Square-lattice Heisenberg Antiferromagnet Research Articles

Quantum disordered state in the J1−J2 square-lattice antiferromagnet Sr2Cu(Te0.95W0.05)O6

The $B$-site ordered double perovskites ${\mathrm{Sr}}_{2}\mathrm{Cu}({\mathrm{Te}}_{1\ensuremath{-}x}{\mathrm{W}}_{x}){\mathrm{O}}_{6}$ provide an excellent arena for investigating exotic phases expected for the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ square-lattice Heisenberg antiferromagnet. Here, combining magnetic susceptibility and specific-heat measurements with electron spin resonance (ESR) and muon spin rotation/relaxation $(\ensuremath{\mu}\mathrm{SR})$ techniques, we explore a spin-liquid-like state in the vicinity of the N\'eel critical end point $(x=0.05--0.1)$. The specific heat and the ESR and muon relaxation rates give evidence for an energy hierarchy of low-energy excitations, reminiscent of randomness-induced singlet states. In addition, the weak transverse $\ensuremath{\mu}\mathrm{SR}$ data show a fraction of frozen magnetic moments in the random-singlet background. The origin of a random-singlet-like state near the phase boundary is discussed in terms of concomitant exchange randomness and local strain generated by the ${\mathrm{W}}^{6+}\text{\ensuremath{-}}\mathrm{for}\text{\ensuremath{-}}{\mathrm{Te}}^{6+}$ substitution.

Giant Pressure Dependence and Dimensionality Switching in a Metal-Organic Quantum Antiferromagnet.

We report an extraordinary pressure dependence of the magnetic interactions in the metal-organic system [CuF_{2}(H_{2}O)_{2}]_{2}pyrazine. At zero pressure, this material realizes a quasi-two-dimensional spin-1/2 square-lattice Heisenberg antiferromagnet. By high-pressure, high-field susceptibility measurements we show that the dominant exchange parameter is reduced continuously by a factor of 2 on compression. Above 18kbar, a phase transition occurs, inducing an orbital re-ordering that switches the dimensionality, transforming the quasi-two-dimensional lattice into weakly coupled chains. We explain the microscopic mechanisms for both phenomena by combining detailed x-ray and neutron diffraction studies with quantitative modeling using spin-polarized density functional theory.

Nearly Deconfined Spinon Excitations in the Square-Lattice Spin- 1/2 Heisenberg Antiferromagnet

We study the dynamic spin structure factor of the spin-$1/2$ square-lattice Heisenberg antiferromagnet and of the $J$-$Q$ model (with 4-spin interactions $Q$ and Heisenberg exchange $J$). Using an improved method for stochastic analytic continuation of imaginary-time correlation functions computed with QMC simulations, we can treat the sharp ($\delta$-function) contribution from spinwaves (magnons) and a continuum at higher energy. The results for the Heisenberg model agree with neutron scattering experiments on Cu(DCOO)$_2$$\cdot$4D$_2$O, where a broad spectral-weight continuum at $q=(\pi,0)$ was interpreted as deconfined spinons. Our results at $(\pi,0)$ show a similar reduction of the magnon weight and a large continuum, while the continuum is much smaller at $q=(\pi/2,\pi/2)$ (as also seen experimentally). Turning on $Q$, we observe a rapid reduction of the $(\pi,0)$ magnon weight to zero, well before the deconfined quantum phase transition into a spontaneously dimerized state. We re-interpret the picture of deconfined spinons at $(\pi,0)$ in the experiments as nearly deconfined spinons---a precursor to deconfined quantum criticality. To further elucidate the picture of a fragile $(\pi,0)$-magnon in the Heisenberg model and its depletion in the $J$-$Q$ model, we introduce an effective model in which a magnon can split into two spinons that do not separate but fluctuate in and out of the magnon space (in analogy with the resonance between a photon and a particle-hole pair in the exciton-polariton problem). The model reproduces the $(\pi,0)$ and $(\pi/2,\pi/2)$ features of the Heisenberg model. It can also account for the rapid loss of the $(\pi,0)$ magnon with increasing $Q$ and a remarkable persistence of a large magnon pole at $q=(\pi/2,\pi/2)$ even at the deconfined critical point.

