Boson Localization in Disordered Spin Systems – BOLODISS

Nuclear magnetic resonance (NMR), as a microscopic local probe for magnetism, is particularly suitable for studies of magnetic field induced/dependent quantum magnetism. Analysing NMR spectra we obtain information on static (average) local spin polarization values. In favourable cases, one can even resolve individual polarizations values of spins around impurities. Measurements of the nuclear spin-lattice relaxation rate, 1/T1, provide access to the low-energy spin dynamics; we can thus quantify both the transverse <S+S-> and longitudinal <SzSz> spin fluctuations. We can also detect spatial inhomogeneity of spin dynamics, which is a hallmark of disordered systems.
In the absence of frustrated interaction, advanced Quantum Monte Carlo (QMC) simulations provide privileged exact access to static properties (local spin polarisation, order parameter, critical temperature) of a spin system of any dimension. Density Matrix Renormalization Group (DMRG) is particularly suitable for studying 1D systems. Matrix Product States (MPS) formalism allows us now to address dynamic properties such as NMR 1/T1 relaxation rate.

The analysis of NMR results on pure DTN compound has allowed us to determine, for the first time, the absolute value of the order parameter in the BEC (Bose-Einstein condensed) phase [1]. Results were modelled by QMC and MPS/DMRG, and compared to approximate analytical descriptions in order to discuss their validity [6]. Theoretical results on dynamics in 1D have provided new basis for the interpretation of the 1/T1 data in quasi-1D systems [5].
Experiments were focused on the Br-doped DTN. By NMR measurements of 1/T1 we have observed and characterized a peak of spin fluctuations appearing at magnetic field value H* = 13.6 T, attributed to a level-crossing (as a function of magnetic field) of the states strongly localized at the dopants [7]. Theoretical modelling allowed us to construct an effective Hamiltonian of the system, enabling investigations of its zero-temperature behaviour. We have thus discovered that the Bose-glass (BG) phase is replaced near H* by a fully ordered (but inhomogeneous) «BEC*« phase, which is a new phase of the «order by disorder« type [8]. In fact, three consecutive phases of this type are separated by the BG sectors at low doping, while they completely cover the whole BG phase at high doping [10].
The first 1/T1 measurements on the DIMPY compound performed in very high magnetic field, up to 29 T and at 0.75 K, have been analysed within the 1D Tomonaga-Luttinger Liquid description, allowing us to establish a direct experimental criterion, by NMR, to test the nature of interactions, attractive or repulsive, in the quantum spin systems [3]. In the BEC phase of DIMPY we have also observed a novel crossover at very low temperature [9] and proposed its theoretical description [4].
**References: see below the «Scientific productions«

The synergy between the experimental, by NMR, and theoretical, by advanced numerical techniques, investigation of the Br-doped DTN compound has led to the discovery of a new magnetic-field-induced phase of the «order by disorder type«, namely the fully 3D-ordered impurity-induced «BEC*« phase, covering partly or fully what was previously expected to be a (localized) Bose-glass regime [7,8,10]. The corresponding theoretical phase diagram is for high doping levels accessible to experiment, and is now being compared to the experimental Tc values determined by NMR for the 13% doped DTN sample. This will bring the final experimental confirmation for the existence of the new BEC* phase. Further theoretical efforts will be focused on details of the critical behavior in doped DTN, to hopefully resolve the current contradiction between the apparent experimental and generally expected theoretical value of the exponent defining the shape of the phase boundaries close to critical fields of the superfluid-to-Bose-glass transition.

