Quantum spin liquid involves fractionalized quasipariticles such as spinons and visons. They are expressed as itinerant Majorana fermions and Z 2 fluxes in the Kitaev model with bond-dependent exchange interactions on a honeycomb spin lattice 1 . The observation has recently attracted attention for a candidate material α-RuCl 3 , showing spin liquid behaviour induced by a magnetic field 2-13 . Since the observable spin excitation is inherently composed of the two quasiparticles, which further admix each other by setting in the magnetic field as well as non-Kitaev interactions 14-17 , their individual identification remains challenging. Here we report an emergent low-lying spin excitation through nuclear magnetic and quadrupole resonance measurements down to ∼ 0.4 K corresponding to 1/500 of the exchange energy under the finely tuned magnetic field across the quantum critical point. We determined the critical behaviour of low-lying excitations and found evolution of two kinds of the spin gap at high fields. The two excitations exhibit repulsive magnetic field dependence, suggesting anti-crossing due to the hybridization between fractionalized quasiparticles.
The microscopic mechanism of the metal-insulator transition is studied by orbital-resolved ^{51}V NMR spectroscopy in a prototype of the quasi-one-dimensional system V6O13. We uncover that the transition involves a site-selective d orbital order lifting twofold orbital degeneracy in one of the two VO6 chains. The other chain leaves paramagnetic moments on the singly occupied d(xy) orbital across the transition. The two chains respectively stabilize an orbital-assisted spin-Peierls state and an antiferromagnetic long-range order in the ground state. The site-selective Mott transition may be a source of the anomalous metal and the Mott-Peierls duality.
LiVO 2 is a model system of the valence bond solid (VBS) in 3d 2 triangular lattice. The origin of the VBS formation has remained controversial. We investigate the microscopic mechanism by elucidating the d orbital character via on-site 51 V NMR measurements in a single crystal up to 550 K across a structural transition temperature T c . The Knight shift, K, and nuclear quadrupole frequency, δν, show that the 3d orbital with local trigonal symmetry are reconstructed into a d yz d zx orbital order below T c . Together with the NMR spectra with three-fold rotational symmetry, we confirm a vanadium trimerization with d-d σ bonds. The Knight shift extracts the large Van-Vleck orbital susceptibility, χ VV = 3.6 × 10 −4 , in a paramagnetic state above T c , which is comparable to the spin susceptibility. The results suggest that orbitally induced Peierls transition in the proximity of the frustrated itinerant state is the dominant driving force of the trimerization transition. PACS numbers: 71.30.+h, 75.40.Gb Valence bond ordering in two-and three-dimensional systems is a manifestation of geometrical frustration.1 Across Mott transition, a valence bond solid (VBS) phase resides nearby unconventional metal 2,3 and superconducting phases 3 in triangular lattice systems. The VBS transition can accompany by d orbital orders with versatile textures, depending on lattice geometry and band filling. 4-9 However, d orbital orders governed by frustrated intersite interactions are not apparent from lattice distortions and need to be detected by microscopic probes. Here we show a tool for detailed characterization of d 2 orbital ordering in a model material LiVO 2 with the triangular lattice.ABX 2 (A:alkali metal; B: transition metal; X: chalcogen ion) with an ordered lock-type structure is a prototype of triangular-lattice antiferromagnet. 9 For Ti 3+ and V 3+ , t 2g orbital degrees of freedom play crucial roles in determining magnetic ground states. Among ABX 2 , LiVO 2 has been extensively investigated as a candidate of VBS.10-14 The crystal structure is comprised of the triangular lattice of V 3+ (3d 2 ) ions in a rhombohedral R3c structure [ Fig. 1(a)]. A trigonal elongation of VO 6 along the c axis splits the t 2g sublevel into a lower a 1g singlet and an upper e15 Calculated orbital occupations are almost equivalent in the a 1g and e ′ g orbitals due to the small trigonal field of 25 meV compared to the bandwidth.15 Below a first-order structural transition temperature T c ∼ 450-500 K, a superlattice Fig. 1(a)] appears in x-ray and electron diffraction measurements.11-14 Recent pair distribution function analyses of synchrotron data propose lowersymmetry lattice distortions depending on the layers. 16 Although the way of displacements of vanadium ions is compatible to trimerization, 12,13,16 the orbital character has not been accessible by the diffraction measurements due to Li deficiency and crystal twinning. Thus, the origin of the spin-singlet state in LiVO 2 remains controversial and to be elucidated via direct obse...
Spin-state crossover beyond a conventional ligand-field theory has been a fundamental issue in condensed matter physics. Here, we report microscopic observations of spin states and low-energy dynamics through orbital-resolved NMR spectroscopy in the prototype compound LaCoO_{3}. The ^{59}Co NMR spectrum shows the preserved crystal symmetry across the crossover, inconsistent with d orbital ordering due to the Jahn-Teller distortion. The orbital degeneracy results in a pseudospin (J[over ˜]=1) excited state with an orbital moment observed as ^{59}Co hyperfine coupling tensors. We found that the population of the excited state evolves above the heart crossover temperature. The crossover involves critical spin-state fluctuations emerging under the magnetic field. These results suggest that the spin-state crossover can be mapped into a statistical problem, analogous to the supercritical liquid in liquid-gas transition.
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