Two-dimensional Heisenberg Antiferromagnet Research Articles

Collapse of Ferrimagnetism in Two-Dimensional Heisenberg Antiferromagnet due to Frustration

We study ferrimagnetism in the ground state of the antiferromagnetic Heisenberg model on the spatially anisotropic kagome lattice, in which ferrimagnetism of the conventional Lieb-Mattis type appears in the region of weak frustration whereas the ground state is nonmagnetic in the isotropic case. Numerical diagonalizations of small finite-size clusters are carried out to examine the spontaneous magnetization. We find that the spontaneous magnetization changes continuously in the intermediate region between conventional ferrimagnetism and the nonmagnetic phase. Local magnetization of the intermediate state shows strong dependence on the site position, which suggests non-Lieb-Mattis ferrimagnetism.

The magnetic order of two-dimensional anisotropic antiferromagnets

We study the two-dimensional quantum Heisenberg antiferromagnet on the square lattice with easy-axis exchange anisotropy by means of Green’s function approach within random phase and Callen’s approximations. The Néel temperature TN, energy gap w0 and staggered magnetization m are calculated. The theoretical predictions of TN and w0 for K2NiF4, Rb2MnF4, K2MnF4, Rb2MnCl4 and (CH3NH3)2MnCl4 fit well to the measured values. The power law behavior of w(T)w(0)=β[m(T)m(0)]ν is also investigated. The exponents β and ν for K2NiF4 are in excellent agreement with the experimental results.

Reentrant enhancement of quantum fluctuations for symmetric environmental coupling

The system-plus-reservoir (SPR) model is the most common and effective approach to study quantum dissipative effects. Indeed, it makes quantization possible by considering the whole energy-conserving system, while the reservoir's degrees of freedom, assumed to be harmonic, can be traced out by the path-integral technique, leading to a formulation that only includes the system of interest. In the standard SPR model the environment is only coupled with the system's coordinate and turns out to quench its quantum fluctuations. However, there are physical systems coupled with an environment whose "coordinates" and "momenta" can be completely interchangeable (e.g., magnets), so an SPR coupling must symmetrically affect both canonical variables. In this paper such a general environmental coupling is studied in the case of a harmonic oscillator. It is found that quantum fluctuations are generally enhanced by environmental coupling with an unexpected nonmonotonic behavior. This leads one to speculate about the possibility that spin-lattice coupling could drive the two-dimensional Heisenberg antiferromagnet to reach its quantum-critical point.

Antiferromagnetic to valence-bond-solid transitions in two-dimensionalSU(N)Heisenberg models with multispin interactions

We study two-dimensional Heisenberg antiferromagnets with additional multi-spin interactions which can drive the system into a valence-bond solid state. For standard SU(2) spins, we consider both four- and six-spin interactions. We find continuous quantum phase transitions with the same critical exponents. Extending the symmetry to SU(N), we also find continuous transitions for N=3 and 4. In addition, we also study quantitatively the cross-over of the order-parameter symmetry from Z4 deep inside the valence-bond-solid phase to U(1) as the phase transition is approached.

Spin transport in the anisotropic easy-plane two-dimensional Heisenberg antiferromagnet

Spin transport in the easy-plane two-dimensional anisotropic Heisenberg antiferromagnet with S=1 is studied. Regular part of spin conductivity is calculated, at zero temperature, using a self-consistent harmonic approximation and the Kubo formalism. Three magnon processes provide the dominant contribution to the spin conductivity. Furthermore, the transport is ballistic and characterized by finite Drude weight.

Hydrodynamic relation in a two-dimensional Heisenberg antiferromagnet in a field

The spin stiffness ${\ensuremath{\rho}}_{s}$ of a two-dimensional (2D) Heisenberg antiferromagnet depends nonanalytically on external magnetic field. We demonstrate that the hydrodynamic relation between ${\ensuremath{\rho}}_{s}$, the uniform susceptibility $\ensuremath{\chi}$, and the spin-wave velocity $c$ is not violated by such a behavior because similar nonanalytic terms from all three quantities mutually cancel out. In this work, explicit expressions for the field-dependent spin stiffness and for the magnon velocity of the 2D square-lattice antiferromagnet are obtained by direct calculation to order $1/S$ and in the whole range of magnetic fields.

