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Progress of Theoretical Physics Supplement

Field and Impurity Induced Ordering in Interacting Dimer Systems

Hans-Jürgen Mikeska, Alexei K. Kolezhuk

Published Jan 1, 2005• 1 citation
Publisher

Abstract

We study the interplay of doping and an external magnetic field H on dimerized antiferromagnetic S = 1/2 systems with a finite spin gap Δ. We show that for sufficiently small three-dimensional coupling J′ the long-range antiferromagnetic order known to result from doping with nonmagnetic impurities is destroyed by a weak magnetic field H>Hc1. The lower critical field Hc1 is proportional to the impurity concentration, above Hc1 the system remains in the disordered (plateau) phase up to the much higher upper critical field Hc2 ≃Δ. We discuss the phase diagram in the (H,J') and (H,T) planes and suggest that the reentrant behavior can be experimentally observed in KCuCl3. It is argued that similar phenomena can arise in other weakly coupled quasi-one-dimensional gapped systems.

DOI
10.1143/ptps.159.376

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We study the interplay of doping and an external magnetic field H on dimerized antiferromagnetic S = 1/2 systems with a finite spin gap Δ. We show that for sufficiently small three-dimensional coupling J′ the long-range antiferromagnetic order known to result from doping with nonmagnetic impurities is destroyed by a weak magnetic field H>Hc1. The lower critical field Hc1 is proportional to the impurity concentration, above Hc1 the system remains in the disordered (plateau) phase up to the much higher upper critical field Hc2 ≃Δ. We discuss the phase diagram in the (H,J') and (H,T) planes and suggest that the reentrant behavior can be experimentally observed in KCuCl3. It is argued that similar phenomena can arise in other weakly coupled quasi-one-dimensional gapped systems.
In spin‐gapped quasi‐one‐dimensional antiferromagnets that do not show phase transitions down to zero temperature, impurities cause phase transitions by inducing local magnetic moments around them between which long‐range correlation is mediated by weak interchain couplings. We investigate the difference between the effects of non‐magnetic impurities and those of spin‐1/2 magnetic ones in the impurity‐induced transition temperatures and the staggered magnetization in the impurity‐induced ordered phase by the quantum Monte Carlo method. We find that the staggered correlation induced by spin‐1/2 impurities grows slower than that done by non‐magnetic ones as the system is cooled and approaches the ground state, while the transition temperature induced by the former is higher than that done by the latter. We argue that this is one of the characteristic aspects of the order‐by‐disorder phenomena in quantum systems.
We study the effect of nonmagnetic Zn2+{\mathrm{Zn}}^{2+}Zn2+ (spin-0) and magnetic Ni2+{\mathrm{Ni}}^{2+}Ni2+ (spin-1) impurities on the ground state and low-lying excitations of the quasi-one-dimensional spin-1/21/21/2 Heisenberg antiferromagnet Sr2CuO3{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}Sr2​CuO3​ using inelastic neutron scattering, specific heat, and bulk magnetization measurements. We show that 1% Ni2+{\mathrm{Ni}}^{2+}Ni2+ doping in Sr2CuO3{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}Sr2​CuO3​ results in a sizable spin gap in the spinon excitations, analogous to the case of Ni doped SrCuO2{\mathrm{SrCuO}}_{2}SrCuO2​ previously reported [Simutis et al., Phys. Rev. Lett. 111, 067204 (2013)]. However, a similar level of Zn2+{\mathrm{Zn}}^{2+}Zn2+ doping in SrCuO2{\mathrm{SrCuO}}_{2}SrCuO2​, investigated here for comparison, did not reveal any signs of a spin gap. Magnetic ordering temperature was found to be suppressed in the presence of both Zn2+{\mathrm{Zn}}^{2+}Zn2+ and Ni2+{\mathrm{Ni}}^{2+}Ni2+ impurities; however, the rate of suppression due to Ni2+{\mathrm{Ni}}^{2+}Ni2+ was found to be much more pronounced than for Zn2+{\mathrm{Zn}}^{2+}Zn2+. Effect of magnetic field on the ordering temperature is investigated. We found that with increasing magnetic field, not only the magnetic ordering temperature gradually increases but the size of specific heat anomaly associated with the magnetic ordering also progressively enhances, which can be qualitatively understood as due to the field induced suppression of quantum fluctuations.