Emergence of a Dimer–Dimer Interaction in the Low-Energy Effective Quantum-Dimer Model of a Diamond-Like-Decorated Square-Lattice Heisenberg Antiferromagnets with Further Neighbor Couplings

We study spin-1/2 Heisenberg antiferromagnets on a diamond-like-decorated square lattice perturbed by two kinds of further neighbor couplings. In our previous study [J. Phys. Soc. Jpn. 85, 094002 (2016)], the second-order effective Hamiltonian for the Heisenberg model perturbed by a further neighbor coupling was found to be a square-lattice quantum-dimer model with a finite hopping amplitude, t>0, and no dimer-dimer interaction, v=0. In this study, we introduce another kind of further neighbor coupling and show that it leads to an attractive interaction between dimers, which suggests the stabilization of the columnar phase of the square-lattice quantum-dimer model. The calculated v/t is presented as a function of the ratio of the two exchange parameters in the Heisenberg model.

Magnetic excitations from the two-dimensional interpenetrating Cu framework in Ba2Cu3O4Cl2

We report detailed neutron scattering studies on Ba$_2$Cu$_3$O$_4$Cl$_2$. The compound consists of two interpenetrating sublattices of Cu, labeled as Cu$_{\rm A}$ and Cu$_{\rm B}$, each of which forms a square-lattice Heisenberg antiferromagnet. The two sublattices order at different temperatures and effective exchange couplings within the sublattices differ by an order of magnitude. This yields an inelastic neutron spectrum of the Cu$_{\rm A}$ sublattice extending up to 300 meV and a much weaker dispersion of Cu$_{\rm B}$ going up to around 20 meV. Using a single-band Hubbard model we derive an effective spin Hamiltonian. From this, we find that linear spin-wave theory gives a good description to the magnetic spectrum. In addition, a magnetic field of 10 T is found to produce effects on the Cu$_{\rm B}$ dispersion that cannot be explained by conventional spin-wave theory.

RVB signatures in the spin dynamics of the square-lattice Heisenberg antiferromagnet

We investigate the spin dynamics of the square-lattice spin- Heisenberg antiferromagnet by means of an improved mean-field Schwinger boson calculation. By identifying both, the long-range Néel and the RVB-like components of the ground state, we propose an educated guess for the mean-field magnetic excitation consisting on a linear combination of local and bond spin flips to compute the dynamical structure factor. Our main result is that when this magnetic excitation is optimized in such a way that the corresponding sum rule is fulfilled, we recover the low- and high-energy spectral weight features of the experimental spectrum. In particular, the anomalous spectral weight depletion at found in recent inelastic neutron scattering experiments can be attributed to the interference of the triplet bond excitations of the RVB component of the ground state. We conclude that the Schwinger boson theory seems to be a good candidate to adequately interpret the dynamic properties of the square-lattice Heisenberg antiferromagnet.

Strong Suppression of Magnetic Ordering in an S = 1/2 Square-Lattice Heisenberg Antiferromagnet Sr2CuTeO6

We report the magnetic susceptibility and the low-temperature specific heat of a double perovskite compound, Sr2CuTeO6, which is expected as the spin-1/2 square-lattice Heisenberg antiferromagnet with nearest-neighbor J1 and next-nearest-neighbor J2 exchange interactions. The specific heat exhibits a sharp lambda-like anomaly at TN = 4.8 K indicative of magnetic ordering, which is much lower than those in isostructural A2CuMO6 with A = Ba, Sr and M = W, Mo. This indicates the strong suppression of magnetic ordering in Sr2CuTeO6. We estimate the exchange constant J1/kB ~ 80 K and J2/J1 < 0.07 from magnetic susceptibility data using Pade approximation of high temperature expansion and quantum Monte Carlo method. The strong suppression of magnetic ordering in Sr2CuTeO6 should be ascribed to the weekness of the interlayer exchange.

