Orbital molecules in vanadium oxide spinels

X-ray scattering and magnetization measurements have been used to explore the extent of orbital molecule formation in a variety of $A{\mathrm{V}}_2{\mathrm{O}}_4$ vanadium oxide spinels. Zn doping suppresses the long-range order of trimer-tetramer pairs that occurs in $\mathrm{Ga}{\mathrm{V}}_2{\mathrm{O}}_4$, but disordered orbital molecules are found across most of the $\mathrm{Z}{\mathrm{n}}_x\mathrm{G}{\mathrm{a}}_{1-x}{\mathrm{V}}_2{\mathrm{O}}_4$ series ($0.06\le x<0.875$). Orbital molecules are not observed in the ground states of $\mathrm{Zn}{\mathrm{V}}_2{\mathrm{O}}_4, \mathrm{Mg}{\mathrm{V}}_2{\mathrm{O}}_4$, or $\mathrm{Li}{\mathrm{V}}_2{\mathrm{O}}_4$ but are likely present in $\mathrm{L}{\mathrm{i}}_{0.5}\mathrm{G}{\mathrm{a}}_{0.5}{\mathrm{V}}_2{\mathrm{O}}_4$, an analog of the former two materials. The ratio of observed to ideal values of the V-V nearest-neighbor distance has been used to rationalize these observations.

Figure 1

(a) Ideal $A{\mathrm{V}}_2{\mathrm{O}}_4$ spinels adopt a cubic $Fd\overline{3}m$ crystal structure in which the $A$-site (green) and vanadium (blue) cations are tetrahedrally and octahedrally coordinated by oxide anions (red), respectively. Each $\mathrm{V}{\mathrm{O}}_6$ octahedron shares edges with six neighbors, such that the vanadium cations themselves form (b) a pyrochlore sublattice of corner-sharing tetrahedra. (c) In $\mathrm{Al}{\mathrm{V}}_2{\mathrm{O}}_4$ and $\mathrm{Ga}{\mathrm{V}}_2{\mathrm{O}}_4, {{\mathrm{V}}_3}^{9+}$ trimers and ${{\mathrm{V}}_4}^{8+}$ tetramers are formed through strong local V–V bonding interactions. In the ground state these order as trimer-tetramer pairs, although the weak interactions between pairs means that each can adopt one of two configurations (${\mathrm{V}}_3-{\mathrm{V}}_4$ or ${\mathrm{V}}_4-{\mathrm{V}}_3$) in (d) the $R\overline{3}m$ average structure. The three vanadium crystallographic sites in this structure are labelled.

Figure 2

Lattice parameters of $\mathrm{Z}{\mathrm{n}}_x\mathrm{G}{\mathrm{a}}_{1-x}{\mathrm{V}}_2{\mathrm{O}}_4$ phases with $x\le 0.125$, from Rietveld refinements of $R\overline{3}m$ ($a_H$ and $c_H$) and $Fd\overline{3}m$ ($a_C$) unit cells against x-ray total scattering data. The rapid suppression of the $R\overline{3}m-Fd\overline{3}m$ distortion at $T_{\mathrm{CO}}$ with increasing $x$ demonstrates that long-range orbital molecule order is highly sensitive to $A$-site disorder.

Figure 3

(a) Average-structure parameters across the $\mathrm{Z}{\mathrm{n}}_x\mathrm{G}{\mathrm{a}}_{1-x}{\mathrm{V}}_2{\mathrm{O}}_4$ system, from Rietveld fits to 90 K total scattering data. Phases with $x\le 0.04$ adopt $R\overline{3}m$ symmetry, which allows ${\mathrm{V}}_3-{\mathrm{V}}_4$ cluster pairs to establish long-range order through a displacive distortion of the ideal $Fd\overline{3}m$ lattice. For $x\ge 0.06$ there is no periodic distortion, but significant displacement of the vanadium cations from their ideal (zero-displacement) position indicates disorder in the average structure that arises from local symmetry lowering. In the inset, $R_w$ values of Rietveld fits with V fixed at its ideal position or displaced as a split site are shown. (b) Refined displacements of the V2 and V3 crystallographic sites of the $R3m$ structural model when fit to $\mathrm{Z}{\mathrm{n}}_x\mathrm{G}{\mathrm{a}}_{1-x}{\mathrm{V}}_2{\mathrm{O}}_4$ PDFs. These remain nonzero through the periodic distortion at low $x$, demonstrating that the orbital molecules persist through this distortion, although the critical-type decrease of the V2-site displacement when approaching $x=0.875$ evidences their eventual decomposition.

Figure 4

(a) Fits to the 5 K $x=0.125$ PDF. Although the average structure has $Fd\overline{3}m$ symmetry a fit of this model (upper, $R_w=28.9\%$) clearly shows that the local structure deviates from this, and is instead well-described by the $R3m$ model used to describe the local structure of $\mathrm{Ga}{\mathrm{V}}_2{\mathrm{O}}_4$ (lower, $R_w=15.9\%$). (b) Analogous fits to the 5 K $x=0.875$ PDF, demonstrating much less local deviation from the cubic average structure ($R_w=12.4\%$ for $Fd\overline{3}m$, upper; 10.0% for $R3m$, lower). (c) V-V distances in the local (filled symbols) and average (open symbols) structures of the $x=0$, 0.125, and 0.875 phases, which illustrate the evolution from a ground state of ordered orbital molecules to ones in which they are disordered, and eventually absent, as $x$ is increased.

