Magnetic phase transitions and spin density distribution in the molecular multiferroic GaV$_4$S$_8$ system

TL;DR

This study investigates the magnetic phase transitions and spin density distribution in GaV$_4$S$_8$, revealing complex magnetic structures, phase transitions, and the distribution of magnetic moments consistent with first-principles calculations.

Contribution

It provides detailed neutron scattering analysis of magnetic phases and spin distribution in GaV$_4$S$_8$, highlighting the coupling between magnetic order and ferroelectricity.

Findings

Long-range magnetic order develops below 13 K with an incommensurate cycloidal structure.

The magnetic form factor indicates spins are distributed over the V$_4$ molecular unit.

The ferromagnetic phase exhibits spins aligned along the [1,1,1] direction with large anisotropy.

Abstract

We have carried out neutron diffraction and small angle neutron scattering measurements on a high quality single crystal of the cubic lacunar spinel multiferroic, GaV$_4$S$_8$, as a function of magnetic field and temperature to determine the magnetic properties for the single electron that is located on the tetrahedrally coordinated V$_4$ molecular unit. Our results are in good agreement with the structural transition at 44 K from cubic to rhombohedral symmetry where the system becomes a robust ferroelectric, while long range magnetic order develops below 13 K in the form of an incommensurate cycloidal magnetic structure, which can transform into a N\'eel-type skyrmion phase in a modest applied magnetic field. Below 5.9(3) K, the crystal enters a ferromagnetic phase, and we find the magnetic order parameter indicates a long range ordered ground state with an ordered moment of 0.23(1) ${\mu}_\mathrm{B}$ per V ion. Both polarized and unpolarized neutron data in the ferroelectric-paramagnetic phase have been measured to determine the magnetic form factor. The data are consistent with a model of the single spin being uniformly distributed across the V$_4$ molecular unit, rather than residing on the single apical V ion, in substantial agreement with the results of first-principles theory. In the magnetically ordered state, polarized neutron measurements are important since both the cycloidal and ferromagnetic order parameters are clearly coupled to the ferroelectricity, causing the structural peaks to be temperature and field dependent. For the ferromagnetic ground state, the spins are locked along the $[1,1,1]$ direction by a surprisingly large anisotropy.