M. Greven

Monte carlo study of correlations in quantum spin ladders

We study antiferromagnetic spin-1/2 Heisenberg ladders, comprised of {ital n}{sub {ital c}} chains (2{le}{ital n}{sub {ital c}}{le}6) with ratio {ital J}{sub {perpendicular}}/{ital J}{sub {parallel}} of interchain to intrachain couplings. The correlation length {xi}({ital T}) is deduced from measurements of the correlation function. For even {ital n}{sub {ital c}}, the static structure factor exhibits a peak at a temperature below the corresponding spin gap. Results for isotropically coupled ladders ({ital J}{sub {perpendicular}}/{ital J}{sub {parallel}}=1) are compared to those for the single chain and the square lattice. For {ital J}{sub {perpendicular}}/{ital J}{sub {parallel}}{le}0.5, the correlation function of the two-chain ladder is in excellent agreement with analytic results from conformal field theory, and {xi}({ital T}) exhibits simple scaling behavior. {copyright} {ital 1996 The American Physical Society.}

Square-Lattice Heisenberg Antiferromagnet at Very Large Correlation Lengths

The correlation length of the square-lattice spin-1/2 Heisenberg antiferromagnet is studied in the low-temperature (asymptotic-scaling) regime. Our novel approach combines a very efficient loop cluster algorithm{emdash}operating directly in the Euclidean time continuum{emdash}with finite-size scaling. This enables us to probe correlation lengths up to {xi}{approx}350,000 lattice spacings, more than 3 orders of magnitude larger than in any previous study. We resolve a conundrum concerning the applicability of asymptotic-scaling formulas to experimentally and numerically determined correlation lengths. Our results have direct implications for the zero-temperature behavior of spin-1/2 ladders. {copyright} {ital 1998} {ital The American Physical Society}

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

We have carried out a neutron scattering investigation of the static structure factorS(q2D) (q2D is the in-plane wave vector) in the two-dimensional spinS=1/2 square-lattice Heisenberg antiferromagnet Sr2CuO2Cl2. For the spin correlation length ξ 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)∼ξ2 for the reduced temperature range 0.16<T/2πρs<0.36, whereas current theories predict that at low temperaturesS(0)∼T2ξ2. 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 anisotropyJXY/J=1.4×10−4. From measurements of the sublattice mangetization we obtain β=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-stiffnessρs reduced by ≈20% from the spin-wave value. As in Sr2CuO2Cl2 we find thatS(0)∼ξ2 for the reduced temperature range 0.22<T/2πρs<0.47.

Soft phonon behavior and magnetism at the low temperature structural phase transition of La1.65Nd0.35CuO4

We report a neutron scattering investigation of a La1.65Nd0.35CuO4 single crystal which undergoes a second order structural transition with decreasing temperature from a high temperature orthorhombic phase (space group Bmab) to a distinct low temperature orthorhombic phase (space group Pccn) atTs=76 K. The transition is induced by the softening of the phonon mode that involves rotations of the tilt axis of the CuO6 octahedra. Antiferromagnetic long range order is established belowTN=316 K, and a hysteretic reorientation to a noncollinear spin structure occurs belowTs. The low energy spin dynamics of La1.65Nd0.35CuO4 aboveTs are closely similar to those of stoichiometric La2CuO4; at 100 K the gaps for in-plane and out-of-plane polarized spin waves are 2.3 meV and 5 meV, respectively. Out-of-plane polarized magnons are little affected by the structural transition, but the gap for in-plane polarized magnons increases markedly belowTs.

Instantaneous spin correlations in (formula presented)

We have carried out a neutron scattering study of the instantaneous spin-spin correlations in La2CuO4 (T_N = 325 K) over the temperature range 337 K to 824 K. Incident neutron energies varying from 14.7 meV to 115 meV have been employed in order to guarantee that the energy integration is carried out properly. The results so-obtained for the spin correlation length as a function of temperature when expressed in reduced units agree quantitatively both with previous results for the two dimensional (2D) tetragonal material Sr2CuO2Cl2 and with quantum Monte Carlo results for the nearest neighbor square lattice S=1/2 Heisenberg model. All of the experimental and numerical results for the correlation length are well described without any adjustable parameters by the behavior predicted for the quantum non-linear sigma model in the low temperature renormalized classical regime. The amplitude, on the other hand, deviates subtly from the predicted low temperature behavior. These results are discussed in the context of recent theory for the 2D quantum Heisenberg model.

Monte-Carlo study of correlations in quantum spin chains at non-zero temperature

Abstract:Antiferromagnetic Heisenberg spin chains with various spin values (S=1/2,1,3/2,2,5/2) are studied numerically with the quantum Monte-Carlo method. Effective spin S chains are realized by ferromagnetically coupling n=2S antiferromagnetic spin chains with S=1/2. The temperature dependence of the uniform susceptibility, the staggered susceptibility, and the static structure factor peak intensity are computed down to very low temperatures, . The correlation length at each temperature is deduced from numerical measurements of the instantaneous spin-spin correlation function. At high temperatures, very good agreement with exact results for the classical spin chain is obtained independent of the value of S. For the S=2 chain which has a gap , the correlation length and the uniform susceptibility in the temperature range are well predicted by the semi-classical theory of Damle and Sachdev.

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.

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 aboveTN. The correlation length, ξ(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 ξ(T) is found with the exact low-temperature result of Hasenfratz and Niedermeyer provided that 2πps is renormalized by ≈20% from the spin-wave value.

Spin correlations in the two-dimensional spin-5/2 Heisenberg antiferromagnet Rb2MnF4

Abstract:We report a neutron scattering study of the instantaneous spin correlations in the two-dimensional spin S=5/2 square-lattice Heisenberg antiferromagnet Rb2MnF4. The measured correlation lengths are quantitatively described, with no adjustable parameters, by high-temperature series expansion results and by a theory based on the quantum self-consistent harmonic approximation. Conversely, we find that the data, which cover the range from about 1 to 50 lattice constants, are outside of the regime corresponding to renormalized classical behavior of the quantum non-linear model. In addition, we observe a crossover from Heisenberg to Ising critical behavior near the Néel temperature; this crossover is well described by a mean-field model with no adjustable parameters.

Correlation Lengths in Quantum Spin Ladders

Analytic expressions for the temperature dependences of the correlation length are given for antiferromagnetic spin-(1)/(2) Heisenberg ladders using a finite-size nonlinear {sigma} model approach. These calculations rely on identifying three successive crossover regimes as a function of temperature. In each of these regimes, precise and controlled approximations are formulated. The analytical results are found to be in excellent agreement with Monte Carlo simulations for the Heisenberg Hamiltonian. {copyright} {ital 1997} {ital The American Physical Society}