Orthorhombic distortion and orbital order in the vanadium spinel ${\mathrm{FeV}}_2{\mathrm{O}}_4$

Using synchrotron and neutron diffraction measurements, we find a low-temperature orthorhombic phase in vanadium spinel ${\mathrm{FeV}}_2{\mathrm{O}}_4$. The orbital order of ${\mathrm{V}}^{3+}$ ions with tetragonal normal modes occurs at 68 K, and this leads to an appearance of the pseudotetragonal phase at a noncollinear ferrimagnetic transition temperature. Below the magnetic transition temperature, unconventional behavior of the orbital state of ${\mathrm{Fe}}^{2+}$ ions accompanied by the emergence of the orthorhombic phase was observed by using the normal mode analysis. We have also studied the structural properties of orbitally diluted materials. The orthorhombic phase, which is significantly affected by the other ions, is intrinsic in ${\mathrm{FeV}}_2{\mathrm{O}}_4$. We suggest the orthorhombic phase is strongly related with the double orbital states of ${\mathrm{Fe}}^{2+}$ and ${\mathrm{V}}^{3+}$ ions.

Figure 1

Temperature dependence of the (a) SPD and NPD patterns around 440 cubic Bragg reflection. Rietveld fitting for (b) SPD pattern at 15 K and (c) NPD pattern at 2 K in ${\mathrm{FeV}}_2{\mathrm{O}}_4$. The crosses, solid lines, and bottom lines represent the observed intensities, the calculated ones, and the differences, respectively. The vertical bars show the position of Bragg peaks (for the NPD pattern, the long and short bars indicate the crystal and magnetic reflections, respectively) with the $Fddd$ space group. The temperature dependencies of (d) the ordered moment size on the ${\mathrm{Fe}}^{2+}$ and ${\mathrm{V}}^{3+}$ cation sites, (e) the magnetization (left axis) as well as the heat capacity (right axis), and (f) the lattice constants in ${\mathrm{FeV}}_2{\mathrm{O}}_4$. The lattice constant in the temperature range of $T_{\mathrm{S}2} \le T \le T_{\mathrm{N}2}$ was calculated by using the LTT model with the $I{4}_1/amd$ space group. Note that the lattice constants in the HTT and LTT phases are shown by the cubic axes for comparison. Typical errors of the lattice constants are less than the size of the data markers. Note that the moments below $T_{\mathrm{N}1}$ are calculated using the $Fddd$ model.

Figure 2

Normal mode analysis in the $Q_2-Q_3$ plane of the ${\mathrm{FeO}}_4$ tetrahedron (solid circles) and ${\mathrm{VO}}_6$ octahedron (squares) in the powder sample of ${\mathrm{FeV}}_2{\mathrm{O}}_4$. The triangles represent the $Q_2$ and $Q_3$ modes of the orthorhombic model for the P-tetra phase at $T_{\mathrm{S}2} < T < T_{\mathrm{N}2}$. Note that the $Q_2$ and $Q_3$ values, which are calculated from the SPD data, are only shown for clarity.

Figure 3

(a) Rietveld fitting by using the orthorhombic model around the 440 cubic Bragg peak for SPD patterns in ${\mathrm{FeV}}_2{\mathrm{O}}_4$ at 40 K. The subscripts “c” and “o” indicate the cubic and orthorhombic axes, respectively. (b) Temperature dependence of the ratio of the FWHM for ${440}_{\mathrm{c}}$ to that for ${044}_{\mathrm{c}}$ reflections. In the orthorhombic phases, the FWHM of the ${440}_{\mathrm{c}}$ reflection is expressed by overlapping the ${440}_{\mathrm{c}}$ and ${404}_{\mathrm{c}}$ reflections. (c) Rietveld analysis of ${\mathrm{FeV}}_2{\mathrm{O}}_4$ for the SPD pattern in the P-tetra phase at 40 K. The profiled-weighted $R$ factor $R_{\mathrm{WP}}$ and the $R$-Bragg factor $R_{\mathrm{I}}$ represent 4.45% and 2.55%, respectively. (d) Temperature dependencies of lattice constants for ${\mathrm{FeV}}_2{\mathrm{O}}_4$ considering the orthorhombic lattice in the P-tetra phase. Note that the lattice constant in the temperature range of $T_{\mathrm{S}2} \le T \le T_{\mathrm{N}2}$ was calculated by using P-tetra model with the $Fddd$ space group. The orbital states of ${\mathrm{Fe}}^{2+}$ ions and the spin alignments of ${\mathrm{Fe}}^{2+}$ and ${\mathrm{V}}^{3+}$ ions are also illustrated schematically.

