Interplay of the Staggered and Three-Body Interaction Potentials on the Quantum Phases of a Spin-1 Ultracold Atom in an Optical Lattice

The interplay of the staggered and the three-body interaction potentials on the quantum phases of a spin-1 Bose Hubbard model using a mean field approximation (MFA) is studied. In the antiferromagnetic (AF) case, a smaller value of the staggered potential (SP) results in the charge and the spin density wave ordering along with the Mott insulator (MI) and the staggered superfluid (SSF) phases. While the competition between two types of the potential leads to the stabilization of the higher order MI and charge density wave (CDW) phases with increasing three-body interaction strength. Further, the spin eigenvalue and nematic order parameters are calculated to scrutinize the spin singlet-nematic formation in the MI and the CDW phases and spin population fractions to analyze the nature of the SSF phase. A signature of the spin density wave (SDW) pattern is also observed in the gapped phase lobes. In case of a purely three-body interaction, the third and higher order insulating lobes become dominant with increasing staggered potential strength. Subsequently, all MFA phase diagrams are then nicely corroborated with the analytical results obtained using a perturbative expansion corresponding to the AF and ferromagnetic cases.     

Monte Carlo simulation of in-plane spin-polarized transport in GaAs/GaAlAs quantum well in the three-subband approximation

We develop a Monte Carlo (MC) tool incorporated with the three-subband approximation model to investigate the in-plane spin-polarized transport in GaAs/GaAlAs quantum well. Using the tool, the effects of the electron occupation of higher subbands and the intersubband scattering on the spin dephasing have been studied. Compared with the corresponding results of the simple one-subband approximation model, the spin dephasing length is reduced four times under 0.125\,kV/cm of driving electric field at 300K by the MC tool incorporated with the three-subband approximation model, indicating that the three-subband approximation model predicts significantly shorter spin dephasing length with temperature increasing. Our simulation results suggest that the effects of the electron occupation of higher subbands and the intersubband scattering on the spin-dependent transport of GaAs 2-dimensional electron gas need to be considered when the driving electric field exceeds the moderate value and the lattice temperature is above 100K. The simulation by using the MC tool incorporated with the three-subband approximation model also indicates that, under a certain driving electric field and lattice temperature, larger channel widths cause spins to be depolarized faster. Ranges of the three components of the spins are different for three different injected spin polarizations due to the anisotropy of spin--orbit interaction.     

One-dimensional spin glass with oscillating long-range interaction

In this paper a long-range interacgion approximation for spin glasses is proposed as an alternative to the Sherrington-Kirkpatrick model. The one-dimensional model of Ising spins with the interaction κV _O cosQ x exp (?κ|x|), where κ?c?Q (c is the spin concentration) is studied in detail. The long-range approximation enables one to describe the spin configuration in terms of slowly varying in space fields of the type of amplitude (ρ) and phase (ψ); the ψ-dependent part of the Hamiltonian is analogous to the Hamiltonian, describing the weak pinning of the charge density waves by impurities. As a result, the phase variable apears to be gaples in equilibrium thermodynamics and parametrizes different metastable states under quasiequilibrium conditions. In the mean field approximation (MFA) (κ»0) in the vicinity of the transition pointT _c =cV ₀, there is a symmetric cusp of the magnetic susceptibility ξ; at low temperatures the heat capacity is proportional toT, whereas the susceptibility does not depend on temperature. The MFA cannot be applied in the close vicinity ofT _c (|τ?(κ/c)^2/3) and at very low temperaturesT?κV ₀ when a gap appears in the distribution of the molecular fielsh ath≈0.     

Spin transport in the Néel and collinear antiferromagnetic phase of the two dimensional spatial and spin anisotropic Heisenberg model on a square lattice

We analyze and compare the effect of spatial and spin anisotropy on spin conductivity in a two dimensional S = 1/2 Heisenberg quantum magnet on a square lattice. We explore the model in both the Néel antiferromagnetic (AF) phase and the collinear antiferromagnetic (CAF) phase. We find that in contrast to the effects of spin anisotropy in the Heisenberg model, spatial anisotropy in the AF phase does not suppress the zero temperature regular part of the spin conductivity in the zero frequency limit–rather it enhances it. In the CAF phase (within the non-interacting approximation), the zero frequency spin conductivity has a finite value, which is suppressed as the spatial anisotropy parameter is increased. Furthermore, the CAF phase displays a spike in the spin conductivity not seen in the AF phase. We also explore the finite temperature effects on the Drude weight in the AF phase (within the collisionless approximation). We find that enhancing spatial anisotropy increases the Drude weight value and increasing spin anisotropy decreases the Drude weight value. Based on these studies, we conclude that antiferromagnets with spatial anisotropy are better spin conductors than those with spin anisotropy at both zero and finite temperatures.     

Study of the first-order transition in the spin-1 Blume–Capel model by using effective-field theory

The spin-1 Blume–Capel model on a square lattice is studied by using an effective-field theory (EFT) with correlation. We propose an expression for the free energy within the EFT. The phase diagram is constructed in the temperature (T) and single-ion anisotropy amplitude (D) plane. The first-order transition line is obtained by Maxwell construction (comparison between free energies). Our results predict first-order transitions at low temperatures and large anisotropy strengths, which correspond in the phase diagram to the existence of a tricritical point (TCP). We compare our results with mean-field approximation (MFA), that show a qualitative correct behavior for the phase diagram.     