Field-induced decay dynamics in square-lattice antiferromagnets

Dynamical properties of the square-lattice Heisenberg antiferromagnet in applied magnetic field are studied for arbitrary value S of the spin. Above the threshold field for two-particle decays, the standard spin-wave theory yields singular corrections to the excitation spectrum with logarithmic divergences for certain momenta. We develop a self-consistent approximation applicable for S >= 1, which avoids such singularities and provides regularized magnon decay rates. Results for the dynamical structure factor obtained in this approach are presented for S = 1 and S = 5/2.

Spin correlations and magnetic order in nonsuperconducting Nd(2-x)Ce(x)CuO(4+/-delta).

We report quantitative neutron scattering measurements of the evolution with doping of the Néel temperature, the antiferromagnetic correlations, and the ordered moment of as-grown, nonsuperconducting Nd(2-x)Ce(x)CuO(4+/-delta) (0</=x</=0.18). The instantaneous correlation length can be effectively described by our quantum Monte Carlo calculations for the randomly site-diluted nearest-neighbor spin-1/2 square-lattice Heisenberg antiferromagnet. However, quantum fluctuations have a stronger effect on the ordered moment, which decreases more rapidly than for the quenched-disorder model.

Density matrix renormalization group calculations for two-dimensional lattices: Application to the spin-half and spin-one square-lattice Heisenberg models

A new density matrix renormalisation group (DMRG) approach is presented for quantum systems of two spatial dimensions. In particular, it is shown that it is possible to create a multi-chain-type 2D DMRG approach which utilises previously determined system and environment blocks {\it at all points}. One firstly builds up effective quasi-1D system and environment blocks of width $L$ and these quasi-1D blocks are then used to as the initial building-blocks of a new 2D infinite-lattice algorithm. This algorithm is found to be competitive with those results of previous 2D DMRG algorithms and also of the best of other approximate methods. An illustration of this is given for the spin-half and spin-one Heisenberg models on the square lattice. The best results for the ground-state energies per bond of the spin-half and spin-one square-lattice Heisenberg antiferromagnets for the $N = 20 \times 20$ lattice using this treatment are given by $E_g/N_B = -0.3321$ and $E_g/N_B = -1.1525$, respectively.

Ground-state phases in a system of two competing square-lattice Heisenbergantiferromagnets

We study a two-dimensional (2D) spin-half Heisenbergmodel related to the quasi-2D antiferromagnets (Ba, Sr)2Cu3O4Cl2by means of exact diagonalization and spin-wave theory. The modelconsists of two inequivalent interpenetrating square-lattice Heisenbergantiferromagnets A and B. While the antiferromagnetic interaction JAAwithin the A subsystem is strong the coupling JBBwithin the B subsystem is much weaker. The coupling JABbetween A and B subsystems is competing, giving rise to interestingfrustration effects. In dependence of the strength of JABwe find a collinear Néel phase, non-collinear states with zero magnetizationsas well as canted and collinear ferrimagnetic phases with non-zeromagnetizations. For not too large values of frustration JAB,which correspond to the situation in (Ba, Sr)2Cu3O4Cl2,we have Néel ordering in both subsystems A and B. In the classicallimit these two Néel states are decoupled. Quantum fluctuations leadto a fluctuational coupling between both subsystems (‘order fromdisorder’) and select the collinear structure. For stronger JABwe find evidence for a novel spin state with coexisting Néel ordering in the Asubsystem and disorder in the B subsystem.

Neutron scattering, magnetometry, and quantum Monte Carlo study of the randomly diluted spin-1/2 square-lattice Heisenberg antiferromagnet

