High temperature expansion for frustrated and unfrustrated S={1 \over 2} spin chains

A computer aided high temperature expansion of the magnetic susceptibility and the magnetic specific heat is presented and demonstrated for frustrated and unfrustrated spin chains. The results are analytic in nature since the calculations are performed in the integer domain. They are provided in the form of polynomials allowing quick and easy fits. Various representations of the results are discussed. Combining high temperature expansion coefficients and dispersion data yields very good agreement already in low order of the expansion which makes this approach very promising for the application to other problems, for instance in higher dimensions. Received 24 February 2000 and Received in final form 5 April 2000     

Ladders in a magnetic field: a strong coupling approach

We show that non-frustrated and frustrated ladders in a magnetic field can be systematically mapped onto an XXZ Heisenberg model in a longitudinal magnetic field in the limit where the rung coupling is the dominant one. This mapping is valid in the critical region where the magnetization goes from zero to saturation. It allows one to relate the properties of the critical phase (H _c ¹, H _c ², the critical exponents) to the exchange integrals and provide quantitative estimates of the frustration needed to create a plateau at half the saturation value for different models of frustration. Received: 7 May 1998 / Revised and Accepted: 10 July 1998     

Magnetic properties of the low dimensional spin system (VO)PO:ESR and susceptibility

Experimental results on magnetic resonance (ESR) and magnetic susceptibility are given for single crystalline (VO)₂P₂O₇. The crystal growth procedure is briefly discussed. The susceptibility is interpreted numerically using a model with alternating spin chains. We determine J =51 K and . Furthermore we find a spin gap of meV from our ESR measurements. Using elastic constants no indication of a phase transition forcing the dimerization is seen below 300 K. Received: 22 December 1997 / Accepted: 17 March 1998     

RVB description of the low-energy singlets of the spin 1/2 kagomé antiferromagnet

Extensive calculations in the short-range RVB (Resonating valence bond) subspace on both the trimerized and the regular (non-trimerized) Heisenberg model on the kagomé lattice show that short-range dimer singlets capture the specific low-energy features of both models. In the trimerized case the singlet spectrum splits into bands in which the average number of dimers lying on one type of bonds is fixed. These results are in good agreement with the mean field solution of an effective model recently introduced. For the regular model one gets a continuous, gapless spectrum, in qualitative agreement with exact diagonalization results. Received 7 March 2000     

On the evaluation of the specific heat and general off-diagonal n-point correlation functions within the loop algorithm

We present an efficient way to compute diagonal and off-diagonal n-point correlation functions for quantum spin-systems within the loop algorithm. We show that the general rules for the evaluation of these correlation functions take an especially simple form within the framework of directed loops. These rules state that contributing loops have to close coherently. As an application we evaluate the specific heat for the case of spin chains and ladders. Recieved 10 January 2000 and Received in final form 9 February 2000     

Magnetic properties of zig-zag ladders

We analyze the phase diagram of a system of spin-1/2 Heisenberg antiferromagnetic chains interacting through a zig-zag coupling, also called zig-zag ladders. Using bosonization techniques we study how a spin-gap or more generally plateaux in magnetization curves arise in different situations. While for coupled XXZchains, one has to deal with a recently discovered chiral perturbation, the coupling term which is present for normal ladders is restored by an external magnetic field, dimerization or the presence of charge carriers. We then proceed with a numerical investigation of the phase diagram of two coupled Heisenberg chains in the presence of a magnetic field. Unusual behaviour is found for ferromagnetic coupled antiferromagnetic chains. Finally, for three (and more) legs one can choose different inequivalent types of coupling between the chains. We find that the three-leg ladder can exhibit a spin-gap and/or non-trivial plateaux in the magnetization curve whose appearance strongly depends on the choice of coupling. Received 11 February 1999 and Received in final form 16 June 1999     

Studies of the exactly dimerized bilayer Heisenberg model via strong coupling expansions

The one-triplet excitation spectra and thermodynamic properties for the dimerized phase of the frustrated bilayer Heisenberg model are studied using strong-coupling expansion theory. The model has an exact dimerized ground state as well as exact one-triplet excitations in a special case that the frustration J₂ is equal to the in-plane coupling J₁. We demonstrate that the models with and without frustrations have distinct excitation spectra, so their thermodynamic properties exhibit quite different behaviors. Especially, the low-temperature behaviors of the frustrated model with J ₁=J ₂ are independent of the inter-dimer couplings, due to the exact one-triplet excitations. Received 16 March 2000 and Received in final form 2 July 2000     

Unconventional antiferromagnetic correlations of the doped Haldane gapsystem Y 2 BaNi 1 - x Zn x O 5

