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     

Soliton Lattice State of Spin—1／2 Antiferromagnetic Chain in an External Magnetic Field

One-dimensional spin-1-2 anisotropic Heisenberg antiferromagnet in a longitudinal external magnetic field is studied using bosonization method and Gaussian wave functional techniques which take account of the spatial structure.The magnetization and the energy of the ground state which depend on the external magnetic field are calculated.For the case of anisotropic parameter △＞△0,increasing of the external magnetic field above the threshold value leads to the appearance of the soliton lattice state in the ground state,until to an another critical field where the ground state changes to the canted state phase.Therefore,with increasing external magnetic field,the ground state experiences four different phases successively,namely,antiferromagnetic Ising,soliton lattice state canted state,and magnetization saturated phases.When △＜△0,the soliton lattice state phase does not appear,with increasing external field,the paramagnetic phase smoothly evolves into the canted state phase,finally reaches magnetization saturated phase.     

Enhancement of next-nearest-neighbouring entanglement in quantum Ising spin chain

Using the method of the Jordan--Wigner transformation for solving different spin--spin correlation functions, we have investigated the generation of next-nearest-neighbouring entanglement in a one-dimensional quantum Ising spin chain with the Gaussian distribution impurities of exchange couplings and external magnetic fields taken into account. The maximal value of entanglement between the next-nearest-neighbouring qubits in the transverse Ising model was analysed in detail by varying the effectively controlled parameters such as interchange coupling, magnetic field and the system impurity. For such systems, where both exchange couplings and external magnetic field disorder appear, we show that it is possible to achieve next-nearest-neighbouring entanglement better than the previously discussed pure Ising spin chain case. We also show that the Gaussian distribution impurity can induce next-nearest-neighbouring entanglement, which can be used as a means to characterize quantum phase transition.     

Quantum tunneling with dissipation and the Ising model over ℝ

We consider a quantum particle in a double-well potential, for simplicity in the two-level approximation, coupled to a phonon field. We show that static and dynamical ground state correlations of the particle and of the field are expressible through expectations in an Ising model over (rather than ). Its free measure is a spin flip process with flip rate , the difference in energy between the ground state and the first excited state. The Ising model has a ferromagnetic pair interaction whose form depends on the couplings to the phonon field and on the dispersion relation of the phonon field. In physical applications the interaction is long ranged and decays ast ^–2 for large distances. In this case we prove that for sufficiently strong coupling the particle becomes localized in one of the wells. The effective tunnel rate is zero. The transition to localization is associated with the generation of an infinite number of low momentum phonons. We apply the Ising technology to our problem and discuss the phase diagram in some detail.     

Phase transition in antiferromagnets with anisotropic exchange interactions and uniaxial anisotropy

Abstract

Following the Bogoliubov variational principle, the equilibrium and stability equations of the free energy for the two sublattice antiferromagnetic system with inter- and intrasublattice exchange interactions and with an external magnetic field are investigated. For the Ising spin system with uniaxial anisotropy, the phase diagrams have been calculated for various values of anisotropy constant d and the ratio of intra- to intersublattice interaction constants γ. It is shown that first-order, as well as second-order transitions, occur for γ > 0, whereas only a second-order transition occurs for γ ≦ 0, irrespective of the sign of d. Furthermore, similar calculations are extended for the anisotropic Heisenberg spin system and quite interesting phase diagrams have been obtained. Next, the effects of the anisotropic exchange interactions on the magnetic ordered states and the magnetizations of the singlet ground state system of spin one and with a uniaxial anisotropy term are investigated in the vicinity of the level crossing field H ? D/gμ _B . A field-induced ordered state without the transverse component of magnetization is shown to appear in a certain range of magnetic field as the spin dimensionality decreases. It has also turned out that the phase transition between this ordered state and the canted antiferromagnetic state ordinarily found for the isotropic singlet ground state system is of first order. Lastly, the stable spin configurations at a temperature of absolute zero for a two-sublattice uniaxial antiferromagnet under an external magnetic field of arbitrary direction are studied. In particular, the effects of a single ionic anisotropy D-term and anisotropy in the exchange interactions on the magnetic phases are investigated. The antiferromagnetic state has turned out to appear only for the external magnetic field along the easy axis of sublattice magnetization, and makes a first-order phase transition to the canted-spin state or the ferromagnetic state. For other field directions, no antiferromagnetic state appears and only a second-order phase transition between the canted-spin and the ferromagnetic states occurs. The critical field as a function of external field direction has been calculated for several D-values.     

