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arXiv:2009.08630 · Journal of the Physical Society of Japan

Frustration-induced Quantum Spin Liquid Behavior in the s = 1/2 Random-bond Heisenberg Antiferromagnet on the Zigzag Chain

Kazuki Uematsu, Toshiya Hikihara, Hikaru Kawamura

Published Nov 9, 2021• 8 citations
arXivHTMLPDF

Abstract

Recent studies have revealed that the randomness-induced quantum spin liquid (QSL)-like state is stabilized in certain frustrated quantum magnets in two and three dimensions. In order to clarify the nature of this gapless QSL-like state, we investigate both zero- and finite-temperature properties of the random-bond one-dimensional (1D) $s=12$ Heisenberg model with the competing nearest-neighbor and next-nearest-neighbor antiferromagnetic interactions, $J_1$ and $J_2$, by means of the exact diagonalization, density-matrix renormalization-group and Hams--de Raedt methods. We find that, on increasing the frustration $J_2$, the gapless nonmagnetic state stabilized in the unfrustrated model with $J_2=0$, the {\it unfrustrated\} random-singlet (RS) state, exhibits a phase transition into different gapless nonmagnetic state, the {\it frustrated\} RS state. This frustrated RS state in 1D has properties quite similar to the randomness-induced QSL-like state recently identified in 2D and 3D frustrated magnets exhibiting the $T$-linear low-temperature ($T$) specific heat, while the unfrustrated RS state is more or less specific to the unfrustrated 1D system exhibiting the $\sim 1(\log T)^3$ low-$T$ specific heat. Universal features and the robustness against perturbations of the frustrated RS state are emphasized.