We have successfully grown sizable single crystals of La 2Cu 1− z (Zn,Mg) z O 4 with up to nearly half of the magnetic Cu sites replaced by non-magnetic Zn and Mg. Neutron scattering, SQUID magnetometry, and complementary quantum Monte Carlo (QMC) simulations demonstrate that this material is an excellent model system for the study of site percolation of the square-lattice Heisenberg antiferromagnet (SLHAF) in the quantum-spin limit S=1/2. Carefully oxygen-reduced samples exhibit Néel order up to the percolation threshold for site dilution, z p≈40.7%. For z>10%, the material exhibits a low-temperature tetragonal (LTT) structural phase, with a transition temperature that increases linearly with doping. Above z≈25%, Néel order occurs in the LTT phase. Up to at least z=35%, the Néel temperature T N( z) of the experimental system corresponds to the temperature at which QMC indicates that the spin correlations for the nearest-neighbor S=1/2 SLHAF have grown to approximately 100 lattice constants. Neutron scattering measurements of the static structure factor in the paramagnetic regime allow the determination of the two-dimensional spin correlations, which are found to be in excellent quantitative agreement with QMC over a wide common temperature and doping range. Neutron scattering and QMC results for the temperature dependence of the static structure factor amplitude S(π,π) are in good agreement as well. As the concentration of non-magnetic sites is increased, the magnetic correlation length ξ( T, z) crosses over from an exponential dependence on ρ s/ T to power-law behavior in the temperature regime studied. Fits to a heuristic cross-over form for ξ( T, z) allow an estimate of the spin stiffness, ρ s= ρ s( z), which approaches zero at z= z p. The combined experimental and numerical data presented here provide valuable quantitative information for tests of theories of the randomly diluted S=1/2 SLHAF.

Effective sublattice magnetization and Néel temperature in quantum antiferromagnets

We present an analytic expression for the finite temperature sublattice magnetization which would be detected by inelastic neutron-scattering experiments performed on a two-dimensional square-lattice quantum Heisenberg antiferromagnet with short-range N\'eel order. Our expression, which has no adjustable parameters, is able to reproduce both the qualitative behavior of the phase diagram $M(T)\ifmmode\times\else\texttimes\fi{}T$ and the experimental values of the N\'eel temperature ${T}_{N}$ for either doped ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.15}$ and stoichiometric ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$ compounds. Finally, we remark that by incorporating frustration and three-dimensional effects as perturbations is sufficient to explain the deviation of the experimental data from our theoretical curves.

Quantum phase transitions of a square-lattice Heisenberg antiferromagnet with two kinds of nearest-neighbor bonds: A high-order coupled-cluster treatment

We study the zero-temperature phase diagram and the low-lying excitations of a square-lattice spin-half Heisenberg antiferromagnet with two types of regularly distributed nearest-neighbor exchange bonds $[J&gt;0$ (antiferromagnetic) and $\ensuremath{-}\ensuremath{\infty}&lt;{J}^{\ensuremath{'}}&lt;\ensuremath{\infty}]$ using the coupled cluster method (CCM) for high orders of approximation (up to LSUB8). We use a N\'eel model state as well as a helical model state as a starting point for the CCM calculations. We find a second-order transition from a phase with N\'eel order to a finite-gap quantum disordered phase for sufficiently large antiferromagnetic exchange constants ${J}^{\ensuremath{'}}&gt;0.$ For frustrating ferromagnetic couplings ${J}^{\ensuremath{'}}&lt;0$ we find indications that quantum fluctuations favor a first-order phase transition from the N\'eel order to a quantum helical state, by contrast with the corresponding second-order transition in the corresponding classical model. The results are compared to those of exact diagonalizations of finite systems (up to 32 sites) and those of spin-wave and variational calculations. The CCM results agree well with the exact diagonalization data over the whole range of the parameters. The special case of ${J}^{\ensuremath{'}}=0,$ which is equivalent to the honeycomb lattice, is treated more closely.

Temperature behavior of the magnon modes of the square-lattice antiferromagnet

A spin-wave theory of short-range order in the square-lattice Heisenberg antiferromagnet is formulated. With growing temperature from $T=0$ a gapless mode is shown to arise simultaneously with opening a gap in the conventional spin-wave mode. The spectral intensity is redistributed from the latter mode to the former. For low temperatures the theory reproduces results of the modified spin-wave theory by Takahashi [Phys. Rev. B 40, 2494 (1989)] and Hirsch et al. [Phys. Rev. B 40, 5000 (1989)], and without fitting parameters gives values of observables in good agreement with Monte Carlo results in the temperature range $0&lt;~T\ensuremath{\lesssim}0.8J$ where J is the exchange constant.