Properties of the ground state in a spin-2 transverse Ising model with the presence of a crystal field

The properties of the ground state in the spin-2 transverse Ising model with the presence of a crystal field are studied by using the effective-field theory with correlations. The longitudinal and transverse magnetizations, the phase diagram and the internal energy in the ground state are given numerically for a honeycomb lattice (z=3).     

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.     

Supersolid phase in spin dimer XXZ systems under a magnetic field

Using the quantum Monte Carlo method, we study, under external magnetic fields, the ground state phase diagram of the two-dimensional spin S=1/2 dimer model with an anisotropic intraplane antiferromagnetic coupling. With the anisotropy 4 greater/approximately Delta greater/approximately 3, a supersolid phase characterized by a nonuniform Bose condensate density that breaks translational symmetry is found. The rich phase diagram also contains a checkerboard solid, an antiferromagnet in the z axis, and a superfluid phase formed by S(z)= +1 spin triplets which has a finite staggered magnetization in the in-plane direction. As we show, the model can be realized as a consequence of including the next nearest neighbor coupling among dimers and our results suggest that spin dimer systems may be an ideal model system to study the supersolid phase.     

Thermal entanglement of two interacting qubits in a static magnetic field

We study systematically the entanglement of a two-qubit Heisenberg XY model in thermal equilibrium in the presence of an external arbitrarily-directed static magnetic field, thereby generalizing our prior work [G. Lagmago Kamta, A.F. Starace, Phys. Rev. Lett. 88, 107901 (2002)]. We show that a magnetic field having a component in the xy-plane containing the spin-spin interaction components produces different entanglement for ferromagnetic (FM) and antiferromagnetic (AFM) couplings. In particular, quantum phase transitions induced by the magnetic field-driven level crossings always occur for the AFM-coupled qubits, but only occur in FM-coupled qubits when the coupling is of Ising type or when the magnetic field has a component perpendicular to the xy-plane. When the magnetic field has a component in the xy-plane, the cut-off temperature above which the entanglement of both the FM- and AFM-coupled qubits vanishes can always be controlled using the magnetic field for any value of the XY coupling anisotropy parameter. Thus, by adjusting the magnetic field, an entangled state of two spins can be produced at any finite temperature. Finally, we find that a higher level of entanglement is achieved when the in-plane component of the magnetic field is parallel to the direction in which the XY exchange coupling is smaller.     

Thermodynamic properties of LiCu2O2 multiferroic compound

A spin model of quasi-one-dimensional LiCu₂O₂ compound with ground state of ellipsoidal helical structure has been adopted. The helical axis is along the diagonal of CuO₄ squares. By taking into account the interchain coupling and exchange anisotropy, the exotic magnetic properties and ferroelectricity induced by spiral spin order have been studied by performing Monte Carlo simulation. The simulation results qualitatively reproduce the main characters of ferroelectric and magnetic behaviors of LiCu₂O₂ compound and confirm the low-temperature noncollinear spiral ordering. Furthermore, by performing the calculations of spin structure factor, we systematically investigate the effects of different exchange couplings on the lower-temperature magnetic transition, and find that the spiral spin order depends not only on the ratio of nearest and next-nearest neighbor inchain spin coupling but also strongly on the exchange anisotropy.     