The doping of quantum Heisenberg antiferromagnets on the kagome lattice by nonmagnetic impurities is investigated within the framework of a generalized quantum dimer model (QDM) describing (a) the valence-bond crystal (VBC), (b) the dimer liquid, and (c) the critical region on equal footing. Following the approach by Ralko et al. [Phys. Rev. Lett. 101, 117204 (2008)] for the square and triangular lattices, we introduce the (minimal) extension of the QDM on the kagome lattice to account for spontaneous creation of mobile S=1/2S=1/2S=1/2 spinons at finite magnetic field. Modulations of the dimer density (at zero or finite magnetic field) and of the local field-induced magnetization in the vicinity of impurities are computed using Lanczos exact diagonalization techniques on small clusters (48 and 75 sites). The VBC is clearly revealed from its pinning by impurities, while, in the dimer liquid, crystallization around impurities involves only two neighboring dimers. We also find that a next-nearest-neighbor ferromagnetic coupling favors VBC order. Unexpectedly, a small-size spinon-impurity bound state appears in some region of the dimer-liquid phase. In contrast, in the VBC phase the spinon delocalizes within a large region around the impurity, revealing the weakness of the VBC confining potential. Lastly, we observe that an impurity concentration as small as 4% enhances dimerization substantially. These results are confronted to the valence-bond glass scenario [R. R. P. Singh, Phys. Rev. Lett. 104, 177203 (2010)] and implications to the interpretation of the nuclear magnetic resonance spectra of the Herbertsmithite compound are outlined.
We consider the one-dimensional gas of electrons interacting via an attractive δ-function potential. The attractive potential leads to the formation of Cooper-pair-like bound states with a spin gap. Without destroying the integrability, we introduce a finite concentration of mixed-valence impurities with two magnetic configurations of spin S and S + {{1}/{2}}, which hybridize with the conduction states of the host. We derive the Bethe ansatz equations diagonalizing the system for the correlated host with impurities and discuss the ground-state properties as functions of the concentration of impurities and the Kondo coupling. For a sufficiently large density of electrons the spin gap is reduced by the impurities and is closed at a critical concentration which depends on the impurity spin and the coupling strength. A ferromagnetic phase of unpaired spin-polarized itinerant electrons is induced for impurity concentrations larger than the critical one. The critical behaviour of the correlation functions is studied in the gapped and gapless regions using the mesoscopic energy spectrum and conformal field theory.
Effects of nonmagnetic impurity doping on an AF spin-1/2 Heisenberg ladder system are studied by the QMC method. A single nonmagnetic impurity induces a localized spin-1/2 moment accompanied by "static" and enhanced AF correlations around it. Small and finite concentration of impurities induces a remarkable change of magnetic and thermodynamic properties with gapless excitations. It also shows rather sharp but continuous crossover around the concentration of about 4%. Above the crossover concentration, all the spins are strongly coupled participating in the enhanced and rather uniform power-law decay of the antiferromagnetic correlation. Below the crossover, each impurity forms an antiferromagnetic cluster only weakly coupled each other. For random distribution of impurities, large Curie-like susceptibility accompanied with small residual entropy is obtained at low temperatures in agreement with recent experimental observation in Zn-doped SrCu2O3SrCu_{2}O_{3}SrCu2​O3​. Temperature dependence of AF susceptibility shows power-law-like but weaker divergence than the single chain AFH in the temperature range studied.
The multiple reentrant quantum phase transitions in the S=1/2S=1/2S=1/2 antiferromagnetic Heisenberg chains with random bond alternation in the magnetic field are investigated by the density matrix renormalization group method combined with the interchain mean field approximation. It is assumed that the odd-th bond is antiferromagnetic with strength JJJ and even-th bond can take the values ${\JS}$ and ${\JW}$ $ ({\JS} > J > {\JW} > 0)$ randomly with probability ppp and 1−p1-p1−p, respectively. The pure version (p=0p=0p=0 and p=1p=1p=1) of this model has a spin gap but exhibits a field induced antiferromagnetism in the presence of interchain coupling if Zeeman energy due to the magnetic field exceeds the spin gap. For 0<p<10 < p < 10<p<1, the antiferromagnetism is induced by randomness at small field region where the ground state is disordered due to the spin gap in the pure case. At the same time, this model exhibits randomness induced plateaus at several values of magnetization. The antiferromagnetism is destroyed on the plateaus. As a consequence, we find a series of reentrant quantum phase transitions between the transverse antiferromagnetic phases and disordered plateau phases with the increase of the magnetic field for moderate strength of interchain coupling. Above the main plateaus, the magnetization curve consists of a series of small plateaus and the jumps between them, It is also found that the antiferromagnetism is induced by infinitesimal interchain coupling at the jumps between the small plateaus. We conclude that this antiferromagnetism is supported by the mixing of low lying excited states by the staggered interchain mean field even though the spin correlation function is short ranged in the ground state of each chain.