Persistent three- and four-atom orbital molecules in the spinel $\mathrm{Al}{\mathrm{V}}_{2}{\mathrm{O}}_{4}$

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Persistent three- and four-atom orbital molecules in the spinel $Al V_{2} O_{4}$

Alexander J. Browne, Simon A. J. Kimber, and J. Paul Attfield

Phys. Rev. Materials 1, 052003(R) – Published 31 October 2017

Abstract

Electronic instabilities in transition-metal compounds may lead to ground states containing orbital molecules when direct metal-metal orbital interactions occur. The spinel $Al V_{2} O_{4}$ was reported to contain $V_{7}^{17 +}$ orbital heptamers that emerge below a 700 K charge ordering transition. Our x-ray total scattering analysis of $Al V_{2} O_{4}$ between 300 and 1100 K reveals a very different picture as the postulated heptamers are found to be pairs of spin-singlet $V_{3}^{9 +}$ trimers and $V_{4}^{8 +}$ tetramers, and these orbital molecules persist to at least 1100 K in a disordered high-temperature cubic phase.

Received 15 August 2017

DOI:https://doi.org/10.1103/PhysRevMaterials.1.052003

Physics Subject Headings (PhySH)

Charge order Orbital order

Oxides

X-ray pair-distribution function analysis

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Alexander J. Browne¹, Simon A. J. Kimber², and J. Paul Attfield^1,*

¹Centre for Science at Extreme Conditions and School of Chemistry, University of Edinburgh, West Mains Road, Edinburgh EH9 3FD, United Kingdom
²Chemical and Engineering Materials Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

^*j.p.attfield@ed.ac.uk

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Vol. 1, Iss. 5 — October 2017

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Figure 1
Structural models for $Al V_{2} O_{4}$ where Al/V/O are green/blue/red atoms. (a) The cubic spinel structure, showing nearest-neighbor V-V connections, which are all equivalent. (b) The previously reported $V_{7}$ cluster model with $R \bar{3} m$ symmetry. The three symmetry-independent vanadium sites are labeled: Site V1 is occupied by paramagnetic $V^{3 +}$ cations, while each heptamer comprises a central V2 atom between two triangles of V3 atoms. (c) The $R 3 m$ model used for PDF fitting, in which $V_{3}$ and $V_{4}$ orbital molecules have long-range ferroelectric order. (d) The split-site $R \bar{3} m$ model used to describe the disordered antiferroelectric average crystal structure in the Rietveld fits. (e) A local configuration showing a statistical distribution of the clusters corresponding to the split-site average in (d). The rhombohedral unit cells in (b)–(e) are projected on the (110) plane with the $c$ axis vertical, and short $(< 2.90 Å)$ orbital molecule V-V distances are shown.
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Figure 2
Comparisons of fits to pair distribution functions (PDFs) of $Al V_{2} O_{4}$ where nearest-neighbor V-V distances lie in the shaded region at $r = 2.4 - 3.2 Å$ . The local vanadium species in each structural model are shown to the right. (a) 300 K PDF, where the upper fit (residual $R_{w} = 16.3 %)$ of the $R \bar{3} m$ $V_{7}$ heptamer model [Fig. 1] agrees poorly in the V-V region, but allowing the central V to move off center to form $V_{3}$ and $V_{4}$ orbital molecules in the $R 3 m$ model [Fig. 1] gives the improved fit shown below $(R_{w} = 13.6 %)$ . (b) 1100 K PDF, where the upper fit of the ideal cubic $F d \bar{3} m$ spinel model [Fig. 1] gives a poor fit in the shaded region $(R_{w} = 16.6 %)$ , but the lower fit of $V_{3}$ and $V_{4}$ orbital molecules in a $R 3 m$ model [Fig. 1] constrained by metrically cubic cell parameters greatly improves the agreement $(R_{w} = 11.6 %)$ .
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Figure 3
(a) Comparison of V-V nearest-neighbor distances in $Al V_{2} O_{4}$ from PDF fits (solid symbols) using the $R 3 m$ structural description, and Rietveld analyses (open symbols) using the split-site $R \bar{3} m$ and cubic $F d \bar{3} m$ spinel models respectively below and above $T_{CO} = 700 K$ . Rietveld V-V distances all converge to a single value above $T_{CO}$ because disordered orbital molecules are not described by a cubic average spinel structure, but PDF fitting shows that they persist above $T_{CO}$ . (The two bonding V-V distances were constrained to be equal in the PDF fits above $T_{CO}$ for refinement stability.) (b) Displacements of V atoms from their ideal sites due to orbital molecule formation, from PDF (solid symbols) and the split-site Rietveld (open symbols) analyses. Both sets of displacements decrease smoothly on heating, but evidence the persistence of orbital molecules to 1100 K.
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Physical Review Materials

Persistent three- and four-atom orbital molecules in the spinel AlV2O4

Alexander J. Browne, Simon A. J. Kimber, and J. Paul Attfield

Phys. Rev. Materials 1, 052003(R) – Published 31 October 2017

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Persistent three- and four-atom orbital molecules in the spinel $Al V_{2} O_{4}$