Orbital ordering and spin-singlet clusters in triangular-based vanadates

We report ⁵¹V NMR spectra in the triangular-lattice vanadates, AV₁₀O₁₅, (3d^2.2), AV₁₃O₁₈ (3d^2.38), and A₂V₁₃O₂2 (3d ^1.92) (A = Ba, Sr). These compounds have orbital degrees of freedom and itinerant electrons arising from the partially occupied t_2g bands. We show microscopic observations of spin-singlet trimers and antiferromagnetic tertramers with orbital orders in BaV₁₀O ₁₅, but no indication of the orbital order and the spin singlet in SrV₁₀O₁₅. The paramagnetic and nonmagnetic spins coexist in BaV₁₃O₂2 but only the nonmagnetic spins are present in AV₁₃O₁₈ (A = Ba, Sr). The spin singlet formation in the incommensurate band filling is understood as the incommensurate charge-density wave induced by the 3d orbital order.