Spontaneous Formation of Vanadium “Molecules” in a Geometrically Frustrated Crystal: ${\mathrm{AlV}}_2{\mathrm{O}}_4$

We investigated the charge-ordered (CO) state in spinel ${\mathrm{AlV}}_2{\mathrm{O}}_4$ by electron diffraction, synchrotron x-ray diffraction, and magnetic measurements. It was found that the CO structure appearing below 700 K is characterized by the formation of V clusters (heptamers), each of which is consisting of 7 vanadium atoms and is in a spin-singlet state as a total. Theoretical consideration indicates that this unique molecularlike V heptamer is stabilized by a strong bonding of vanadium $t_{2g}$ orbitals.

Figure 1

(a) Complete reciprocal lattice in the CO phase of ${\mathrm{AlV}}_2{\mathrm{O}}_4$. Large and small circles show fundamental spots due to the cubic spinel structure ($Fd\overline{3}m$ indexing) and superlattice spots at $1/2$ $1/2$ $1/2$-type positions, respectively. The solid line is a guide to the eye. (b) Thick solid lines indicate the rhombohedral unit cell in the CO phase. The small cubic (8 of which forms large cubic) refers to the unit cell of original cubic spinel lattice. Small circles depicted Al ions. (c) Portion of the Rietveld fit of the synchrotron x-ray powder diffraction pattern for ${\mathrm{AlV}}_2{\mathrm{O}}_4$ at room temperature ($\lambda =0.12060\mathrm{nm}$.)

Figure 2

(a) The crystal structure in the CO phase of ${\mathrm{AlV}}_2{\mathrm{O}}_4$ are shown schematically. There are three inequivalent V ions (V1, V2, V3), and V-V bond lengths are substantially different. Heptamers, each of which is made of one V2 (red) and six V3 ions (blue) connected by the shorter V-V bonds (shown by red lines) can be seen. The V1 (yellow) is a left-alone ion from the heptamer formation. (b) Schematic electronic bonds in the heptamer are shown. There are six “intratrimer bonds” and three “intertrimer bonds” in one heptamer. Each bond consists of $d_{xy}$, $d_{yz}$, or $d_{yz}$ orbitals, as illustrated by different colors.

Figure 3

Temperature variation of inverse magnetic susceptibility for the parent compound, ${\mathrm{AlV}}_2{\mathrm{O}}_4$ (open circles), and three derivatives with no charge ordering, ${\mathrm{Al}}_{0.9}{\mathrm{Mg}}_{0.1}{\mathrm{V}}_2{\mathrm{O}}_4$ (thin dashed line), ${\mathrm{AlV}}_{1.8}{\mathrm{Cr}}_{0.2}{\mathrm{O}}_4$ (dotted line), ${\mathrm{AlV}}_2{\mathrm{O}}_{4.2}$ (dot-dashed line), and ${\mathrm{MgV}}_2{\mathrm{O}}_4$ (thin solid line). A thick solid line is the fitting of the ${\mathrm{AlV}}_2{\mathrm{O}}_4$ data by one Curie-Weiss term and one spin-gap term. The inset shows the magnetic susceptibility of ${\mathrm{AlV}}_2{\mathrm{O}}_4$ (open circles), its fitting (solid line), and two components of the fitting function, a Curie-Weiss term (dot-dashed line) and a spin-gap term (dotted line).