We make a new proposal to describe the very low temperature susceptibility of the doped Haldane gap compound Y₂BaNi_1-xZn_xO₅. We propose a new mean field model relevant for this compound. The ground state of this mean field model is unconventional because antiferromagnetism coexists with random dimers. We present new susceptibility experiments at very low temperature. We obtain a Curie-Weiss susceptibility χ( T ) ∼ C /(Θ + T ) as expected for antiferromagnetic correlations but we do not obtain a direct signature of antiferromagnetic long range order. We explain how to obtain the “impurity” susceptibility ( T ) by subtracting the Haldane gap contribution to the total susceptibility. In the temperature range [1 K, 300 K] the experimental data are well fitted by T ( T ) = C _imp 1 + T _imp / T . In the temperature range [100 mK, 1 K] the experimental data are well fitted by T ( T ) = A ln( T / T _c ), where T _c increases with x. This fit suggests the existence of a finite Néel temperature which is however too small to be probed directly in our experiments. We also obtain a maximum in the temperature dependence of the ac-susceptibility ( T ) which suggests the existence of antiferromagnetic correlations at very low temperature. Received 17 July 2001     

Random magnetic interactions and spin glass order competing with superconductivity: Interference of the quantum Parisi phase

We analyse the competition between spin glass (SG) order and local pairing superconductivity (SC) in the fermionic Ising spin glass with frustrated fermionic spin interaction and nonrandom attractive interaction. The phase diagram is presented for all temperatures T and chemical potentials μ. SC-SG transitions are derived for the relevant ratios between attractive and frustrated-magnetic interaction. Characteristic features of pairbreaking caused by random magnetic interaction and/or by spin glass proximity are found. The existence of low-energy excitations, arising from replica permutation symmetry breaking (RPSB) in the Quantum Parisi Phase, is shown to be relevant for the SC-SG phase boundary. Complete 1-step RPSB-calculations for the SG-phase are presented together with a few results for -step breaking. Suppression of reentrant SG-SC-SG transitions due to RPSB is found and discussed in context of ferromagnet-SG boundaries. The relative positioning of the SC and SG phases presents a theoretical landmark for comparison with experiments in heavy fermion systems and high superconductors. We find a crossover line traversing the SG-phase with as its quantum critical (end)point in complete RPSB, and scaling is proposed for its vicinity. We argue that this line indicates a random field instability and suggest Dotsenko-Mézard vector replica symmetry breaking to occur at low temperatures beyond. Received 26 November 1998 and Received in final form 25 January 1999     

Vortices in quantum spin systems

We examine spin vortices in ferromagnetic quantum Heisenberg models with planar anisotropy on two-dimensional lattices. The symmetry properties and the time evolution of vortices built up from spin-coherent states are studied in detail. Although these states show a dispersion typical for wave packets, important features of classical vortices are conserved. Moreover, the results on symmetry properties provide a construction scheme for vortex-like excitations from exact eigenstates, which have a well-controlled time evolution. Our approach works for arbitrary spin length both on triangular and square lattices. Received 2 October 1998     

Magnetic susceptibility in quasi one-dimensional Ba<Subscript>a2</Subscript>V<Subscript>3</Subscript>O<Subscript>9</Subscript>: chain segmentation versus the staggered field effect

A pronounced Curie-like upturn of the magnetic susceptibility χ( T ) of the quasi one-dimensional spin chain compound Ba₂V₃O₉ has been found recently [#!kaul:02!#]. Frequently this is taken as a signature for a staggered field mechanism due to the presence of g-factor anisotropy and Dzyaloshinskii-Moriya interaction. We calculate this contribution within a realistic structure of vanadium 3 d- and oxygen 2 p-orbitals and conclude that this mechanism is far too small to explain experimental results. We propose that the Curie term is rather due to a segmentation of spin chains caused by broken magnetic bonds which leads to uncompensated S = ? spins of segments with odd numbers of spins. Using the finite-temperature Lanczos method we calculate their effective moment and show that ∼ 1% of broken magnetic bonds is sufficient to reproduce the anomalous low-T behavior of χ( T ) in Ba₂V₃O₉. Received 19 December 2002 / Received in final form 29 January 2003 Published online 14 March 2003     

The two dimensional classical anisotropic Heisenberg ferromagnetic model with nearest- and next-nearest neighbor interactions

We use the self-consistent harmonic approximation (SCHA) to study the two-dimensional classical Heisenberg anisotropic (easy-plane) ferromagnetic model including nearest- and next-nearest neighbor exchange interactions. For temperatures much lower than the Kosterlitz-Thouless phase transition temperature T _KT, spin waves must be the most relevant excitations in the system and the SCHA must account for its behavior. However, for temperatures near T _KT, we should expect vortex pairs to be quite important. The effect of these vortex excitations on the phase transition temperature is included in our theory as a renormalization of the exchange interactions. Then, combining the SCHA theory to the renormalization effect due to vortex pairs, we calculate the dependence of T _KT as a function of the easy-plane anisotropies and exchange interactions. Received 3 April 2001 and Received in final form 20 September 2001     

