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Physical review. B, Condensed matter

Dimer liquid state in the quantum antiferromagnet compound LiCu2O2

Sergei A. Zvyagin, Gang Cao, Y. Xin, S. McCall, T. Caldwell, W. G. Moulton, Louis Claude Brunel, Alexander Angerhofer, Jack E. Crow

Published Aug 20, 2002• 44 citations
Publisher

Abstract

Results of systematic structural, magnetic, electron-spin resonance, and specific-heat investigations of the $S=1/2$ quantum antiferromagnet compound ${\mathrm{LiCu}}_{2}{\mathrm{O}}_{2}$ are presented. A spin-singlet ground state is revealed at temperatures above $T\ensuremath{\sim}23\mathrm{K}.$ In this temperature region ${\mathrm{LiCu}}_{2}{\mathrm{O}}_{2}$ may be regarded as a quantum $S=1/2$ chain with competing nearest- and next-nearest-neighbor interactions in the intermediate range of the ${J}_{2}{/J}_{1}$ ratio $({\ensuremath{\alpha}}_{c1}<{J}_{2}{/J}_{1}<{\ensuremath{\alpha}}_{c2}).$ The size of the energy gap between the spin-singlet ground state and the first excited triplet, \ensuremath{\Delta}, is found to be \ensuremath{\sim}72 K. The study confirms a magnetic phase transition in ${\mathrm{LiCu}}_{2}{\mathrm{O}}_{2},$ which results in the collapse of the spin-singlet ground state at a temperature below 23 K. In addition, a second low-temperature transition was found at $T\ensuremath{\sim}9\mathrm{K}.$ Peculiarities of the magnetic excitation spectrum in the dimer phase of ${\mathrm{LiCu}}_{2}{\mathrm{O}}_{2}$ and its magnetic structure are discussed.

