Neutron scattering study of the two-dimensional spinS=1/2 square-lattice Heisenberg antiferromagnet Sr2CuO2Cl2

We have carried out a neutron scattering investigation of the static structure factorS(q _2D ) (q _2D is the in-plane wave vector) in the two-dimensional spinS=1/2 square-lattice Heisenberg antiferromagnet Sr₂CuO₂Cl₂. For the spin correlation length we find quantitative agreement with Monte Carlo results over a wide range of temperature. The combined Sr₂CuO₂Cl₂-Monte Carlo data, which cover the length scale from 1 to 200 lattice constants, are predicted without adjustable parameteres by renormalized classical theory for the quantum nonlinear sigma model. For the structure factor peakS(0), on the other hand, we findS(0) ² for the reduced temperature range 0.16<T/2 _s <0.36, whereas current theories predict that at low temperaturesS(0)T ^{2 2}. This discrepancy has important implications for the interpretation of many derivative quantities such as NMR relaxation rates. In the ordered phase, we have measured the temperature dependence of the out-of-plane spin-wave gap. Its low-temperature value of 5.0 meV corresponds to an XY anisotropyJ _XY /J=1.4×10^–4. From measurements of the sublattice mangetization we obtain =0.22±0.01 for the order parameter exponent. This may either reflect tricricality as in La₂CuO₄, or it may indicate finite-size two-dimensional XY behavior as suggested by Bramwell and Holdsworth. As in theS=1 system K₂NiF₄, the gap energy in Sr₂CuO₂Cl₂ scales linearly with the order parameter up to the Néel temperature. We also reanalyze static structure factor data for K₂NiF₄ using the exact low temperature result for the correlation length of Hasenfratz and Niedermayer and including the Ising anisotropy explicitly. Excellent agreement between experiment and theory is obtained for the correlation length, albeit with the spin-stiffness _s reduced by 20% from the spin-wave value. As in Sr₂CuO₂Cl₂ we find thatS(0) ² for the reduced temperature range 0.22<T/2 _s <0.47.     

First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice

We study the exact low energy spectra of the spin 1/2 Heisenberg antiferromagnet on small samples of the kagomé lattice of up to N=36 sites. In agreement with the conclusions of previous authors, we find that these low energy spectra contradict the hypothesis of Néel type long range order. Certainly, the ground state of this system is a spin liquid, but its properties are rather unusual. The magnetic () excitations are separated from the ground state by a gap. However, this gap is filled with nonmagnetic () excitations. In the thermodynamic limit the spectrum of these nonmagnetic excitations will presumably develop into a gapless continuum adjacent to the ground state. Surprisingly, the eigenstates of samples with an odd number of sites, i.e. samples with an unsaturated spin, exhibit symmetries which could support long range chiral order. We do not know if these states will be true thermodynamic states or only metastable ones. In any case, the low energy properties of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice clearly distinguish this system from either a short range RVB spin liquid or a standard chiral spin liquid. Presumably they are facets of a generically new state of frustrated two-dimensional quantum antiferromagnets. Received: 27 November 1997 / Accepted: 29 January 1998     

RVB theory of the Hubbard model on the triangular lattice

We propose a Green's function technique, to investigate finite-temperature properties of the Hubbard model on the triangular lattice. The lattices are covered by dimers. The method is exact in two limits:U=0 or decoupled dimers. We apply this approximate method to calculate the ground state energy, the specific heat and the single-particle spectral weight for the 1/2-filled case. The largest lattice considered has 16×16 sites. The approximate ground state energy as a function of the on-site interactionU oscillates around the exact energyin the 1/2-filled case. We find two peaks in the specific heat. ForU5t the single-particle spectral weight splits into upper and lower Hubbard bandasymmetrically. Thus in the 1/2-filled case the chemical potential is placed in the upper band leading to a metallic state. The approximate technique yields a finite zero-point entropy for mediumU. All the investigations signal a RVB state in the range of mediumU as formerly proposed by Callaway.     

Spin dynamics and spin correlations in the spinS=1 two-dimensional square-lattice Heisenberg antiferromagnet La2NiO4

The static and dynamic spin fluctuations in the spinS=1, two-dimensional (2D) square-lattice antiferromagnet La₂NiO₄ have been studied over a wide temperature range using neutron scattering techniques. The spin correlations in La₂NiO₄ exhibit a crossover from two- to three-dimensional (3D) behavior as the Néel temperature is approached from above. Critical slowing down of the low-energy spin fluctuations is also observed just aboveT _N . The correlation length, (T), and the static structure factor,S(0), have been measured and are compared with recent theoretical calculations for the quantum 2D Heisenberg antiferromagnet using microscopic parameters determined from previous spin-wave measurements. Good agreement for (T) is found with the exact low-temperature result of Hasenfratz and Niedermeyer provided that 2 p _s is renormalized by 20% from the spin-wave value.     

Modified spin-wave theory for the S = 1 frustrated antiferromagnetic Heisenberg chain

We study the one-dimensional isotropic spin-1 Heisenberg magnet with antiferromagnetic nearest-neighbor (nn) and next-nearest-neighbor (nnn) interactions by using the modified spin wave theory (MSWT). The ground state energy and the singlet-triplet energy gap are obtained for several values of j, defined as the ratio of the nnn interaction constant to the nn one. We also compare two different ways of implementing the MSWT currently found in the literature, and show that, despite the remarkable differences between the equations to be solved in each procedure, the results given by both are equivalent, except for the predicted value of the j_max, the maximum value of j accessible in each treatment. Here, we suggest that j_max is related to the disorder point of the first kind. Our results show that the ground state and the gap energies increase with j, for j ≤j_max, in accordance to previous numerical results.     

