Magnetic field induced ordering in quasi-one-dimensional quantum magnets

Three-dimensional magnetic ordering transitions are studied theoretically in strongly anisotropic quantum magnets. An external magnetic field can drive quasi-one-dimensional subsystems with a spin gap into a gapless regime, thus inducing long-range three-dimensional magnetic ordering due to weak residual magnetic coupling between the subsystems. Compounds with higher spin degrees of freedom, such as N-leg spin-1/2 ladders, are shown to have cascades of ordering transitions. At high magnetic fields, zero-point fluctuations within the quasi-1D subsystems are suppressed, causing quantum corrections to the ordering temperature to be reduced. Received 24 March 2000     

Spin-wave spectrum of a two-dimensional itinerant electron system: Analytic results for the incommensurate spiral phase in the strong-coupling limit

We study the zero-temperature spin fluctuations of a two-dimensional itinerant-electron system with an incommensurate magnetic ground state described by a single-band Hubbard Hamiltonian. We introduce the (broken-symmetry) magnetic phase at the mean-field (Hartree-Fock) level through a spiral spin configuration with characteristic wave vector Q different in general from the antiferromagnetic wave vector Q _AF, and consider spin fluctuations over and above it within the electronic random-phase (RPA) approximation. We obtain a closed system of equations for the generalized wave vector and frequency dependent susceptibilities, which are equivalent to the ones reported recently by Brenig. We obtain, in addition, analytic results for the spin-wave dispersion relation in the strong-coupling limit of the Hubbard Hamiltonian and find that at finite doping the spin-wave dispersion relation has a hybrid form between that associated with the (localized) Heisenberg model and that associated with the (long-range) RKKY exchange interaction. We also find an instability of the spin-wave spectrum in a finite region about the center of the Brillouin zone, which signals a physical instability toward a different spin- or, possibly, charge-ordered phase, as, for example, the stripe structures observed in the high-T _c materials. We expect, however, on physical grounds that for wave vectors external to this region the spin-wave spectrum that we have determined should survive consideration of more sophisticated mean-field solutions. Received 15 September 2000     

Magnetic ground state and transition of a quantum multiferroic LiCu2O2

Based on resonant soft x-ray magnetic scattering, we report that LiCu2O2 exhibits a large interchain coupling which suppresses quantum fluctuations along spin chains, and a quasi-2D short-range magnetic order prevails at temperatures above the magnetic transition. These observations unravel the fact that the ground state of LiCu2O2 possesses long-range 2D-like incommensurate magnetic order rather than being a gapped spin liquid as expected from the nature of quantum spin-1/2 chains. In addition, the spin coupling along the c axis is found to be essential for inducing electric polarization.     

Magnetic excitations in charge ordered a' - {N_a}{V_2}{O_5}

An investigation of the spin excitation spectrum of charge ordered (CO) NaV₂O₅ is presented. We discuss several different exchange models which may be relevant for this compound, namely in-line and zig-zag chain models with weak as well as strong inter-chain coupling and also a ladder model and a CO/MV (mixed valent) model. We put special emphasis on the importance of large additional exchange across the diagonals of V-ladders and the presence of exchange anisotropies on the excitation spectrum. It is shown that the observed splitting of transverse dispersion branches may both be interpreted as anisotropy effect as well as acoustic-optic mode splitting in the weakly coupled chain models. In addition we calculate the field dependence of excitation modes in these models. Furthermore we show that for strong inter-chain coupling, as suggested by recent LDA + U results, an additional high energy optical excitation appears and the spin gap is determined by anisotropies. The most promising CO/MV model predicts a spin wave dispersion perpendicular to the chains which agrees very well with recent results obtained by inelastic neutron scattering. Received 30 April 1999 and Received in final form 5 October 1999     

Low temperature thermodynamics of inverse square spin models in one dimension

We present a field-theoretic renormalization group calculation in two loop order for classical O(N)-models with an inverse square interaction in the vicinity of their lower critical dimensionality one. The magnetic susceptibility at low temperatures is shown to diverge like with a=(N-2)/(N-1) and . From a comparison with the exactly solvable Haldane-Shastry model we find that the same temperature dependence applies also to ferromagnetic quantum spin chains. Received: 20 February 1998 / Revised: 27 April 1998 / Accepted: 30 April 1998     

Long-range spin-pairing order and spin defects in quantum spin- $${1 \over 2}$$ ladders