DOI
10.1103/physrevb.66.064424

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Results of systematic structural, magnetic, electron-spin resonance, and specific-heat investigations of the S=1/2S=1/2S=1/2 quantum antiferromagnet compound LiCu2O2{\mathrm{LiCu}}_{2}{\mathrm{O}}_{2}LiCu2​O2​ are presented. A spin-singlet ground state is revealed at temperatures above T\ensuremath∼23K.T\ensuremath{\sim}23\mathrm{K}.T\ensuremath∼23K. In this temperature region LiCu2O2{\mathrm{LiCu}}_{2}{\mathrm{O}}_{2}LiCu2​O2​ may be regarded as a quantum S=1/2S=1/2S=1/2 chain with competing nearest- and next-nearest-neighbor interactions in the intermediate range of the J2/J1{J}_{2}{/J}_{1}J2​/J1​ ratio (\ensuremathαc1<J2/J1<\ensuremathαc2).({\ensuremath{\alpha}}_{c1}<{J}_{2}{/J}_{1}<{\ensuremath{\alpha}}_{c2}).(\ensuremathαc1​<J2​/J1​<\ensuremathαc2​). The size of the energy gap between the spin-singlet ground state and the first excited triplet, \ensuremath{\Delta}, is found to be \ensuremath{\sim}72 K. The study confirms a magnetic phase transition in LiCu2O2,{\mathrm{LiCu}}_{2}{\mathrm{O}}_{2},LiCu2​O2​, which results in the collapse of the spin-singlet ground state at a temperature below 23 K. In addition, a second low-temperature transition was found at T\ensuremath∼9K.T\ensuremath{\sim}9\mathrm{K}.T\ensuremath∼9K. Peculiarities of the magnetic excitation spectrum in the dimer phase of LiCu2O2{\mathrm{LiCu}}_{2}{\mathrm{O}}_{2}LiCu2​O2​ and its magnetic structure are discussed.
The nature of quantum spin liquids is studied for the spin-1/21/21/2 antiferromagnetic Heisenberg model on a square lattice containing exchange interactions between nearest-neighbor sites, J1J_1J1​, and those between next-nearest-neighbor sites, J2J_2J2​. We perform variational Monte Carlo simulations together with the quantum-number-projection technique and clarify the phase diagram in the ground state together with its excitation spectra. We obtain the nonmagnetic phase in the region 0.4<J2/J1≤0.60.4< J_2/J_1\le 0.60.4<J2​/J1​≤0.6 sandwiched by the staggered and stripe antiferromagnetic (AF) phases. Our direct calculations of the spin gap support the notion that the triplet excitation from the singlet ground state is gapless in the range of 0.4<J2/J1≤0.50.4 < J_2/J_1 \le 0.50.4<J2​/J1​≤0.5, while the gapped valence-bond-crystal (VBC) phase is stabilized for 0.5<J2/J1≤0.60.5 < J_2/J_1 \le 0.60.5<J2​/J1​≤0.6. The VBC order is likely to have the columnar symmetry with a spontaneous symmetry breaking of the C4vC_{4v}C4v​ symmetry. The power-law behaviors of the spin-spin and dimer-dimer correlation functions in the gapless region are consistent with the emergence of the algebraic quantum-spin-liquid phase (critical phase). The exponent of the spin correlation ⟨S(0)S(r)⟩∝1/rz+η\langle S(0)S(r)\rangle \propto 1/r^{z+η}⟨S(0)S(r)⟩∝1/rz+η at a long distance rrr appears to increase from z+η∼1z+η\sim 1z+η∼1 at J2/J1∼0.4J_2/J_1\sim0.4J2​/J1​∼0.4 toward the continuous transition to the VBC phase at J1/J1∼0.5J_1/J_1\sim0.5J1​/J1​∼0.5. Our results, however, do not fully exclude the possibility of a direct quantum transition between the staggered AF and VBC phases with a wide critical region and deconfined criticality.
We study the spin-12\frac{1}{2}21​ Heisenberg model on the triangular lattice with antiferromagnetic first- (J1)({J}_{1})(J1​) and second- (J2)({J}_{2})(J2​) nearest-neighbor interactions using density matrix renormalization group. By studying the spin correlation function, we find a ${120}^{\ensuremath{\circ}}$ magnetic order phase for ${J}_{2}\ensuremath{\lesssim}0.07{J}_{1}$ and a stripe antiferromagnetic phase for ${J}_{2}\ensuremath{\gtrsim}0.15{J}_{1}$. Between these two phases, we identify a spin-liquid region characterized by exponential decaying spin and dimer correlations, as well as large spin singlet and triplet excitation gaps on finite-size systems. We find two near degenerating ground states with distinct properties in two sectors, which indicates more than one spin-liquid candidate in this region. While the sector with spinons is found to respect time reversal symmetry, the even sector without spinons breaks such a symmetry for finite-size systems. Furthermore, we detect the signature of the fractionalization by following the evolution of different ground states with inserting spin flux into the cylinder system. Moreover, by tuning the anisotropic bond coupling, we explore the nature of the spin-liquid phase and find the optimal parameter region for gapped Z2{Z}_{2}Z2​ spin liquids.
