Magnons and a two-component spin gap in ${\mathrm{FeV}}_2{\mathrm{O}}_4$

The spinel vanadates have become a model family for exploring orbital order on the frustrated pyrochlore lattice, and recent debate has focused on the symmetry of local crystal fields at the cation sites. Here, we present neutron scattering measurements of the magnetic excitation spectrum in ${\mathrm{FeV}}_2{\mathrm{O}}_4$, a recent example of a ferrimagnetic spinel vanadate which is available in single-crystal form. We report the existence of two emergent magnon modes at low temperatures, which draw strong parallels with the closely related material, ${\mathrm{MnV}}_2{\mathrm{O}}_4$. We were able to reproduce the essential elements of both the magnetic ordering pattern and the dispersion of the inelastic modes with semiclassical spin-wave calculations, using a minimal model that implies a sizable single-ion anisotropy on the vanadium sublattice. Taking into account the direction of ordered spins, we associate this anisotropy with the large trigonal distortion of VO${}_6$ octahedra, previously observed via neutron powder diffraction measurements. We further report on the spin gap, which is an order of magnitude larger than that observed in ${\mathrm{MnV}}_2{\mathrm{O}}_4$. By looking at the overall temperature dependence, we were able to show that the gap magnitude is largely associated with the ferro-orbital order known to exist on the iron sublattice, but the contribution to the gap from the vanadium sublattice is in fact comparable to what is reported in the Mn compound. This reinforces the conclusion that the spin canting transition is associated with the ordering of vanadium orbitals in this system, and closer analysis indicates closely related physics underlying orbital transitions in ${\mathrm{FeV}}_2{\mathrm{O}}_4$ and ${\mathrm{MnV}}_2{\mathrm{O}}_4$.

Figure 1

(a) Heat capacity and magnetization data for the single-crystal sample from the current neutron scattering study. Peaks in heat capacity identify transitions at 138, 107, and 60 K. Magnetization was measured under field-cooled [upper solid (blue) line] and zero-field-cooled [lower solid (red) line] conditions, with the field oriented along the cubic (001) direction. (b) Variation of the structural (400) Bragg peak, as measured by elastic neutron scattering. Temperatures were chosen in each of the previously identified phases. Solid lines are fits to Gaussian curves. (c), (d) Elastic scattering intensity of the cubic (220) position (c), reflecting the square magnitude of ordered moments on the Fe${}^{2+}$ sublattice, and the cubic (200) position (d), reflecting the canting component of spins on the V${}^{3+}$ sublattice; data were measured using the HB3 (c) and the CTAX (d) triple-axis spectrometers. Solid lines represent fits to Eq. (1) and are discussed in the text.

Figure 2

(a)–(d) Contour plots of neutron scattering intensity in several energy-momentum transfer planes, showing the Q dependence of magnon excitations along several symmetric directions in reciprocal space. Especially notable are the dispersive magnetic excitations which arise about points (2 0 0) and (4 0 0) and symmetric equivalents. (e) Plot of scattering intensity versus (H 0 0) in the energy range $E=8$–16 meV, revealing peaks at ($-$4 0 0) and ($\pm$2 0 0). (f) Plot of scattering intensity versus energy transfer at (2 2 0) and (2 0 0). In all plots, we use the high-temperature cubic basis to index the reciprocal lattice cell.

Figure 3

(a)–(c) Plots of inelastic neutron scattering intensity along the line (2 H 0) in reciprocal space, as measured with the SEQUOIA spectrometer. Shown are data taken at (a) $T=4$ K, (b) $T=85$ K, and (c) $T=125$ K. Solid lines are spin-wave fits described in the text. Curves in (b) are shifted by 5 meV. (d) Plots of neutron scattering intensity versus energy transfer for all three temperatures at the point (2 2 0).

Figure 4

(a) Constant-Q scans on the HB3 triple-axis spectrometer at the cubic (2 2 0) position. Shown are scans at temperatures above and well below the ordering temperatures in ${\mathrm{FeV}}_2{\mathrm{O}}_4$ on logarithmic (inset) and linear (main panel) scales. (b) Constant-Q scans at the (2 0 0) and (2 4 0) positions, which are symmetrically equivalent. (c), (d) Temperature evolution of the constant-Q scans at (2 2 0), as measured with the HB3 (c) and CTAX (d) spectrometers.

Figure 5

Temperature dependence of the excitation gap at the cubic (2 2 0) position in ${\mathrm{FeV}}_2{\mathrm{O}}_4$. Included are data from the HB3 (diamonds) and CTAX (circles) spectrometers. Lines are fits to the power-law temperature dependence, assuming one (dashed) or two (solid) order parameters. The latter was a better description of the data, and the parameters from that fit are shown explicitly.