Nuclear Magnetic Resonance Reveals Disordered Level-Crossing Physics in the Bose-Glass Regime of the Br-Doped Ni(Cl1−xBrx

Abstract

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...

Disorder-Induced Revival of the Bose-Einstein Condensation inNi(Cl1−xBrxDupont1, Capponi2, Laflorencie3 2017Phys. Rev. Lett.Self Cite145280View full textAdd to dashboardCite

“…However, the Br-doped bonds introduce a new energy scale in DTNX, as shown by an enhanced NMR relaxation around a cross-over field H * 13.6 T [28]. In close analogy with impurity-induced LRO at zero field [16], we show using large scale quantum Monte Carlo (QMC) simulations that in the vicinity of H * localized states hosted by doped bonds can interact and display macroscopic coherence, as sketched in Fig.…”

“…In this Letter, building on recent nuclear magnetic resonance (NMR) experiments [28], we achieve a realistic theoretical study of the high magnetic field regime of Ni(Cl 1−x Br x ) 2 -4SC(NH 2 ) 2 (DTNX): a threedimensional antiferromagnetic (AF) system made of weakly coupled chains of S = 1 spins subject to singleion anisotropy [panels (b-c) of Fig. 1].…”

“…Theoretical modelling of DTNX.-Recent neutron [39] and NMR [28] experiments on DTNX at various Br concentration 0.04 ≤ x ≤ 0.13 have both shown the existence of a localized level above H c2 . Building on NMR data [28], the microscopic parameters for Br-doped bonds [there are two non-equivalent Cl sites in each J bond, but only one of these can be doped by a Br, see panel (b) of Fig.…”

“…Building on NMR data [28], the microscopic parameters for Br-doped bonds [there are two non-equivalent Cl sites in each J bond, but only one of these can be doped by a Br, see panel (b) of Fig. 1] can be precisely determined in order to match the observed spin relaxation peak at H * 13.6 T, attributed to the crossing between S z = 2 and S z = 1 levels of impurity states [panel (d) of Fig.…”

“…1], combined with the local magnetizations from NMR shifts. DTNX is therefore described by the following S = 1 model [28,40]:…”