Collective excitations in a two-dimensional antiferromagnet in a strong magnetic field

We discuss spin-$\frac{1}{2}$ two-dimensional (2D) Heisenberg antiferromagnet (AF) on a square lattice at $T=0$ in strong magnetic field $H$ near its saturation value ${H}_{c}$. A perturbation approach is proposed to obtain spectrum of magnons with momenta not very close to AF vector in the leading order in small parameter $({H}_{c}\ensuremath{-}H)/{H}_{c}$. We find that magnons are well-defined quasiparticles at $H>0.9{H}_{c}$ although the damping is quite large near the zone boundary. A characteristic rotonlike local minimum in the spectrum is observed at $\mathbf{k}=(\ensuremath{\pi},0)$, accompanied by a decrease in the damping near $(\ensuremath{\pi},0)$. The suggested approach can be used in discussion of short-wavelength excitations in other 2D Bose gases of particles or quasiparticles.

Spin transport in antiferromagnets in one and two dimensions calculated using the Kubo formula

We study spin transport in one- and two-dimensional Heisenberg antiferromagnets. In one dimension we take spin S=1. The longitudinal spin conductivity is calculated using the Kubo formula. The magnetic properties of low-dimensional systems are significantly modified by strong correlations effects. The models studied here show unconventional transport behavior: the computed spin conductivity exhibits a nonzero Drude weight at finite temperatures and thus a ballistic character. We present results for the regular part of the conductivity as a function of the frequency.

Quantum effects inS= 1/2 two-dimensional Heisenberg antiferromagnet in applied magnetic field

Quantum effects in<i>S</i>= 1/2 two-dimensional Heisenberg antiferromagnet in applied magnetic field

Bootstrap approximations in contractor renormalization

We propose a bootstrap method for approximating the long-range terms in the contractor renormalization method. The idea is tested on the two-dimensional Heisenberg antiferromagnet and the frustrated ${J}_{2}\text{\ensuremath{-}}{J}_{1}$ model. We obtain renormalization group flows that directly reveal the N\'eel phase of the unfrustrated Heisenberg antiferromagnet and the existence of a phase transition in the ${J}_{2}\text{\ensuremath{-}}{J}_{1}$ model for weak frustration. However, we find that this bootstrap method is dependent on blocking and truncation schemes. For this reason, we discuss these dependencies and unresolved issues that researchers who use this approach must consider.

Biconical structures in two-dimensional anisotropic Heisenberg antiferromagnets

Square lattice Heisenberg and $XY$ antiferromagnets with uniaxial anisotropy are studied in a field along the easy axis. Based on ground-state considerations and Monte Carlo simulations, the role of biconical structures in the transition region between the antiferromagnetic and spin-flop phases is analyzed. In particular, on adding a single-ion anisotropy to the $XXZ$ antiferromagnet, one observes, depending on the sign of that anisotropy, either an intervening biconical phase or a direct transition of first order separating the two phases. In the case of the anisotropic $XY$ model, the degeneracy of the ground state, at a critical field, in antiferromagnetic, spin-flop, and bidirectional structures seems to result, as in the case of the $XXZ$ model, in a narrow disordered phase between the antiferromagnetic and spin-flop phases, dominated by bidirectional fluctuations.

Universal Alternating Order around Impurities in Antiferromagnets

The study of impurities in antiferromagnets is of considerable interest in condensed matter physics. In this Letter we address the elementary question of the effect of vacancies on the orientation of the surrounding magnetic moments in an antiferromagnet. In the presence of a magnetic field, alternating magnetic moments are induced, which can be described by a universal expression that is valid in any ordered antiferromagnet and turns out to be independent of temperature over a large range. The universality is not destroyed by quantum fluctuations, which is demonstrated by quantum Monte Carlo simulations of the two-dimensional Heisenberg antiferromagnet. Physical predictions for finite doping are made, which are relevant for experiments probing Knight shifts and the order parameter.

