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

We have carried out neutron diffraction and small-angle neutron scattering measurements on a high-quality single crystal of the cubic lacunar spinel multiferroic, ${\mathrm{GaV}}_4{\mathrm{S}}_8$, as a function of magnetic field and temperature to determine the magnetic properties for the single electron that is located on the tetrahedrally coordinated ${\mathrm{V}}_4$ 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 Néel-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 ${\mathrm{V}}_4$ 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.

Figure 1

(a) Crystal structure of ${\mathrm{GaV}}_4{\mathrm{S}}_8$ in the cubic phase and (b) rhombohedral phase, where the apical V2 becomes inequivalent to the three V1 ions. (c) The effective “cubic” lattice parameters from neutron-diffraction data. The inset is a contour plot of the neutron diffraction data for the (3, 3, 3) Bragg peak as it splits with temperature below the cubic to rhombohedral phase transition.

Figure 2

Small-angle scattering measurements of the wave vector and intensity of the cycloid as a function of temperature and magnetic field. (a) Integrated intensity of one of the peaks, with the solid curve a simple fit to mean field theory to estimate the ordering temperature of 12.8(3) K. The inset shows a typical example of the observed SANS data, with some background intensity around the beam stop in the center and six diffraction peaks from different domains of the cycloid. Labels 1 and 2 are a reference to where the other data in this figure were taken. Sector averages were taken $\pm {11}^{\circ }$ about the centers of these peaks. (b) Wave vector of the cycloid is strongly temperature dependent, while (c) it is essentially independent of applied magnetic field. (d) The intensity, on the other hand, is strongly field dependent.

Figure 3

(a) Magnetic intensity of the (1,1,1)-type Bragg reflections at 20 K. Unpolarized neutron data are plotted against magnetic moment squared per V atom, $M^2$ (${\mu }_B^2$/V), on the left axis, where the solid line is a guide to the eye. This result was confirmed by employing polarized neutron measurements, shown by the solid squares and plotted against magnetic moment per V atom, $M$ (${\mu }_B$/V), up to the maximum field for this technique of 2 T. (b) Magnetic form factor obtained from the polarized beam data plotted against moment per ${\mathrm{V}}_4$ cluster and using the assumption that the electron is equally likely to be found on the 4 V. The solid curve is the spherical average form factor for a singly ionized V atom. This function was fit to the data, and both data and function are scaled by the saturated moment at high field. (c) Alternative extracted form factor assuming the electron is localized on the apical V, where the solid curve is the spherical average for a singly ionized V atom. This function was fit to the data and both data and function are scaled by the saturated moment at high field.

Figure 4

(a) Magnetic form factor determined at 15 K, showing that the assumption of all 4 V having approximately the same moment provides a substantially better description of the data than the assumption that all the moment resides solely on the apical V. The solid curve is the spherical average form factor for a singly ionized V atom. This function was fit to the 4 V modeled data, and both data and function are scaled to match the saturated moment at high field. The dashed curve is also the spherical average form factor for a singly ionized V atom but was fit to the apical only model. This curve and data were scaled by the same factor as for the 4 V data. (b) Field-induced intensity for the ($2,0,0$) peak at 15 K, just above the cycloidal ordering temperature. The intensity first decreases with field, indicating that the structural intensity is field dependent at this temperature.

Figure 5

(a) Temperature dependence of the integrated intensity of the (1,1,1) peak. The solid curve is a fit to mean-field theory to estimate the Curie temperature of 5.9 K. (b) Polarized beam data of the (1,1,1) peak showing a splitting of the ($++$) and ($--$) scatterings at the ferromagnetic transition. The spin-flip scattering shows that the beam is becoming depolarized below the transition with just a guide field applied to the sample. (c), (d) Ground-state (3 K) polarized beam data with high instrumental resolution for the cubic (1,1,1) peak, which splits into the ${(1,1,1)}_r$ peak from rhombohedral domain 1 (d1) and the ${(0,0,-1)}_r$, ${(0,-1,0)}_r$, and ${(-1,0,0)}_r$ peaks from rhombohedral domains 2, 3, and 4 (d2–d4), respectively. Essentially, all the magnetic intensity occurs on the d2–d4 peaks even with a 2 T vertical field applied, indicating that the magnetic anisotropy is large enough that the field is insufficient to rotate the spins fully along the vertically applied field direction.