A new paradigm for two-dimensional spin liquids

Motivated by the geometry of the materials Na2Ti2As2O and Na2Ti2Sb2O, we study a square-lattice Heisenberg antiferromagnet, with spins located at the bond centers. The largest exchange constant J couples neighboring spins in a given row or column. This leads to a mesh of isolated spin chains running along the X and Y axes. A weaker exchange constant J′ couples the nearest-neighbor spins on the lattice. Classically, J′ fails to fix the relative spin orientation for different chains and hence the ground state is highly degenerate. Quantum order by disorder effect is studied by spin-wave theory and numerical methods. It is shown that a four-sublattice order is favored by quantum fluctuations. However, several arguments are presented that suggest that the ground state of the system remains disordered, thus providing us with a paradigm for a two-dimensional spin liquid.

Various series expansions for the bilayer S= Heisenberg antiferromagnet

Various series expansions have been developed for the two-layer, S=, square-lattice Heisenberg antiferromagnet. High-temperature expansions are used to calculate the temperature dependence of the susceptibility and specific heat. At T=0, Ising expansions are used to study the properties of the N\'eel-ordered phase, while dimer expansions are used to calculate the ground-state properties and excitation spectra of the magnetically disordered phase. The antiferromagnetic order-disorder transition point is determined to be (${\mathrm{J}}_{2}$/${\mathrm{J}}_{1}$${)}_{\mathrm{c}}$=2.537(5). Quantities computed include the staggered magnetization, the susceptibility, the triplet spin-wave excitation spectra, the spin-wave velocity, and the spin-wave stiffness. We also estimate the ratio of the intralayer and interlayer exchange constants to be ${\mathrm{J}}_{2}$/${\mathrm{J}}_{1}$\ensuremath{\simeq}0.07 for the cuprate superconductor ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{6.2}$, a factor of 2 smaller than Schwinger-boson mean-field theory would suggest.

Square-lattice Heisenberg antiferromagnet with two kinds of nearest-neighbor regular bonds.

We study the zero-temperature phase diagram of a square-lattice S=1/2 Heisenberg antiferromagnet with two types of regularly distributed nearest-neighbor exchange constants, ${\mathit{J}}_{1}$\ensuremath{\gtrsim}0 (antiferromagnetic) and -\ensuremath{\infty}${\mathit{J}}_{2}$\ensuremath{\infty}, using spin-wave series based on appropriate mean-field Hamiltonian and exact-diagonalization data for small clusters. At a semiclassical level, the model displays two critical points separating the N\'eel state from (i) a helicoidal magnetic phase for relatively small frustrating ferromagnetic couplings ${\mathit{J}}_{2}$0 (${\mathit{J}}_{2}$/${\mathit{J}}_{1}$-1/3 for classical spins), and (ii) a finite-gap quantum paramagnetic phase for large enough antiferromagnetic exchange constants ${\mathit{J}}_{2}$\ensuremath{\gtrsim}0. The quantum order-disorder transition (ii) is similar to the one recently studied in two-layer Heisenberg antiferromagnets and is a pure result of the zero-point spin fluctuations. On the other hand, the melting of the N\'eel state in the ferromagnetic region, ${\mathit{J}}_{2}$0, is a combined effect of the frustration and quantum spin fluctuations. The second-order spin-wave calculations of the ground-state energy and on-site magnetization are in accord with our exact-diagonalization data in a range away from the quantum paramagnetic phase. In approaching the phase boundary, the theory fails due to the enhanced longitudinal-spin fluctuations, as it has recently been argued by Chubukov and Morr.

Spin Dependence of Correlations in Two-Dimensional Square-Lattice Quantum Heisenberg Antiferromagnets

We present a series expansion study of spin-S square-lattice Heisenberg antiferromagnets. The numerical data are in excellent agreement with recent neutron scattering measurements. Our key result is that the correlation length for S>1/2 strongly deviates from the exact T->0 (renormalized classical, or RC) scaling prediction for all experimentally and numerically accessible temperatures. We note basic trends with S of the experimental and series expansion correlation length data and propose a scaling crossover scenario to explain them.

Ground-state phase relationships and level ordering for frustrated quantum antiferromagnets

We present arguments in favor of the suggestion that the Marshall-Peierls phase relationships and the Lieb-Mattis level ordering survive the frustration in the squarelattice Heisenberg antiferromagnet for relatively strong frustration parameters.