For w-legged antiferromagnetic spin-1/2 Heisenberg ladders, a long-range spin pairing order can be identified which enables the separation of the space spanned by finite-range (covalent) valence-bond configurations into w +1 subspaces. Since every subspace has an equivalent counter subspace connected by translational symmetry, twofold degeneracy, breaking translational symmetry is found except for the subspace where the ground state of w = even belongs to. In terms of energy ordering, (non)degeneracy and the discontinuities introduced in the long-range spin pairing order by topological spin defects, the differences between even and odd ladders are explained in a general and systematic way. Received 19 July 1999 and Received in final form 8 October 1999     

Ground-state magnetic properties of the spin-2 transverse Ising model

The ground-state magnetic properties of the spin-2 transverse Ising model with a longitudinal crystal field are studied within the framework of mean-field theory (MFT) and effective-field theory (EFT), respectively. The phase diagrams and magnetization curves are examined in detail. It is found that the system exhibits a tricritical behavior in the ground-state phase diagrams. Some interesting phenomena have been found, especially the first-order phase transition from one ordered phase to the other ordered phase, which is due to the high spin. The spin correlation has important effect on the magnetic properties of the system. We also find that the ground-state phase diagrams of the spin-2 transverse Ising model are very different from those of the spin-3/2 transverse Ising model.     

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     

Absence of a spontaneous long-range order in a mixed spin-(1/2, 3/2) Ising model on a decorated square lattice due to anomalous spin frustration driven by a magnetoelastic coupling

The mixed spin-(1/2, 3/2) Ising model on a decorated square lattice, which takes into account lattice vibrations of the spin-3/2 decorating magnetic ions at a quantum-mechanical level under the assumption of a perfect lattice rigidity of the spin-1/2 nodal magnetic ions, is examined via an exact mapping correspondence with the effective spin-1/2 Ising model on a square lattice. Although the considered magnetic structure is in principle unfrustrated due to bipartite nature of a decorated square lattice, the model under investigation may display anomalous spin frustration driven by a magnetoelastic coupling. It turns out that the magnetoelastic coupling is a primary cause for existence of the frustrated antiferromagnetic phases, which exhibit a peculiar coexistence of antiferromagnetic long-range order of the nodal spins with a partial disorder of the decorating spins with possible reentrant critical behavior. Under certain conditions, the anomalous spin frustration caused by the magnetoelastic coupling is responsible for unprecedented absence of spontaneous long-range order in the mixed-spin Ising model composed from half-odd-integer spins only.     

Magnetization and magnetic susceptibility of the Ising ferromagnetic/antiferromagnetic superlattice

A linear cluster mean-field approximation is used to study the magnetic properties of the Ising ferromagnetic/antiferromagnetic superlattice, which is composed of a spin-1/2 ferromagnetic monolayer and a spin-1 antiferromagnetic monolayer with a single-ion anisotropy alternatively. By using the transfer matrix method, we calculate the magnetization and the initial magnetic susceptibility as functions of temperature for different interlayer coupling, single-ion anisotropy. We summarize the changing behaviors of the spin structure in ferromagnetic and antiferromagnetic layers and the characteristics of the corresponding magnetic susceptibilities, give the transition temperature as a function of the interlayer exchange coupling for different single-ion anisotropy, and analyze the features of the magnetization and the magnetic susceptibility.     

Thermodynamic properties of the XXZ double chain with long-range interactions

Using the Jordan-Wigner transformation and cut-off approximation, the Letter studies the one-dimensional spin-1/2 XXZ double chain with z-directional uniform long-range interactions in the external magnetic field. Thermodynamic properties as the Helmholtz free energy, internal energy, specific heat and magnetization of the system are obtained. The first and second-order phase transition of the system at a finite temperature are also given. Our results agree with those of the other literatures.     

Phase diagram of frustrated mixed-spin ladders in the strong-coupling limit

We study the ground-state properties of frustrated Heisenberg ferrimagnetic ladders with antiferromagnetic exchange interactions and two types of alternating sublattice spins. In the limit of strong rung couplings, we show that the mixed spin-1/2 and spin-1 ladders can be systematically mapped onto a spin-1/2 Heisenberg model with additional next-nearest-neighbor exchanges. The system is either in a ferrimagnetic state or in a critical spin-liquid state depending on the competition between the spin exchanges along the legs and the diagonal exchanges.     

