We report a 51 V nuclear magnetic resonance investigation of the frustrated spin-1/2 chain compound LiCuVO4, performed in pulsed magnetic fields and focused on high-field phases up to 55 T. For the crystal orientations H c and H b we find a narrow field region just below the magnetic saturation where the local magnetization remains uniform and homogeneous, while its value is field dependent. This behavior is the first microscopic signature of the spin-nematic state, breaking spin-rotation symmetry without generating any transverse dipolar order, and is consistent with theoretical predictions for the LiCuVO4 compound.PACS numbers: 75.10. Kt, 75.30.Kz, The search for new states of quantum matter is one of the most active research fields in condensed-matter physics. In this respect frustrated magnetic systems attract a lot of interest as they accommodate various unconventional quantum states, having no direct classical analogues, ordered and disordered, induced by the competing interactions [1]. One particularly interesting state is the spin-nematic phase, in which the quantum magnet behaves like a liquid crystal. Taking an external magnetic field H as the reference direction, a spin-nematic phase is defined as a state without any transverse dipolar (i.e., vector-type) order, (−1) i S + i + H.c. = 0, but possessing instead a transverse quadrupolar (tensor-type) order,The quadrupolar order parameter develops on the bonds between neighboring spins and can be described as a condensate of two-magnon pairs. It breaks the spin-rotational symmetry about the magnetic field, but only partially as π-rotations transform the order parameter into itself. The also broken translational symmetry of the order parameter is invisible in the dipolar channel. There is also an analogy between the spin-nematic phase and the superconducting state: the nematic phase can be considered as a "bosonic" superconductor formed as a result of two-magnon condensation [1,2].The concept of a spin-nematic state was developed by Andreev and Grishchuk more than 30 years ago [3], which incited intense search for a realization in real materials. However, a definite experimental proof for the existence of such a phase has not been provided yet. Several magnetic insulators have been proposed as possible candidates, including the two-dimensional magnet NiGa 2 S 4 (spin-1 system) [4-6] and thin films of 3 He [7][8][9].In the past 10 years a large number of theoretical studies have supported the formation of the spinnematic phase in frustrated zig-zag 1D (chain) systems [10][11][12][13][14]. Amongst these, orthorhombic LiCuVO 4 is one of the most promising candidates [15,16]. It consists of spin-1/2 Cu 2+ chains along the orthorhombic b axis with a dominant nearest-neighbor ferromagnetic interaction J 1 = −1.6 meV, a frustrated next-nearest-neighbor antiferromagnetic interaction J 2 = 3.8 meV, and an interchain coupling J = −0.4 meV [17,18]. At zero magnetic field an incommensurate planar spiral structure is realized below T N = 2.3 K, having the moments lying...

By measuring the nuclear magnetic resonance (NMR) T −1 1 relaxation rate in the Br (bond) doped DTN compound, Ni(Cl1−xBrx)2-4SC(NH2)2 (DTNX), we show that the low-energy spin dynamics of its high magnetic field "Bose-glass" regime is dominated by a strong peak of spin fluctuations found at the nearly doping-independent position H * ∼ = 13.6 T. From its temperature and field dependence we conclude that this corresponds to a level crossing of the energy levels related to the doping-induced impurity states. Observation of the local NMR signal from the spin adjacent to the doped Br allowed us to fully characterize this impurity state. We have thus quantified a microscopic theoretical model that paves the way to better understanding of the Bose-glass physics in DTNX, as revealed in the related theoretical study [M. Dupont, S. Capponi, and N. Laflorencie, Phys. Rev. Lett. 118, 067204 (2017) The NiCl 2 -4SC(NH 2 ) 2 (DTN) compound [1], consisting of weakly coupled chains of S = 1 (Ni-ion) spins with an easy-plane single-ion anisotropy (D), is one of the most studied quantum spin materials [2]. Between the two critical magnetic fields H c1 and H c2 , it presents a magnetic-field-induced low-temperature (T ) 3D-ordered phase, described as a Bose-Einstein condensate (BEC) [2][3][4][5]. DTN is particularly convenient for studying this phase; for a magnetic field (H) applied along the chain c axis, its (body-centered) tetragonal symmetry [6] ensures the required axial symmetry of the spin Hamiltonian with respect to H. The values of its exchange couplings and [7,8] make the BEC phase easily accessible, with H c2 = 12.32 T [9-11] and the phase transition temperature T c below T cmax = 1.2 K. The system can be reasonably considered as quasi-one-dimensional (1D), with J a,b /J c = 0.08.Br-doped DTN, Ni(Cl 1−x Br x ) 2 -4SC(NH 2 ) 2 (DTNX), allows studying the effect of a bond disorder, which may lead to the appearance of a localized Bose-glass (BG) phases adjacent to the (now inhomogeneous) BEC phase [12], as suggested from the thermodynamic measurements [13]. The BG state, first discussed for quantum wires [14] and superfluid 4 He absorbed in porous media [15,16], remains elusive, with only a few experimental examples [17][18][19][20], particularly rare for condensed-matter systems in the thermodynamic limit [21], such as DTNX [13].We present here the first microscopic information on the high-field (H > H c2 ) disordered state in DTNX, where the low-energy spin fluctuations (dynamics) are measured by 1 H and 14 N nuclear spin-lattice relaxation rate (T −1 1 ), while the NMR spectra revealed the local spin polarization [22]. As compared to pure DTN, the main feature of spin dynamics in DTNX is a peak of T −1 1 appearing at H * ∼ = 13.6 T independently of the doping level. This is attributed to the level crossing of singleparticle states strongly localized at the doped-bond position, which is then somewhat distributed/disordered by the mutual interaction of these states. The disorder is seen by NMR as the inhomogeneous relaxat...