Spin waves and quantum criticality in the frustrated XY pyrochlore antiferromagnet Er2Ti2O7

We report detailed measurements of the low temperature magnetic phase diagram of Er2Ti2O7. Heat capacity and time-of-flight neutron scattering studies of single crystals reveal unconventional low-energy states. Er3+ magnetic ions reside on a pyrochlore lattice in Er2Ti2O7, where local XY anisotropy and antiferromagnetic interactions give rise to a unique frustrated system. In zero field, the ground state exhibits coexisting short and long-range order, accompanied by soft collective spin excitations previously believed to be absent. The application of finite magnetic fields tunes the ground state continuously through a landscape of noncollinear phases, divided by a zero temperature phase transition at micro{0}H{c} approximately 1.5 T. The characteristic energy scale for spin fluctuations is seen to vanish at the critical point, as expected for a second order quantum phase transition driven by quantum fluctuations.     

Magnetic properties of 2D nano-islands I: Ising spin model

An Ising spin effective field theory (EFT) is developed as a framework for a detailed analysis of the magnetic properties of two-dimensional (2D) nano-islands on a nonmagnetic substrate with an out of plane magnetization. The Hamiltonian with nearest neighbor exchange interactions and single-atom magnetic anisotropy defines the ground state. The calculation yields the single site spin correlations, the magnetizations, and the isothermal susceptibilities for the core and periphery domains, and the island core phase diagrams. The choice of a spin S=1 for the atoms permits the analysis of the effects of spin fluctuations via the single site spin correlations. In particular we investigate the effects due to the different anisotropies and reduced dimensionalities for the core and periphery domains. The present model calculations are developed for different 2D nano-islands lattices. Detailed theoretical results are presented for the square and hexagonal lattices, with numerical applications for the 2D Co nano-islands on Pt. The derived transition temperature for the hexagonal lattice nano-islands is in good agreement with the experimental data for Co nano-islands on Pt. Though both the core and the periphery domains have the same order-disorder transition temperature, the magnetization of each domain attains this transition differently. The temperature behavior of the spin correlations is also fundamentally different for the periphery and core sites, which entails distinctly different isothermal susceptibilities, and yields statistically averaged nano-islands susceptibilities that do not correspond to a second order phase transition. The experimental susceptibility results for 2D Co nano-islands on Pt can be interpreted within our EFT Ising model without reference to a transition from a blocking state of the particle to a superparamagnetic behavior. The results for the different lattices are formally comparable, and demonstrate the robustness and general character of the model.     

Phase diagram of the frustrated asymmetric ferromagnetic spin ladder

We present a systematic investigation on the ground state of an asymmetric two-leg spin ladder (where exchange couplings of the legs are unequal) with ferromagnetic (FM) nearest-neighbor interaction and diagonal anti-ferromagnetic frustration using the density matrix renormalization group method. When the ladder is strongly asymmetric with moderate frustration, a magnetic canted state is observed between an FM state and a singlet dimerized state. The phase boundaries are dependent on the asymmetric strength. On the other hand, when the asymmetric strength is intermediate, a so-called spin-stripe state (spins align parallel on the same legs, but antiparallel on rungs) is discovered, and the system experiences a first-order phase transition from the FM state to the spin-stripe state upon increasing frustration. Numerical evidence is presented for interpretation of the phase diagram in terms of frustration and the asymmetric strength.     

耦合作用下有机铁磁链的临界行为

利用平均场，我们研究了一个具有链间耦合作用的有机铁磁模型，并给出了该模型的全相图。计算表明，链间耦合强烈影响其基态的磁序。当链间耦合达到某临界值时，高自旋基态消失，整个系统由铁磁相转变为近藤单态（Kondo-singlet）相。     

Mixed Ising ferrimagnets with next-nearest-neighbour couplings on square lattices

We study Ising ferrimagnets on square lattices with antiferromagnetic exchange couplings between spins of values S = 1/2 and 1 on neighbouring sites, couplings between S = 1 spins at next-nearest-neighbour sites of the lattice and a single-site anisotropy term for the S = 1 spins. Using mainly ground state considerations and extensive Monte Carlo simulations, we investigate various aspects of the phase diagram, including compensation points, critical properties and temperature-dependent anomalies. In contrast to previous belief, the next-nearest-neighbour couplings, when being of antiferromagnetic type, may lead to compensation points.     