DOI
10.7566/jpsj.90.124703

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We investigate the ground-state and finite-temperature properties of the bond-random s=1/2s=1/2s=1/2 Heisenberg model on a honeycomb lattice with frustrated nearest- and next-nearest-neighbor antiferromagnetic interactions, J1J_1J1​ and J2J_2J2​, by the exact diagonalization and the Hams--de Raedt methods. The ground-state phase diagram of the model is constructed in the randomness versus the frustration (J2/J1J_2/J_1J2​/J1​) plane, with the aim of clarifying the effects of randomness and frustration in stabilizing a variety of distinct phases. We find that the randomness induces the gapless quantum spin liquid (QSL)-like state, the random-singlet state, in a wide range of parameter space. The observed robustness of the random-singlet state suggests that the gapless QSL-like behaviors might be realized in a wide class of frustrated quantum magnets possessing a certain amount of randomness or inhomogeneity, without fine-tuning the interaction parameters. Possible implications to recent experiments on the honeycomb-lattice magnets Ba3_33​CuSb2_22​O9_99​ and 6HB-Ba3_33​NiSb2_22​O9_99​ exhibiting the gapless QSL-like behaviors are discussed.
In frustrated magnets, the experimental realization of a quantum disordered ground state (QDGS), especially quantum spin liquid (QSL) ground state, is a central topic in condensed matter physics.Several promising candidates were reported, and a number of QSL-like behavior, such as excitation continuum, Tlinear specific heat, and so on, were observed.However, whether the QSL-like behavior is owing to the synergy between spin frustration and quantum fluctuation or bond randomness effects has not been clarified yet.Several theoretical studies have demonstrated that the synergy effect between the magnetic frustration and the bond randomness suppresses magnetic ordering and induces a QSL-like state.This QSL-like state was proposed to be a random-singlet (RS) state, where not only nearest-neighbor spins but also distant spins form singlet pairs with random coupling energy.Since thermodynamic properties of RS and QSL are predicted to be similar to each other, it is important to elucidate the microscopic nature of randomness-induced QDGSs.However, its experimental verifications are still insufficient due to a lack of model materials.In this work, I synthesized polycrystalline samples of SrLaCuSbO 6 (SLCSO) and SrLaCuNbO 6 (SLCNO) by a solid-state reaction.Magnetic Cu 2+ ions with S = 1/2 Heisenberg spins form a square lattice with nearest-neighbor (J 1 ) and next-nearest-neighbor (J 2 ) exchange interaction.Thus, SLCSO and SLCNO were magnetically described as quasi-two-dimensional S = 1/2 J 1 -J 2 square lattice Heisenberg antiferromagnet (SLHAF).The temperature dependence of the magnetic susceptibilities of both compounds shows a broad maximum characteristic of an S = 1/2 SLHAF.However, both compounds undergo magnetic phase transitions at T N = 13.6 and 15.7 K for SLCSO and SLCNO, respectively, due to weak inter-layer interactions.Neutron powder diffraction measurements reveal contrasting spin structures in both compounds.The spin structures of SLCSO and SLCNO below T N are Néel antiferromagnetic and collinear antiferromagnetic, respectively.This result demonstrates that the nearest-neighbor interaction is dominant in SLCSO, whereas the next-nearest-neighbor interaction is dominant in SLCNO.The magnitude of the ordered moment was evaluated at 3.5 K to be m = 0.39(3) µ B for SLCSO and 0.37(1) µ B for SLCNO, which are significantly reduced from 1µ B expected in the classical spin case.The shrink of the ordered magnetic moment was caused by not only magnetic frustration effects but also bond randomness effects arising from the site disorder of Sr 2+ and La 3+ ions.Next, I synthesized the mixed system SrLaCuSb 1-x Nb x O 6 with 0.1 ≤ x ≤
Abstract The nature of the randomness-induced quantum spin liquid state, the random-singlet state, is investigated in two dimensions (2D) by means of the exact-diagonalization and the Hams-de Raedt methods for several frustrated lattices, e.g. the triangular, the kagome and the J 1 - J 2 square lattices. Properties of the ground state, the low-energy excitations and the finite-temperature thermodynamic quantities are investigated. The ground state and the low-lying excited states consist of nearly isolated singlet-dimers, clusters of resonating singlet-dimers, and orphan spins. Low-energy excitations are either singlet-to-triplet excitations, diffusion of orphan spins accompanied by the recombination of nearby singlet-dimers, creation or destruction of resonating singlet-dimers clusters. The latter two excitations give enhanced dynamical ‘liquid-like’ features to the 2D random-singlet state. Comparison is made with the random-singlet state in a 1D chain without frustration, the similarity and the difference between in 1D and in 2D being highlighted. Frustration in a wide sense, not only the geometrical one but also including the one arising from the competition between distinct types of interactions, play an essential role in stabilizing this frustrated random singlet state. Recent experimental situations on both organic and inorganic materials are reviewed and discussed.
We investigate the quantum spin-1/2 zigzag chain with frustrated ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg interactions, incorporating additional off-diagonal exchange interactions known as the $\mathrm{\ensuremath{\Gamma}}$ term, both with and without an applied magnetic field. Based on the density-matrix renormalization group calculation, we map out the ground-state phase diagram that shows a variety of magnetic and nonmagnetic phases including multicritical points and several exactly solvable points. Upon introducing a finite $\mathrm{\ensuremath{\Gamma}}$ term, we observe the persistent dimer-singlet state of the ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model, sustaining a nonzero spin gap, while also hosting a gapless nonmagnetic excitation that manifests in the substantial zero-energy peak in the nematic dynamical structure factor. This gapless peak-mode, remaining almost as a fluctuation to the ground state, induces a dilute but robust concentration of nematicity on top of singlets on dimers, which we call the nematic singlet-dimer phase. When the whole nematic excited mode condenses and replaces the singlet, the nematic-dimer phase transforms into the Ising-type ferromagnetic or antiferromagnetic long-range orders. The $\mathrm{\ensuremath{\Gamma}}$ term spontaneously selects magnetic easy axes, and their orientations dictate the type of magnetic order under geometric frustration effects as predicted by Landau's mean-field theory. These theoretical findings provide insights into the exotic low-temperature phase observed in YbCuS2{\mathrm{YbCuS}}_{2}YbCuS2​, characterized by gapless excitations and seemingly nonmagnetic behavior.
We study the effects of bond randomness in the spin-1/21/21/2 ${J}_{1}\ensuremath{-}{J}_{2}$ triangular Heisenberg model using exact diagonalization and density-matrix renormalization group. With increasing bond randomness, we identify a randomness-induced spin-liquid-like phase without any magnetic order, dimer order, spin-glass order, or valence-bond-glass order. The finite-size scaling of gaps suggests the gapless nature of both spin triplet and singlet excitations, which is further supported by the broad continuum of the dynamical spin structure factor. By studying the bipartite entanglement spectrum of the system on cylinder geometry, we identify the features of the low-lying entanglement spectrum in the spin-liquid-like phase, which may distinguish this randomness-induced spin-liquid-like phase and the intrinsic spin-liquid phase in the clean ${J}_{1}\ensuremath{-}{J}_{2}$ triangular Heisenberg model. We further discuss the nature of this spin-liquid-like phase and the indication of our results for understanding spin-liquid-like materials with triangular-lattice structure.