Figure 5

(a) Magnetic susceptibilities of all synthesized $\mathrm{Z}{\mathrm{n}}_x\mathrm{G}{\mathrm{a}}_{1-x}{\mathrm{V}}_2{\mathrm{O}}_4$ phases. Their gradual variation with $x$ is consistent with the gradual changes found in the structural analysis. In the inset, the discontinuity seen in the $x=0.04$ susceptibility at $T_{\mathrm{CO}}=370\mathrm{K}$ is shown. Fits of these susceptibilities between 100 and 300 K with Eq. (1) determine (b) the parameters $A$, C, and θ, which vary as the V–V bonds found in $\mathrm{Ga}{\mathrm{V}}_2{\mathrm{O}}_4$ weaken then decompose as $x$ increases. The susceptibilities also all show a magnetic transition at temperature $T_{\mathrm{spin}}$, below which nonbonding V cations establish a spin-glass or antiferromagnetic ordered state. Also shown (red squares) are the parameters obtained from an analogous fit to the susceptibility of $\mathrm{L}{\mathrm{i}}_{0.5}\mathrm{G}{\mathrm{a}}_{0.5}{\mathrm{V}}_2{\mathrm{O}}_4$ [Fig. 8], which is isoelectronic with $\mathrm{Zn}{\mathrm{V}}_2{\mathrm{O}}_4$.

Figure 6

Phase diagram of the $\mathrm{Z}{\mathrm{n}}_x\mathrm{G}{\mathrm{a}}_{1-x}{\mathrm{V}}_2{\mathrm{O}}_4$ system. Orbital molecules (OMs) form in most compositions, although they only establish long-range order at low $T$ and when $A$-site disorder is minimal. V–V bonding weakens as $x$ increases and is fully suppressed near $x=0.875$. The orbitally ordered (OO) tetragonal ground state of $\mathrm{Zn}{\mathrm{V}}_2{\mathrm{O}}_4$ is established at low $T$ around $x=1$.

Figure 7

(a) Rietveld analysis of x-ray total scattering patterns of $\mathrm{Zn}{\mathrm{V}}_2{\mathrm{O}}_4$. The upper pattern was collected at 100 K and shows an $Fd\overline{3}m$ average structure ($R_w=2.08\%$) while the lower was collected at 10 K and shows an $I{4}_1/amd$ average structure ($R_w=1.96\%$). In the expanded region shown in the insets, the broadening of the cubic 400 ($Q=2.99{\AA }^{-1}$) and 331 ($Q=3.26{\AA }^{-1}$) reflections by the tetragonal distortion can be seen but the additional reflections of other proposed tetragonal symmetries cannot. (b) Fits to the 10 K x-ray PDF of $\mathrm{Zn}{\mathrm{V}}_2{\mathrm{O}}_4$. The upper fit is of an $I{4}_1/amd$ model in which the vanadium site has a fixed position ($R_w=12.0\%$) and the lower is of a $P{4}_1{2}_{1}2$ model in which it can displace ($R_w=10.9\%$).

Figure 8

(a) Rietveld fit to the powder-neutron-diffraction pattern of $\mathrm{L}{\mathrm{i}}_{0.5}\mathrm{G}{\mathrm{a}}_{0.5}{\mathrm{V}}_2{\mathrm{O}}_4$ collected at 4.2 K ($R_w=3.71\%$). Tick marks correspond to the $Fd\overline{3}m$ spinel phase (pink) and a ${\mathrm{V}}_2{\mathrm{O}}_3$ impurity with 2.2% weight fraction (gray). The additional reflections that would be allowed if the spinel phase adopted $F\overline{4}3m$ symmetry are not observed (expanded region shown in inset). (b) The cubic lattice parameter $a_C$ increases steadily between 4.2 and 300 K. However, its magnetic behavior shows a transition at $T_{\mathrm{spin}}=16\mathrm{K}$, and a fit of Eq. (1) between 100 and 300 K reveals similarity to the $\mathrm{Z}{\mathrm{n}}_x\mathrm{G}{\mathrm{a}}_{1-x}{\mathrm{V}}_2{\mathrm{O}}_4$ phases with disordered orbital molecule ground states [Fig. 5].

Figure 9

The PDFs of $\mathrm{Li}{\mathrm{V}}_2{\mathrm{O}}_4$ at 290 K (upper) and 5 K (lower). Both are well fit by an $Fd\overline{3}m$ model consistent with the average structure adopted over this temperature range ($R_w=11.6$ and 12.3%, respectively).

Figure 10

Phase diagram incorporating all $A{\mathrm{V}}_2{\mathrm{O}}_4$ spinels in this study. $d/d_{\mathrm{ideal}}$ is the ratio of observed to ideal values of the V-V nearest-neighbor distance as defined in the text, and $n$ is the average number of $d$ electrons per V cation. The shift in $d/d_{\mathrm{ideal}}$ for $\mathrm{Li}{\mathrm{V}}_2{\mathrm{O}}_4$ upon compression to 21 GPa, where V–V bond shortening and a low-temperature lattice distortion have been reported [50], is also shown.