Ising自旋S=1,具有次近邻相互作用的面心立方格子的反铁磁体在外场下的基态能量

本文用文献[4]中提出的方法,变S=1的Ising体系成一个粒子数不守恒的费密体系,严格地求得了具有最近邻及次近邻相互作用的反铁磁Ising晶格在任意外场下的基态能量,得到了零温的相图。 关键词：     

The spin-2 antiferromagnet on the Bethe lattice

The complete phase diagrams of the antiferromagnetic spin-2 Blume-Capel Ising system is studied on the Bethe lattice by the use of exact recursion relations. In order to specify the states of the system, i.e. the different spin configurations, the ground state phase diagram is obtained on the (H/|J|, D/|J|) plane corresponding to the reduced external magnetic and crystal fields, respectively. As a result, the thermal change of the order-parameters, the magnetisations belonging to the two sublattice system, was investigated to obtain the full phase diagrams of the system on the (H/|J|, kT/|J|) planes. The behavior of the order-parameters with respect to the external magnetic field was also studied for the given values of D/|J|. Besides the interesting thermal and external magnetic field change of the sublattice magnetisations, the system also exhibits interesting critical behaviors including first- and second-order phase transitions, therefore, triciritical points and the reentrant behavior. The calculations are carried out for the coordination number q=4, corresponding to the square lattice, only.     

Exact ground state of a spin ladder with a quantum phase transition

We introduce a spin ladder with Ising interactions along the legs and intrinsically frustrated Heisenberg-like ferromagnetic interactions on the rungs. The model is solved exactly in the subspaces relevant for the ground state by mapping to the quantum Ising model, and we show that a first order quantum phase transition separates the classical from quantum regime, with the spin correlations on the rungs being either ferromagnetic or antiferromagnetic, and different spin excitations in both regimes. The present case resembles the quantum phase transition found in the compass model in one and two dimensions.     

Continuous quantum phase transitions in the one-dimensional spin-1/2 axial next-nearest-neighbour Ising model in two orthogonal magnetic fields

We have investigated the one-dimensional spin-1/2 axial next-nearest-neighbour Ising (ANNNI) model in two orthogonal magnetic fields at zero temperature. There are four different possible ground state configurations for the ANNNI model in a longitudinal field, in the thermodynamic limit. The inclusion of a transverse field introduces quantum fluctuations which destroy the existing spin order along certain critical lines. The effects of the fluctuations in three of the four ordered regions were investigated using the finite-size scaling technique. The phase boundaries of the ANNNI model in two orthogonal magnetic fields were thus determined numerically. For certain limits of the Hamiltonian we compared the obtained results with the existing literature and our results were in good agreement with the results in the existing literature.     

Duality Between Spin Networks and the 2D Ising Model

The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a fermionic and a bosonic Gaussian integral formulation for each of these functions and we show that they are the inverse of each other (up to some explicit constants) by exhibiting a supersymmetry relating the two formulations. We investigate three aspects and applications of this duality. First, we propose higher order supersymmetric theories that couple the geometry of the spin networks to the Ising model and for which supersymmetric localization still holds. Secondly, after interpreting the generating function of spin network evaluations as the projection of a coherent state of loop quantum gravity onto the flat connection state, we find the probability distribution induced by that coherent state on the edge spins and study its stationary phase approximation. It is found that the stationary points correspond to the critical values of the couplings of the 2D Ising model, at least for isoradial graphs. Third, we analyze the mapping of the correlations of the Ising model to spin network observables, and describe the phase transition on those observables on the hexagonal lattice. This opens the door to many new possibilities, especially for the study of the coarse-graining and continuum limit of spin networks in the context of quantum gravity.