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When a one-dimensional band is partially filled with electrons in a one-dimensional lattice, the lattice undergoes Peierls distortion with a new periodicity that can create a bandgap at the Fermi level. When the one-dimensional band is half(quarter)-filled, the Peierls distortion results in a two(four)-fold periodicity of the original lattice. Spinel-type transition metal compounds with partially filled xy, yz, or zx orbitals often exhibit lattice distortions that can be interpreted as Peierls distortions of one-dimensional xy bands along the (1,1,0) and (1,-1,0) chains, yzbands along the (0,1,1) and (0,1,-1) chains, or zx bands along the (1,0,1) and (1,0,-1) chains of the pyrochlore lattice formed by the transition metal sites. For example, in CuIr₂S₄, the Ir pyrochlore lattice undergoes octamerization because of Peierls distortion (Ir–Ir dimerization), and it displays a four-fold periodicity along the (1,1,0) and (1,-1,0) directions, which are selected by the Ir 5d orbital polarization (in which only the xy band is partially filled). This microscopic description of multimer formation is called the orbitally-induced Peierls mechanism.

In spinel-type AlV₂O₄, the vanadium pyrochlore lattice contains vanadium trimers and tetramers. It is difficult to describe this complicated distortion using the orbitally-induced Peierls mechanism. Using hard-X-ray photoemission spectroscopy (HAXPES) performed at SPring-8, Okawa et al. showed that V²⁺and V³⁺ coexisted in a 1:1 ratio in AlV₂O₄. The main and shoulder peaks of the V 2p_3/2 core-level HAXPES spectra were assigned to V²⁺ with a d³configuration and V³⁺ with a d² configuration, respectively. Based on the charge disproportionation of V²⁺:V³⁺=1:1, the formation of V trimers and tetramers in AlV₂O₄ is explained by an orbitally-induced Peierls mechanism, in which the half-filled xy, yz, and zx bands along the (1,-1,0), (0,1,-1), and (-1,0,1) chains yield V³⁺ trimers. The extra electrons of V²⁺ are accommodated in the xy, yz, and zxbands along the (1,1,0), (0,1,1), and (1,0,1) chains, thereby creating quarter-filled bands. The short V–V bonds were created by Peierls distortions with a four-fold periodicity and connected to the trimers. Half of the V³⁺(d²) trimers were transformed into V²⁺(d³) tetramers. This work suggests that the interaction between the charge and orbital degrees of freedom plays a vital role in the multimer formation of various transition metal compounds.

(Written by T. Mizokawa and T. Saitoh on behalf of all the authors)