Small crystal distortion and long-range antiferro-orbital ordering in the spinel oxide $\mathrm{Co}{\mathrm{V}}_2{\mathrm{O}}_4$

In frustrated spinel oxide $\mathrm{Co}{\mathrm{V}}_2{\mathrm{O}}_4$, the knowledge of orbital, lattice, and spin structures has been fragmentary thus far. To investigate the structural and magnetic phase transitions in $\mathrm{Co}{\mathrm{V}}_2{\mathrm{O}}_4$, we performed high-resolution neutron powder diffraction, single crystal synchrotron radiation diffraction, and magnetization and specific heat measurements for high-quality samples. Extremely small crystal distortion from cubic to tetragonal phase ($1-c/a<0.06\%$) was observed using the high-resolution neutron diffraction measurement below $T^{*}\sim 95\mathrm{K}$, where a cusp was observed in the temperature dependence of magnetization. The single crystal diffraction experiment revealed that the structural phase transition accompanied by a change in the space group from $I{4}_1/amd$ to $I{4}_1/a$ occurred at $T_2=59\mathrm{K}$, where the phase transition was observed in the specific heat measurement. Crystal and magnetic structure analysis was carried out with the neutron data, and the results suggest that the magnetic phase transition from collinear to noncollinear magnetic ordering occurs at $T^{*}$ and the antiferro-orbital ordering occurs below $T_2$. We discuss the observed small crystal distortion and orbital characteristics in the light of the boundary between localization and delocalization.

Figure 1

Neutron diffraction pattern and the result of the Rietveld fitting of $\mathrm{Co}{\mathrm{V}}_2{\mathrm{O}}_4$ at 300 K obtained from the backward bank. The circles and solid lines are the observed and calculated intensities, respectively, and the vertical bars and bottom curves are the peak positions and differences between the observed and calculated intensities, respectively.

Figure 2

Temperature dependences of (a) specific heat $C_{\mathrm{p}}$ for cooling and heating processes, (b) magnetization $M$ for zero-field cooling (ZFC), field cooling (FC), and field warming (FW) processes for the polycrystalline sample of $\mathrm{Co}{\mathrm{V}}_2{\mathrm{O}}_4$.

Figure 3

(a) Neutron diffraction patterns of $\mathrm{Co}{\mathrm{V}}_2{\mathrm{O}}_4$ at 171, 81, and 12 K obtained from the 90° bank. (b) Temperature dependences of integrated intensities of the 111 and 220 reflections.

Figure 4

Temperature dependences of the peak profiles around (a) 222 and (b) 400 reflections and (c) FWHM of the 222 and 400 peaks obtained from the high-resolution area of the PSDs for the backward bank.

Figure 5

Results of the Le Bail fitting of the data at 58 K by assuming that the crystal symmetries are (a) cubic and (b) tetragonal. The insets represent the fitting results around the cubic Bragg 400 peaks, where the subscript “c” indicates the index based on the pseudocubic axes. (c) Temperature dependence of the GOF for the Le Bail analysis under the assumption of cubic and tetragonal crystal symmetries. (d) Temperature dependence of the lattice constant obtained by the Le Bail fitting, where the typical errors are less than the size of the marks.

Figure 6

Simulation of peak profiles (solid lines) of the 400 reflection for the resolution $\mathrm{\Delta }d/d$ of (a) 0.07% and (b) 0.2% on the assumption that the lattice distortion of $c_{\mathrm{c}}/a_{\mathrm{c}}=0.99936$ occurs. Red and blue broken lines represent ${400}_{\mathrm{c}}$ and ${004}_{\mathrm{c}}$ reflections, respectively, where the subscript “c” denotes the indices base on the pseudocubic axes. The FWHM's for ${400}_{\mathrm{c}}$ and ${004}_{\mathrm{c}}$ peaks of (a) and (b) are 0.0021 and $0.0060{\AA }^{-1}$, respectively, and the apparent FWHM's of the peaks represented by arrows of (a) and (b) are 0.0032 and $0.0063{\AA }^{-1}$, respectively.

Figure 7

Temperature dependences of synchrotron diffraction patterns of (a) ${311}_{\mathrm{c}}$ and (b) ${640}_{\mathrm{c}}$ reflections of the single crystal.

Figure 8

Temperature dependences of (a) atomic distances between metal atoms and oxygen and (b) each component of magnetic moment. (c) The magnetic structure at the lowest temperature.

Figure 9

Temperature dependences of (a) the $Q_2,Q_3$, and (b) the $Q_t$ modes, and (c) normal mode analysis in the $Q_2\text{−}{Q}_3$ plane of the $\mathrm{V}{\mathrm{O}}_6$ octahedron. The triangle shows the value of $Q_2\text{−}{Q}_3$ for $\mathrm{Mn}{\mathrm{V}}_2{\mathrm{O}}_4$ referred by the study [25]. (d) Schematic model of the antiferro-OO.