1. R. Blinder, Étude par Résonance Magnétique Nucléaire de nouveaux états quantiques induits sous champ magnétique : condensation de Bose-Einstein dans le composé DTN, Ph.D thesis, Université Grenoble Alpes, 2015, tel.archives-ouvertes.fr/tel-01235600.
2. N. Laflorencie, Physics Report 643, 1-59 (2016).
3. M. Jeong, D. Schmidiger, H. Mayaffre, M. Klanjšek, C. Berthier, W. Knafo, G. Ballon, B. Vignolle, S. Krämer, A. Zheludev, and M. Horvatic, Phys. Rev. Lett. 117, 106402 (2016).
4. S. C. Furuya, M. Dupont, S. Capponi, N. Laflorencie, and T. Giamarchi, Phys. Rev. B 94, 144403 (2016).
5. M. Dupont, S. Capponi, N. Laflorencie, Phys. Rev. B 94, 144409 (2016), Editors' Suggestion.
6. R. Blinder, M. Dupont, S. Mukhopadhyay, M. S. Grbic, N. Laflorencie, S. Capponi, H. Mayaffre, C. Berthier, A. Paduan-Filho, and M. Horvatic, Phys. Rev. B 95, 020404(R) (2017), Editors' Suggestion.
7. A. Orlova, R. Blinder, E. Kermarrec, M. Dupont, N. Laflorencie, S. Capponi, H. Mayaffre, C. Berthier, A. Paduan-Filho, and M. Horvatic, Phys. Rev. Lett. 118, 067203 (2017).
8. M. Dupont, S. Capponi, and N. Laflorencie, Phys. Rev. Lett. 118, 067204 (2017).
9. M. Jeong, H. Mayaffre, C. Berthier, D. Schmidiger, A. Zheludev, and M. Horvatic, Phys. Rev. Lett. 118, 167206 (2017).
10. M. Dupont, S. Capponi, M. Horvatic, N. Laflorencie, Phys. Rev. B, in press (2017), arXiv:1705.07166.
11. Elmer V. H. Doggen, Gabriel Lemarié, Sylvain Capponi, and Nicolas Laflorencie, preprint arXiv:1704.02257.

Based on the microscopic information obtained from nuclear magnetic resonance (NMR) measurements coupled to advanced theoretical numerical analysis, we aim at understanding of topical, magnetic-field-induced phenomena in antiferromagnetic quantum spin systems (QSS) of the Bose-Einstein condensation (BEC) type, focusing on the effect of impurities leading to localization and the "Bose-glass" phase.

In general, QSS are representative for strongly correlated many-body physics, with the advantage that the number of particles, described theoretically as hard-core bosons, is directly and easily controlled by the applied magnetic field. The QSS compounds are insulators modelled by effective spin Hamiltonians, and the most relevant microscopic experimental techniques are neutron scattering and NMR, where only the latter one can access the highest field values. The NMR directly probes the low-energy limit of excitations, and in disordered compounds NMR spectra reflect the distribution of local spin polarizations. Investigations of QSS have been a principal research activity of the NMR group at LNCMI-Grenoble. In collaboration with theory groups, they have brought major achievements in some archetypal compounds, as e.g. i) the determination of the spin superstructure in the magnetic plateaus of SrCu2(BO3)2, corresponding to the Wigner crystallization, ii) the verification of the Tomonaga-Luttinger Liquid description in the spin ladder compound (C5H12N)2CuBr4 (BPCB), and iii) the first characterisation of quantum critical spin dynamics and its scaling properties in BPCB and in NiCl24SC(NH2)2, (DTN). We also mention the BaCuSi2O6 compound (Han-purple), initially supposed to be the archetype for the 2D BEC, which has turned out to be more complex and has stimulated theoretical description of a new, superfluid but not Bose-condensed state. The successful synergy of NMR measurements and description from the theory group at LPT Toulouse established in that investigation is the basis for the collaboration between the two partners of this project.

Based on previous experience on undoped compounds, this project is addressing new topics of QSS investigation, focused on the effects of impurities leading to a Bose-glass phase adjacent to an inhomogeneous BEC, as, e.g., described in a recent publication based on macroscopic measurements in doped DTN [Nature 489, 379 (2012)]. This publication contains predictions regarding microscopic structure of these phases, which will be verified by the NMR on Br-doped DTN. We also intend to follow the modification of the (critical) spin dynamics induced by doping. Comparative NMR measurements may be carried out on another bond-doped system, Cl-doped BPCB.

Previous studies of QSS have been performed mostly in spin-dimer or equivalent systems, corresponding to the repulsive interaction between the hard-core bosons. Only one representative for the regime of attractive interaction has been recognised recently, namely the spin ladder (C7H10N)2CuBr4 (DIMPY), in which our NMR results have directly confirmed this behaviour. Compared to most dimer-based systems, the site-doping by non-magnetic impurity in this case creates a local response of much longer correlation length, making it a candidate of choice to study the effects of disorder by NMR. The Zn-doped DIMPY will be studied focusing on the vicinity of its critical field, where disorder is expected to provoke unusual magnetic response.

Fundamental questions raised by this project are of great general interest, in particular regarding unconventional bosonic states of matter. In such a context, and in constant interaction with NMR experiments, several issues will be addressed theoretically, with a strong emphasis on:
i) the microscopic nature of the Bose glass and the role of dimensional crossovers in a random environment and
ii) the dynamical response in QSS, and in particular in the Bose glass state, with possible observation of a many-body localization physics.