Spin-singlet trimer state induced by competing orbital order in triangular-lattice BaV₁₀O₁₅

Local spin and orbital textures are investigated by 51V NMR measurements on a triangular-lattice compound BaV₁₀O₁₅ with orbital degrees of freedom and itinerant electrons. The Knight shift shows the spin-singlet V trimer formation in a itinerant phase above the semiconductor-insulator transition temperature T_SI=140 K. Below T_SI, the observation of the asymmetric electric hyperfine coupling tensor agrees with the orbital order giving direct d-d bonds of the trimer. The remaining paramagnetic spins on a V tetramer exhibit an antiferromagnetic long-range order accompanied by a ferro-type order. The coexistence of the trimer and tetramer with the two opposite magnetism is ascribed to the orbitally induced Peierls instability on a non-half-filling triangular lattice with nonuniform V-V separation.