCr$_2$O$_4$.

Abstract

The multiferroic behavior of CoCr$_2$O$_4$ 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 CoCr$_2$O$_4$ 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 CoCr$_2$O$_4$.