The linear spin-12\frac{1}{2}21​ Heisenberg antiferromagnet with exchanges J1{J}_{1}J1​ and J2{J}_{2}J2​ between first and second neighbors has a bond-order wave (BOW) phase that starts at the fluid-dimer transition at J2/J1=0.2411{J}_{2}/{J}_{1}=0.2411J2​/J1​=0.2411 and is particularly simple at J2/J1=1/2{J}_{2}/{J}_{1}=1/2J2​/J1​=1/2. The BOW phase has a doubly degenerate singlet ground state, broken inversion symmetry, and a finite-energy gap Em{E}_{m}Em​ to the lowest-triplet state. The interval 0.4<J2/J1<1.00.4<{J}_{2}/{J}_{1}<1.00.4<J2​/J1​<1.0 has large Em{E}_{m}Em​ and small finite-size corrections. Exact solutions are presented up to N=28N=28N=28 spins with either periodic or open boundary conditions and for thermodynamics up to N=18N=18N=18. The elementary excitations of the BOW phase with large Em{E}_{m}Em​ are topological spin-12\frac{1}{2}21​ solitons that separate BOWs with opposite phase in a regular array of spins. The molar spin susceptibility ${\ensuremath{\chi}}_{M}(T)$ is exponentially small for T⪡EmT⪡{E}_{m}T⪡Em​ and increases nearly linearly with TTT to a broad maximum. J1{J}_{1}J1​ and J2{J}_{2}J2​ spin chains approximate the magnetic properties of the BOW phase of Hubbard-type models and provide a starting point for modeling alkali-tetracyanoquinodimethane salts.
We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (J1FJ_1^FJ1F​) and antiferromagnetic (J1AJ_1^AJ1A​) nearest-neighbor interactions and ferromagnetic next-nearest-neighbor interaction (J2FJ_2^FJ2F​). In this model frustration is induced by the non-zero J2FJ_2^FJ2F​ and the effect of dimerization is realized by changing the strength of J1AJ_1^AJ1A​ for a fixed value of J1FJ_1^FJ1F​. The model with site spin sss behaves like a Haldane spin chain with site spin 2sss in the limit of vanishing J2FJ_2^FJ2F​ and large J1F/J1AJ_1^F/J_1^AJ1F​/J1A​. We show that the exact ground state of the model can be found along a line in the parameter space. The phase diagram in the space of J1A−J2FJ_1^A-J_2^FJ1A​−J2F​ is determined using numerical techniques complemented by some analytical calculations. A number of quantities, including the ground state spin, energy gap, structure factor, entanglement entropy, and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and application-wise important feature of this model is that it exhibits a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.
The density matrix renormalization group and quantum Monte Carlo methods are used to describe coupled trimer chains in a magnetic field hhh. The Hamiltonian contains exchange terms involving the intratrimer coupling J1{J}_{1}J1​ (taken as the unit of energy) and the intertrimer coupling J2{J}_{2}J2​, plus the Zeeman interaction for a magnetic field hhh along the zzz direction. Results for the magnetization per trimer mmm are calculated in regimes of positive and negative values of the ratio J=J2/J1J={J}_{2}/{J}_{1}J=J2​/J1​, from which the rich field-induced ground state phase diagram hhh versus JJJ is derived, with the presence of a Luttinger liquid, the 1/3 plateau (m=1/2m=1/2m=1/2), and the one of fully polarized magnetization (m=3/2m=3/2m=3/2). Also, zero-field Lanczos calculation of the spin-wave dispersion from the 1/3 plateau for Sz=1{S}^{z}=1Sz=1 is shown at the previous regimes of JJJ values. In addition, we also report on the decay of correlation functions of trimers along open chains, as well as the average two-magnon distribution. The ground state is ferrimagnetic for $0<J\ensuremath{\le}1$, and is a singlet for $\ensuremath{-}1\ensuremath{\le}J<0$. In the singlet phase, the spin correlation functions along the legs present an antiferromagnetic power-law decay, similar to the spin-1/2 linear chain, thus suggesting that the ground state is made of three coupled antiferromagnetically oriented chains. In the singlet phase, the dimensionless thermal magnetic susceptibility per site normalized by 1/∣J∣1/|J|1/∣J∣ gets closer to $1/{\ensuremath{\pi}}^{2}$ as the temperature $T\ensuremath{\rightarrow}0$. For the ferrimagnetic phase, we fit the susceptibility to the experimental data for the compound Pb3Cu3(PO4)4{\mathrm{Pb}}_{3}{\mathrm{Cu}}_{3}{({\mathrm{PO}}_{4})}_{4}Pb3​Cu3​(PO4​)4​ and estimate the model exchange couplings: J1=74.8K{J}_{1}=74.8\phantom{\rule{4pt}{0ex}}\text{K}J1​=74.8K and J=0.4J=0.4J=0.4. These values imply a range of energies for the magnon excitations that are in accord with the data from neutron scattering experiments on Pb3Cu3(PO4)4{\mathrm{Pb}}_{3}{\mathrm{Cu}}_{3}{({\mathrm{PO}}_{4})}_{4}Pb3​Cu3​(PO4​)4​ for two excitation modes. The 1/3 plateau closes only at 1/∣J∣=01/|J|=01/∣J∣=0 with J<0J<0J<0.
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