Independent magnon states on magnetic polytopes

For many spin systems with constant isotropic antiferromagnetic next-neighbour Heisenberg coupling the minimal energies E _min(S) form a rotational band, i.e. depend approximately quadratically on the total spin quantum number S, a property which is also known as Landé interval rule. However, we find that for certain coupling topologies, including recently synthesised icosidodecahedral structures this rule is violated for high total spins. Instead the minimal energies are a linear function of total spin. This anomaly results in a corresponding jump of the magnetisation curve which otherwise would be a regular staircase. Received 27 August 2001 and Received in final form 18 October 2001     

Finite-size-scaling analyses of the chiral ordert in the Josephson-junction ladder with half a flux quantum per plaquette

Chiral order of the Josephson-junction ladder with half a flux quantum per plaquette is studied by means of the exact diagonalization method. We consider an extreme quantum limit where each superconductor grain (order parameter) is represented by S=1/2 spin. So far, the semi-classical case, where each spin reduces to a plane rotator, has been considered extensively. We found that in the case of S=1/2, owing to the strong quantum fluctuations, the chiral (vortex lattice) order becomes dissolved except in a region, where attractive intrachain and, to our surprise, repulsive interchain interactions both exist. On the contrary, for considerably wide range of parameters, the superconductor (XY) order is kept critical. The present results are regarded as a demonstration of the critical phase accompanying chiral-symmetry breaking predicted for frustrated XXZ chain field-theoretically. Received 20 February 2000     

Effective scaling behavior of magnetization and Hamming distance in Ising thin films under a surface field

The recent improvements on the technology for developing high-quality thin magnetic films has renewed the interest in the study of surface effects in both static and dynamic magnetic responses. In this work, we use a Monte-Carlo algorithm with Metropolis dynamics together with a spreading of damage technique to study the interplay between the effects of finite thickness and surface ordering field in thin ferromagnetic Ising (S=1/2) films. We calculate, near the bulk critical temperature and several values of the surface field, the dependence on the film thickness of the average magnetization M and Hamming distance D. We employ a finite size scaling analysis to show that both obey an effective one-parameter scaling but exhibit distinct characteristic surface fields. At their corresponding characteristic surface fields both M and D become roughly thickness independent and we estimate the critical exponent characterizing the behavior of the typical scaling lengths. Received 29 March 1999 and Received in final form 21 April 1999     

Low temperature specific heat of molecular rings: a study on the effects of the internal guest substitution and on the lattice contribution

The effects of the internal guest substitution within hexa-iron molecular rings (Na:Fe6 and Li:Fe6) have been investigated by means of low temperature specific heat (LTSH) measurements. By changing Na to Li as central metal ion, the Schottky anomaly shifts towards lower temperatures. The data analysis is supported by the study of the LTSH of the non-magnetic Na:Ga6 compound which has the same core structure as the iron rings. For the non-magnetic Na:Ga6, significant deviations from the simple Debye law were found and the use of conventional C vs. T fitting curves is critically discussed. The singlet-triplet energy gap ( K) and its zero-field splitting ( K) evaluated from the magnetic contribution of the Li:Fe6 LTSH are compared to values estimated by high field torque magnetometry. Received 25 November 1999     

Classical spin liquid properties of the infinite-component spin vector model on a fully frustrated two dimensional lattice

Thermodynamic quantities and correlation functions (CFs) of the classical antiferromagnet on the checkerboard lattice are studied for the exactly solvable infinite-component spin-vector model, D↦∞. In contrast to conventional two-dimensional magnets with continuous symmetry showing extended short-range order at distances smaller than the correlation length, r ξ _c∝ exp(T ^*/T), correlations in the checkerboard-lattice model decay already at the scale of the lattice spacing due to the strong degeneracy of the ground state characterized by a macroscopic number of strongly fluctuating local degrees of freedom. At low temperatures, spin CFs decay as < >∝ 1/r ² in the range a ₀≪r≪ξ _c∝T ^-1/2, where a₀ is the lattice spacing. Analytical results for the principal thermodynamic quantities in our model are very similar with MC simulations, exact and analytical results for the classical Heisenberg model (D = 3) on the pyrochlore lattice. This shows that the ground state of the infinite-component spin vector model on the checkerboard lattice is a classical spin liquid. Received 16 November 2001 and Received in final form 12 February 2002     

Characterization of ferrimagnetic Heisenberg chains according to the constituent spins

The low-energy structure and the thermodynamic properties of ferrimagnetic Heisenberg chains of alternating spins S and s are investigated by the use of numerical tools as well as the spin-wave theory. The elementary excitations are calculated through an efficient quantum Monte Carlo technique featuring imaginary-time correlation functions and are characterized in terms of interacting spin waves. The thermal behavior is analyzed with particular emphasis on its ferromagnetic and antiferromagnetic dual aspect. The extensive numerical and analytic calculations lead to the classification of the one-dimensional ferrimagnetic behavior according to the constituent spins: the ferromagnetic (S>2s), antiferromagnetic (S<2s), and balanced (S=2s) ferrimagnetism. Received 27 August 1999 and Received in final form 15 November 1999