We report the observation of magnetic superstructure in a magnetization plateau state of SrCu 2 (BO 3 ) 2 , a frustrated quasi-two-dimensional quantum spin system. The Cu and B nuclear magnetic resonance (NMR) spectra at 35 millikelvin indicate an apparently discontinuous phase transition from uniform magnetization to a modulated superstructure near 27 tesla, above which a magnetization plateau at 1/8 of the full saturation has been observed. Comparison of the Cu NMR spectrum and the theoretical analysis of a Heisenberg spin model demonstrates the crystallization of itinerant triplets in the plateau phase within a large rhomboid unit cell (16 spins per layer) showing oscillations of the spin polarization. Thus we are now in possession of an interesting model system to study a localization transition of strongly interacting quantum particles.Published in Science 298, 395 (2002).

NMR and magnetization measurements in Li2VOSiO4 and Li2VOGeO4 are reported. The analysis of the susceptibility shows that both compounds are two-dimensional S = 1/2 Heisenberg antiferromagnets on a square lattice with a sizable frustration induced by the competition between the superexchange couplings J1 along the sides of the square and J2 along the diagonal. Li2VOSiO4 undergoes a low-temperature phase transition to a collinear order, as theoretically predicted for J2/J1>0.5. Just above the magnetic transition the degeneracy between the two collinear ground states is lifted by the onset of a structural distortion.

The main characteristic of Mott insulators, as compared to band insulators, is to host low-energy spin fluctuations. In addition, Mott insulators often possess orbital degrees of freedom when crystal-field levels are partially filled. While in the majority of Mott insulators, spins and orbitals develop long-range order, the possibility for the ground state to be a quantum liquid opens new perspectives. In this paper, we provide clear evidence that the spin-orbital SUð4Þ symmetric Kugel-Khomskii model of Mott insulators on the honeycomb lattice is a quantum spin-orbital liquid. The absence of any form of symmetry breakinglattice or SUðNÞ-is supported by a combination of semiclassical and numerical approaches: flavor-wave theory, tensor network algorithm, and exact diagonalizations. In addition, all properties revealed by these methods are very accurately accounted for by a projected variational wave function based on the -flux state of fermions on the honeycomb lattice at 1=4 filling. In that state, correlations are algebraic because of the presence of a Dirac point at the Fermi level, suggesting that the symmetric Kugel-Khomskii model on the honeycomb lattice is an algebraic quantum spin-orbital liquid. This model provides an interesting starting point to understanding the recently discovered spin-orbital-liquid behavior of Ba 3 CuSb 2 O 9 . The present results also suggest the choice of optical lattices with honeycomb geometry in the search for quantum liquids in ultracold four-color fermionic atoms.

Below Eq. (2) in Ref. [1], there is a misprint in the formula relating the scalar product of spin and quadrupolar operators to the permutation operator. The sign in front of the permutation is wrong, and the correct formula readsAs it is written in the Letter, Eq. (5) is valid for pure quadrupolar states (real d 0 s), but not for the general case of complex d 0 s. The correct form of Eq. (5) for the general case readsThis does not affect any of the results reported in the Letter. We have only used this equation to discuss the relationship between the sign of the biquadratic coupling and the type of quadrupolar order (ferroquadrupolar versus antiferroquadrupolar). The determination of the phase diagram has been performed using a different parametrization.