On the ground state and phase transition fors=1/2 triangular lattice Heisenberg antiferromagnet with NN and NNN interactions

We consider quantum Heisenbergs=1/2 antiferromagnet on a triangular lattice with nearest (J) and next-nearest (J) neighbour exchange interactions. The ground state is constructed from block states-exact solutions of the problem for triangular block. The structure of quantum ground state and its relationship with the classical one is investigated in detail. The approach involved leads to considerable shift of the point of transition between two phases 0.1 (compared with the semiclassical result 0.125). Consideration of spin excitations confirms that spin fluctuations do not destroy the state at the transition point, so the transition is the firstorder one.     

Schwinger-boson mean-field theory of spin-1/2 2D antiferromagnet

A consistent Schwinger-boson mean field theory is developed for a spin-1/2 2D antiferromagnet. It predicts that there are two branches of the Schwinger-boson excitation spectrum: an acoustic branch, essentially the same as that predicted by Arovas and Auerbach theory, and a new optical branch. The present theory provides a natural explanation of the mystery of the Raman two magon scattering from La₂CuO₄.     

Phase diagram of the Ising antiferromagnet with nearest-neighbor and next-nearest-neighbor interactions on a square lattice

The phase diagram of the Ising model in the presence of nearest-neighbor (J₁) and next-nearest-neighbor (J₂) interactions on a square lattice is studied within the framework of the differential operator technique. The Hamiltonian is solved by effective-field theory in finite cluster (we have chosen N=4 spins). We have proposed a functional for the free energy (similar to Landau expansion) to obtain the phase diagram in the (T,α) space (α=J₂/J₁), where the transition line from the superantiferromagnetic (SAF) to the paramagnetic (P) phase is of first-order in the range 1/2<α<0.95 in contrast to previous study of CVM (Cluster Variational Method) that predict first-order transition for α=1.0. Our results for α=1.0 are in accordance with MC (Monte Carlo) simulations, that predict a second-order transition.     

Exact diagonalization of the S = 1/2 XY ferromagnet on finite bcc lattices to estimate T = 0 properties on the infinite lattice

In this paper finite bcc lattices are defined by a triple of vectors in two different ways - upper triangular lattice form and compact form. In Appendix A are lists of some 260 distinct and useful bcc lattices of 9 to 32 vertices. The energy and magnetization of the S = 1/2 XY ferromagnet have been computed on these bcc lattices in the lowest states for S _z = 0, 1/2, 1 and 3/2. These data are studied statistically to fit the first three terms of the appropriate finite lattice scaling equations. Our estimates of the T = 0 energy and magnetization agree very well with spin wave and series expansion estimates. Received 1st August 2000 and Received in final form 22 December 2000     

Bond operator theory for the frustrated anisotropic Heisenberg antiferromagnet on a square lattice

The quantum anisotropic antiferromagnetic Heisenberg model with single ion anisotropy, spin S=1 and up to the next-next-nearest neighbor coupling (the J₁–J₂–J₃ model) on a square lattice, is studied using the bond-operator formalism in a mean field approximation. The quantum phase transitions at zero temperature are obtained. The model features a complex T=0 phase diagram, whose ordering vector is subject to quantum corrections with respect to the classical limit. The phase diagram shows a quantum paramagnetic phase situated among Neél, spiral and collinear states.     

The frustrated Heisenberg antiferromagnet on the honeycomb lattice: J1-J2 model

We study the ground-state phase diagram of the frustrated spin-[Formula: see text] antiferromagnet with J(2) = xJ(1) > 0 (J(1) > 0) on the honeycomb lattice, using the coupled-cluster method. We present results for the ground-state energy, magnetic order parameter and plaquette valence-bond crystal (PVBC) susceptibility. We find a paramagnetic PVBC phase for x(c(1)) < x < x(c(2)), where x(c(1)) ≈ 0.207 ± 0.003 and x(c(2)) ≈ 0.385 ± 0.010. The transition at x(c(1)) to the Néel phase seems to be a continuous deconfined transition (although we cannot exclude a very narrow intermediate phase in the range 0.21 ? x ? 0.24), while that at x(c(2)) is of first-order type to another quasiclassical antiferromagnetic phase that occurs in the classical version of the model only at the isolated and highly degenerate critical point [Formula: see text]. The spiral phases that are present classically for all values x > 1/6 are absent for all x ? 1.     

Quadrupolar phases of the s=1 bilinear-biquadratic Heisenberg model on the triangular lattice

Using mean-field theory, exact diagonalizations, and SU(3) flavor theory, we have precisely mapped out the phase diagram of the S = 1 bilinear-biquadratic Heisenberg model on the triangular lattice in a magnetic field, with emphasis on the quadrupolar phases and their excitations. In particular, we show that ferroquadrupolar order can coexist with short-range helical magnetic order, and that the antiferroquadrupolar phase is characterized by a remarkable 2/3 magnetization plateau, in which one site per triangle retains quadrupolar order while the other two are polarized along the field. Implications for actual S=1 magnets are discussed.     

Thermodynamics of the anisotropic spin-1/2 Heisenberg chain and related quantum chains

The free energy and correlation lengths of the spin-1/2XYZ chain are studied at finite temperature. We use the quantum transfer matrix approach and derive non-linear integral equations for all eigenvalues. Analytic results are presented for the low-temperature asymptotics, in particular for the criticalXXZ chain in an external magnetic field. These results are compared to predictions by conformal field theory. The integral equations are solved numerically for the non-criticalXXZ chain and the related spin-1 biquadratic chain at arbitrary temperature.Work performed within the research program of the Sonderforschungsbereich 341, Köln-Aachen-Jülich