Exploring contractor renormalization: Perspectives and tests on the two-dimensional Heisenberg antiferromagnet

Contractor Renormalization (CORE) is a numerical renormalization method for Hamiltonian systems that has found applications in particle and condensed matter physics. There have been few studies, however, on further understanding of what exactly it does and its convergence properties. The current work has two main objectives. First, we wish to investigate the convergence of the cluster expansion for a two-dimensional Heisenberg Antiferromagnet(HAF). This is important because the linked cluster expansion used to evaluate this formula non-perturbatively is not controlled by a small parameter. Here we present a study of three different blocking schemes which reveals some surprises and in particular, leads us to suggest a scheme for defining successive terms in the cluster expansion. Our second goal is to present some new perspectives on CORE in light of recent developments to make it accessible to more researchers, including those in Quantum Information Science. We make some comparison to entanglement-based approaches and discuss how it may be possible to improve or generalize the method.

Two-Dimensional Heisenberg Antiferromagnets: Syntheses, X-ray Structures, and Magnetic Behavior of [Cu(pz)2](ClO4)2, [Cu(pz)2](BF4)2, and [Cu(pz)2(NO3)](PF6)

We report on the syntheses, crystal structures, and magnetic susceptibilities of a family of copper pyrazine (pz)-based antiferromagnets with moderate in-plane magnetic exchange. These materials fall into two classes: monoclinic complexes [Cu(pz)2]A2 for A = ClO4 (1) or BF4 (2) and the tetragonal complex [Cu(pz)2(NO3)]PF6 (3). Compound 1 and its deuterated version [Cu(pz-d4)2](ClO4)2 (1a) crystallize in the space group C2/m at room temperature with disordered perchlorate anions. For both 1 and 2, the C centering of the Cu(II), S = 1/2, site yields four equivalent nearest neighbors, producing layers of Cu(II) ions bridged by the pz molecules, which map onto a square magnetic lattice. The layers are offset such that Cu(II) ions lie above and below the holes of adjacent layers. Compound 3 crystallizes in the space group I4/mcm with a layer structure similar to those of 1 and 2 but with Cu(II) ions of adjacent layers stacked above each other and bridged by semicoordinate NO3- ions. The variable-temperature susceptibilities in these compounds approximate a two-dimensional Heisenberg antiferromagnet with J values within the layers of 17.5(3) K (1), 15.3(3) K (2), and 10.8(3) K (3). Ordering transitions are observed in the magnetic data at 4.2(3) and 4.3(5) K for 1 and 2, respectively.

Finite-temperature order-disorder phase transition in a frustrated bilayer quantum Heisenberg antiferromagnet in strong magnetic fields

We investigate the thermodynamic properties of the frustrated bilayer quantum Heisenberg antiferromagnet at low temperatures in the vicinity of the saturation magnetic field. The low-energy degrees of freedom of the spin model are mapped onto a hard-square gas on a square lattice. We use exact diagonalization data for finite spin systems to check the validity of such a description. Using a classical Monte Carlo method we give a quantitative description of the thermodynamics of the spin model at low temperatures around the saturation field. The main peculiarity of the considered two-dimensional Heisenberg antiferromagnet is related to a phase transition of the hard-square model on the square lattice, which belongs to the two-dimensional Ising model universality class. It manifests itself in a logarithmic (low-)temperature singularity of the specific heat of the spin system observed for magnetic fields just below the saturation field.

Hidden zero-temperature bicritical point in the two-dimensional anisotropic Heisenberg model: Monte Carlo simulations and proper finite-size scaling

By considering the appropriate finite-size effect, we explain the connection between Monte Carlo simulations of two-dimensional anisotropic Heisenberg antiferromagnet in a field and the early renormalization group calculation for the bicritical point in $2+\epsilon$ dimensions. We found that the long length scale physics of the Monte Carlo simulations is indeed captured by the anisotropic nonlinear $\sigma$ model. Our Monte Carlo data and analysis confirm that the bicritical point in two dimensions is Heisenberg-like and occurs at T=0, therefore the uncertainty in the phase diagram of this model is removed.