Figure 4

(a) SPD patterns around the 440 cubic Bragg peak for ${\mathrm{Fe}}_{1-x}{\mathrm{Mn}}_x{\mathrm{V}}_2{\mathrm{O}}_4$ at 15 K. (b) Ratios of FWHM for the ${440}_{\mathrm{c}}$ reflection to that for the ${044}_{\mathrm{c}}$ reflection in ${\mathrm{Fe}}_{1-x}{\mathrm{Mn}}_x{\mathrm{V}}_2{\mathrm{O}}_4$ and $\mathrm{Fe}[{\mathrm{V}}_{2-x}{\mathrm{Fe}}_x]{\mathrm{O}}_4$.

Figure 5

(a) Normal mode analysis in the $Q_2-Q_3$ plane of the ${\mathrm{FeO}}_4$ tetrahedron and the ${\mathrm{VO}}_6$ octahedron for $\mathrm{Fe}\left[{\mathrm{V}}_{1.9}{\mathrm{Fe}}_{0.1}\right]{\mathrm{O}}_4$ and the ${\mathrm{Fe}}_{1+\delta }{\mathrm{V}}_{2-\delta }{\mathrm{O}}_4$ single crystal. Note that the $Q_2$ and $Q_3$ values in the single crystal are from Ref [11]. (b) $Q_2$ and $Q_3$ modes of the ${\mathrm{FeO}}_4$ tetrahedron for ${\mathrm{FeV}}_2{\mathrm{O}}_4, {\mathrm{Fe}[\mathrm{V}}_{1.9}{\mathrm{Fe}}_{0.1}]{\mathrm{O}}_4$, and ${\mathrm{Fe}}_{0.9}{\mathrm{Mn}}_{0.1}{\mathrm{V}}_2{\mathrm{O}}_4$. PC and SC denote the polycrystalline and the single-crystal samples, respectively.

Figure 6

The FZ equipment (a) before and (b) after crystal growth. The black powder attached on the surface of the quartz tube after the crystal growth.

Figure 7

(a) SPD patterns for the black powder and the outer and inner regions of the crystal. The Bragg peaks of black powder can be indexed as a cubic system with the space group $Im\overline{3}m$. The asterisks indicate the Bragg peaks derived from the impurity of ${\mathrm{V}}_2{\mathrm{O}}_3$. The inset shows the section of seed rods after crystal growth. (b) The ratio of Fe ($\alpha$) and V ($\beta$) cations was determined by the chemical composition analysis. Note that PC and SC denote the polycrystalline and the single-crystal samples, respectively.

Figure 8

(a) Single-crystalline synchrotron diffraction patterns around the 800 cubic Bragg peak. (b) Temperature dependencies of lattice constants. (c) Temperature dependencies of the magnetization and the specific heat for ${\mathrm{Fe}}_{1+\delta }{\mathrm{V}}_{2-\delta }{\mathrm{O}}_4$ single crystal [17]. Temperature dependencies of (d) the specific heat and (e) the lattice constant of the $a$ axis for single-crystal (SC) and polycrystalline (PC) ${\mathrm{FeV}}_2{\mathrm{O}}_4$ samples.