Magnetic properties and spin waves of bilayer magnets in a uniform field

The two-layer square lattice quantum antiferromagnet with spins 12 shows a zero-field magnetic order-disorder transition at a critical ratio of the inter-plane to intra-plane couplings. Adding a uniform magnetic field tunes the system to canted antiferromagnetism and eventually to a fully polarized state; similar behavior occurs for ferromagnetic intra-plane coupling. Based on a bond operator spin representation, we propose an approximate ground state wavefunction which consistently covers all phases by means of a unitary transformation. The excitations can be efficiently described as independent bosons; in the antiferromagnetic phase these reduce to the well-known spin waves, whereas they describe gapped spin-1 excitations in the singlet phase. We compute the spectra of these excitations as well as the magnetizations throughout the whole phase diagram. Received 23 April 2001     

Quantum corrections of the Dzyaloshinskii-Moriya interaction on the spin-$\frac{1}{2}$ AF-Heisenberg chain in an uniform magnetic field

We have investigated the ground state phase diagram of the 1D AF spin- Heisenberg model with the staggered Dzyaloshinskii-Moriya (DM) interaction in an external uniform magnetic field H. We have used the exact diagonalization technique. In the absence of the uniform magnetic field (H=0), we have shown that the DM interaction induces a staggered chiral phase. The staggered chiral phase remains stable even in the presence of the uniform magnetic field. We have identified that the ground state phase diagram consists of four Luttinger liquid, staggered chiral, spin-flop, and ferromagnetic phases.     

Field-induced Tomonaga-Luttinger liquid phase of a two-leg spin-1/2 ladder with strong leg interactions

We study the magnetic-field-induced quantum phase transition from a gapped quantum phase that has no magnetic long-range order into a gapless phase in the spin-1/2 ladder compound bis(2,3-dimethylpyridinium) tetrabromocuprate (DIMPY). At temperatures below about 1 K, the specific heat in the gapless phase attains an asymptotic linear temperature dependence, characteristic of a Tomonaga-Luttinger liquid. Inelastic neutron scattering and the specific heat measurements in both phases are in good agreement with theoretical calculations, demonstrating that DIMPY is the first model material for an S=1/2 two-leg spin ladder in the strong-leg regime.     

Exact results of a mixed spin-1/2 and spin-1 Ising chain with both longitude and transverse single-ion anisotropies

The mixed spin-1/2 and spin-1 Ising chain with both longitude and transverse single-ion anisotropies Dz and Dx is solved exactly by means of a mapping to the spin-1/2 Ising chain with the alternating transverse fields and the Jordan-Wigner transformation. The analytical expressions of the quasi-particles' spectra Λk, the minimal energy gap Δ₀ for exciting a fermion quasi-particle, the minimal energy gap Δh for exciting a hole, and the ground state energy are obtained. The phase diagram of the ground state is also given. The results show that when Dz?0 for any finite value of Dx, there is no quantum critical point and the ground state is always in a spin ordered phase disregard of the boundary condition in the present system.     

Temperature fluctuations for a finite system of classical spin-1/2 particles

For sufficiently large but finite N independent spin-1/2 paramagnets in a constant magnetic field, the orientation of every spin has the same probability to be parallel or anti-parallel to that of the magnetic field. In our statistical ensemble treatment, all fundamental thermodynamic quantities fluctuate, including the entropy and temperature, and all fluctuations are gradually vanishing as the temperature itself approaches zero. Our approach presents a remedy of infinite temperature fluctuations and reproduces other reasonable results that are given by standard theory.     

Spectral density method in quantum nonextensive thermostatistics and magnetic systems with long-range interactions

Motived by the necessity of explicit and reliable calculations, as a valid contribution to clarify the effectiveness and, possibly, the limits of the Tsallis thermostatistics, we formulate the Two-Time Green Functions Method in nonextensive quantum statistical mechanics within the optimal Lagrange multiplier framework, focusing on the basic ingredients of the related Spectral Density Method (SDM). Besides, to show how the SDM works, we have performed, to the lowest order of approximation, explicit calculations of the low-temperature properties for a quantum d-dimensional spin-1/2 Heisenberg ferromagnet with long-range interactions decaying as 1/r^p ( r is the distance between spins in the lattice).     

Phase transitions in the mixed Ashkin-Teller model

By using a mean-field approximation (MFA) and Monte-Carlo (MC) simulations, we have studied the effect on the phase diagrams of mixed spins ( and S =1) in the Ashkin-Teller model (ATM) on a hypercubic lattice. By varying the strength describing the four spin interaction and the single ion potential, we have obtained by these two methods quite rich phase diagrams with several multicritical points. This model exhibits a new partially ordered phase which does not exist neither in the spin-1/2 ATM nor in the spin-1 ATM. While MFA yields phase diagrams which are sometimes qualitatively incorrect, accurate results are obtained from MC simulations. From the critical exponents which have been calculated using finite-size scaling ideas, we have shown that all phase transitions are Ising-like except for the paramagnetic-Baxter critical surface on which the critical exponents vary continuously, by varying only the strength of the coupling interaction independently of the value of the single ion potential. Received 5 July 1999 and Received in final form 4 July 2000