Field dependence of the magnetic spectrum in anisotropic and Dzyaloshinskii-Moriya antiferromagnets. I. Theory

We consider theoretically the effects of an applied uniform magnetic field on the magnetic spectrum of anisotropic two-dimensional and Dzyaloshinskii-Moriya layered quantum Heisenberg antiferromagnets. The first case is relevant for systems such as the two-dimensional square lattice antiferromagnet Sr(2)CuO(2)Cl(2), while the later is known to be relevant to the physics of the layered orthorhombic antiferromagnet La(2)CuO(4). We first establish the correspondence betwenn the low-energy spectrum obtained within the anisotropic non-linear sigma model and by means of the spin-wave approximation for a standard easy-axis antiferromagent. Then, we focus on the field-theory approach to calculate the magnetic field dependence of the magnon gaps and spectral intensities for magnetic fields applied along the three possible crystallographic directions. We discuss the various possible ground states and their evolution with temperature for the different field orientations, and the occurrence of spin-flop transitions for fields perpendicular to the layers (transverse fields) as well as for fields along the easy axis (longitudinal fields). Measurements of the one-magnon Raman spectrum in Sr(2)CuO(2)Cl(2) and La(2)CuO(4) and a comparison between the experimental results and the predictions of the present theory will be reported in part II of this research work [L. Benfatto et al., cond-mat/0602664].

Effect of Quantum Fluctuation on Two-Dimensional SpatiallyAnisotropic Heisenberg Antiferromagnet with IntegerSpin

In the present paper, we calculate the Gaussian correctionto the critical value J⊥c caused by quantum spin fluctuationin a two-dimensional spatially anisotropic Heisenbergantiferromagnet with integer spin S. Previously, some authors computedthis quantity by the mean-field theory based on the Schwinger boson representationof spin operators. However, for S = 1, their result is much less than the onederived by numerical calculations. By taking the effect of quantum spin fluctuationinto consideration, we are able to produce a greatlyimproved result.

Quantum disorder and Griffiths singularities in bond-diluted two-dimensional Heisenberg antiferromagnets

We investigate quantum phase transitions in the spin-1/2 Heisenberg antiferromagnet on square lattices with inhomogeneous bond dilution. It is shown that quantum fluctuations can be continuously tuned by inhomogeneous bond dilution, eventually leading to the destruction of long-range magnetic order on the percolating cluster. Two multicritical points are identified at which the magnetic transition separates from the percolation transition, introducing a novel quantum phase transition. Beyond these multicritical points a quantum-disordered phase appears, characterized by an infinite percolating cluster with short ranged antiferromagnetic order. In this phase, the low-temperature uniform susceptibility diverges algebraically with non-universal exponents. This is a signature that the novel quantum-disordered phase is a quantum Griffiths phase, as also directly confirmed by the statistical distribution of local gaps. This study thus presents evidence of a genuine quantum Griffiths phenomenon in a two-dimensional Heisenberg antiferromagnet.

Magnetic susceptibility anisotropies in a two-dimensional quantum Heisenberg antiferromagnet with Dzyaloshinskii-Moriya interactions

The magnetic and thermodynamic properties of the two-dimensional quantum Heisenberg antiferromagnet (QHAF) that incorporates both a Dzyaloshinskii-Moriya and pseudodipolar interactions are studied within the framework of a generalized nonlinear sigma model. We calculate the static uniform susceptibility and sublattice magnetization as a function of temperature and we show that (i) the magnetic response is anisotropic and differs qualitatively from the expected behavior of a conventional easy-axis QHAF; (ii) the N\'eel second-order phase transition becomes a crossover, for a magnetic field $B\ensuremath{\perp}\mathrm{Cu}{\mathrm{O}}_{2}$ layers. We provide a simple and clear explanation for all the recently reported unusual magnetic anisotropies in the low-field susceptibility of ${\mathrm{La}}_{2}\mathrm{Cu}{\mathrm{O}}_{4}$ [L. N. Lavrov et al., Phys. Rev. Lett. 87, 017007 (2001)], and we demonstrate explicitly why ${\mathrm{La}}_{2}\mathrm{Cu}{\mathrm{O}}_{4}$ cannot be classified as an ordinary easy-axis antiferromagnet.