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arXiv:cond-mat/0611615 · New Journal of Physics

Field induced disordered-local-moment phase in site-diluted spin-gap antiferromagnets

Rong Yu, Tommaso Roscilde, Stephan Haas

Published Jan 25, 2008• 9 citations
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Abstract

Site dilution of spin-gapped antiferromagnets leads to localized free moments, which can order antiferromagnetically in two and higher dimensions. Here we show how a weak magnetic field drives this order-by-disorder state into a novel disordered-local-moment (DLM) phase, characterized by the formation of local singlets between neighboring moments and by localized moments aligned antiparallel to the field. This disordered phase is characterized by the absence of a gap, as is the case in a Bose glass. The associated field-driven quantum phase transition is consistent with the universality of a superfluid-to-Bose-glass transition. The robustness of the DLM phase and its prominent features, in particular a series of pseudo-plateaus in the magnetization curve, makes it accessible and relevant to experiments.

DOI
10.1088/1367-2630/10/1/013034

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Site dilution of spin-gapped antiferromagnets leads to localized free moments, which can order antiferromagnetically in two and higher dimensions. Here we show how a weak magnetic field drives this order-by-disorder state into a novel disordered-local-moment (DLM) phase, characterized by the formation of local singlets between neighboring moments and by localized moments aligned antiparallel to the field. This disordered phase is characterized by the absence of a gap, as is the case in a Bose glass. The associated field-driven quantum phase transition is consistent with the universality of a superfluid-to-Bose-glass transition. The robustness of the DLM phase and its prominent features, in particular a series of pseudo-plateaus in the magnetization curve, makes it accessible and relevant to experiments.
We numerically investigate the phase diagram of two-dimensional site-diluted coupled dimer systems in an external magnetic field. We show that this phase diagram is characterized by the presence of an extended Bose glass, not accessible to mean-field approximation, and stemming from the localization of two distinct species of bosonic quasiparticles appearing in the ground state. On the one hand, nonmagnetic impurities doped into the dimer-singlet phase of a weakly coupled dimer system are known to free up local magnetic moments. The deviations of these local moments from full polarization along the field can be mapped onto a gas of bosonic quasiparticles, which undergo condensation in zero and very weak magnetic fields, corresponding to transverse long-range antiferromagnetic order. An increasing magnetic field lowers the density of such quasiparticles to a critical value at which a quantum phase transition occurs, corresponding to the quasiparticle localization on clusters of local magnets (dimers, trimers, etc.) and to the onset of a Bose glass. Strong finite-size quantum fluctuations hinder further depletion of quasiparticles from such clusters, and thus lead to the appearance of pseudoplateaus in the magnetization curve of the system. On the other hand, site dilution hinders the field-induced Bose-Einstein condensation of triplet quasiparticles on the intact dimers, and it introduces instead a Bose glass of triplets. A thorough numerical investigation of the phase diagram for a planar system of coupled dimers shows that the two above-mentioned Bose glass phases are continuously connected, and they overlap in a finite region of parameter space, thus featuring a two-species Bose glass. The quantum phase transition from Bose glass to magnetically ordered phases in two dimensions is marked by novel universal exponents ($z\ensuremath{\approx}2$, $\ensuremath{\beta}\ensuremath{\approx}0.9$, and $\ensuremath{\nu}\ensuremath{\approx}1$). Hence we conclude that doped quantum antiferromagnets in a field represent an ideal setting for the study of fundamental dirty-boson physics.
The field-induced antiferromagnetic ordering in systems of weakly coupled S = 1/2 dimers at zero temperature can be described as a Bose-Einstein condensation of triplet quasiparticles (singlet quasiholes) in the ground state. For the case of a Heisenberg bilayer, it is here shown how the above picture is altered in the presence of site dilution of the magnetic lattice. Geometric randomness leads to quantum localization of the quasiparticles or quasiholes and to an extended Bose-glass phase in a realistic disordered model. This localization phenomenon drives the system towards a quantum-disordered phase well before the classical geometric percolation threshold is reached.
Effects of the site dilution on spin-gapped Heisenberg antiferromagnets with S=12S=\frac{1}{2}S=21​ and S=1S=1S=1 on a square lattice of coupled dimerized chains are investigated by means of the quantum Monte Carlo method. It is found that effective magnetic moments induced around the diluted sites exhibit the antiferromagnetic long-range order in the medium of spin-singlet pairs. Their microscopic structure is examined in detail and important roles of higher dimensionality other than one in the phenomenon are discussed.
We study the interplay between disorder and interactions for emergent bosonic degrees of freedom induced by an external magnetic field in the Br-doped spin-gapped antiferromagnetic material $\mathrm{Ni}{({\mathrm{Cl}}_{1\ensuremath{-}x}{\mathrm{Br}}_{x})}_{2}\ensuremath{-}4\mathrm{SC}{({\mathrm{NH}}_{2})}_{2}$ (DTNX\mathrm{DTN}XDTNX). Building on nuclear magnetic resonance experiments at high magnetic field [A. Orlova et al., Phys. Rev. Lett. 118, 067203 (2017)], we describe the localization of isolated impurity states, providing a realistic theoretical modeling for DTNX\mathrm{DTN}XDTNX. Going beyond single impurity localization we use quantum Monte Carlo simulations to explore many-body effects from which pairwise effective interactions lead to a (impurity-induced) Bose-Einstein condensation (BEC) revival [M. Dupont, S. Capponi, and N. Laflorencie, Phys. Rev. Lett. 118, 067204 (2017)]. We further address the question of the existence of a many-body localized Bose-glass (BG) phase in DTNX\mathrm{DTN}XDTNX, which is found to compete with a series of a new kind of BEC regimes made out of the multi-impurity states. The global magnetic field--temperature phase diagram of DTNX\mathrm{DTN}XDTNX reveals a very rich structure for low impurity concentration, with consecutive disorder-induced BEC minidomes separated by intervening many-body localized BG regimes. Upon increasing the impurity level, multiple mini-BEC phases start to overlap, while intermediate BG regions vanish.