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     

New effective-field theory with correlations; application to disordered magnets

The Ising model of spin 1/2 with nearest-neighbour interaction is investigated. Within the effective-field theory introduced by Honmura and Kaneyoshi, a new type of decoupling approximation is introduced for treating the multispin correlation functions. The critical temperature, the spontaneous magnetization, and the two-site spin c correlation function are calculated for a two- (or three-) dimensional lattice. The present formalism yields results better than those of Bethe-Peierls approximation and is extended to disordered magnets. The thermodynamical quantities of quenched random-bond magnets, such as magnetization, susceptibility and so on, are studied, We find that in particular the twosite spin correlation functions of the disordered magnets exhibit some interesting behavior.     

Effect of single ion anisotropy on the critical temperature of classical quasi-one-dimensional magnets

The effect of single ion anisotropy energy on the three-dimensional ordering temperature of a classical quasi-one-dimensional magnetic chain is estimated using a mean field approximation for the interchain coupling and a classical spin field model for a chain. Numerical results are presented for T_c as a function of the interchain and interchain exchange interactions and the single ion anisotropy.     

Spin dependent 2D electron scattering by nanomagnets

The 2D scattering problem of an electron by a magnetized nanoparticle is solved in the Born approximation with account of the dipole-dipole interaction of the magnetic moments of electron and nanomagnet. The scattering amplitudes in this problem are the two-component spinors. They are obtained as functions of the electron spin orientation, the electron energy and show anisotropy in scattering angle. The initially polarized beam of electrons scattered by the nanomagnet consists of electrons with no spin flipped and spin flipped. The majority of electrons with no spin flipped are scattered by small angles. The majority electrons with spin flipped are scattered in the vicinity of the scattering angles π/2 and 3π/2. This can be used as one more method of controlling the spin currents.     

Transverse susceptibilities of ferromagnetic spin wave interacting with phonon reservoir, II: Temperature dependence of line shapes

A form of the transverse magnetic susceptibility of a ferromagnetic spin system with a uniaxial anisotropy energy and an anisotropic exchange interaction, interacting with a phonon reservoir, is derived in the spin-wave approximation using the TCLE method, where the phonon reservoir interacts with not only the x and y components of each spin but also its z component. The transverse magnetic susceptibility is numerically and analytically studied for the system of one-dimensional infinite spins in the lowest spin-wave approximation, by assuming a damped oscillator model of the phonon reservoir. The temperature dependence and wave number dependence of the susceptibility are numerically investigated for the half-widths and peak-heights of the line shapes in the resonance region. It is shown that as the temperature increases, the half-widths of the line shapes increase and the peak heights decrease in the resonance region, and that as the wave number increases, the half-widths of the line shapes decrease and the peak heights increase in the resonance region. It is also shown that as the uniaxial anisotropy energy of the z direction increases or as the exchange interaction between the z components of spins increases, the half-widths of the line shapes decrease and the peak heights increase in the resonance region. It is besides shown that as the characteristic frequency of the phonon increases, the line shapes show ‘motional broadening’ at the low temperature and show ‘motional narrowing’ at the high temperature. Furthermore, the resonance frequency is shown to increase as the wave number increases or as the temperature increases. The numerical results are examined analytically.     

Thermodynamical properties of the transverse Ising model

A new effective field theory is proposed and used to derive the thermodynamical properties of the transverse Ising model. The formalism is based on an exact formal spin identity for the two-state transverse Ising model and utilizes an exponential operator technique. The method, which can explicitly and systematically include correlation effects, is illustrated in several lattice structures by employing its simplest approximation version (in which spin-spin correlations are neglected). The lines of critical points in the Ω-T plane as well as the thermal behaviour of both transverse and longitudinal magnetizations are analysed for square and simple cubic lattices. It is shown that the present formalism, in spite of its simplicity, yields results which represent a remarkable improvement on the standard mean field treatment (MFA).     

Spin compensation temperatures in the mean-field approximation of a mixed spin-2 and spin-5/2 Ising ferrimagnetic system

The magnetic behaviors of a mixed spin-2 and spin-5/2 Ising ferrimagnetic system on a square lattice are studied with the mean-field approximation (MFA) based on the Bogoliubov inequality for the free energy. A Landau expansion of the free energy in the order parameter is also described in this work. In particular, we investigate the effect of a single-ion anisotropy on the compensation phenomenon.     

Electron correlations in alloys of simple and transition metals

The effect of dynamical electron-electron correlations on the electronic structure of the paramagnetic disordered binary alloy of the transition and simple metals is studied for the Anderson model extended to arbitrary concentration of the transition metal impurities. We use the terminal-point approximation for the many-body quantities, which allows us to solve the random part of the problem within the single-site approximation. The many-body part of the problem is treated within the selfconsistent T-matrix approximation, valid for low, but finite concentration of particles ( ? 0.3/atom/spin). For low concentration of the transition metal impurities we obtain results identical with those for the Anderson model. The theory is illustrated numerically for a simple bandstructure model.     

Fundamentals of a Technique for Determining Electron Distribution Functions by Multi-Term Even-Order Expansion in Legendre Polynomials. 2. Comprehensive Investigation of a Model Plasma

Applying the new technique for finding the converged solution of the Boltzmann equation in a weakly ionized plasma, which was developed in the first part of this paper, a comprehensive study of the electron velocity distribution function for a model plasma with elastic and exciting collisions is performed by solving the Boltzmann equation with increasing order of approximation. The purpose of this investigation is that of calculating the isotropic distribution f₀, the first contribution f₁ to the anisotropy of the velocity distribution, the important macroscopic quantities and, more generally, that of studying the total anisotropy as well as the changes of all these quantities when the approximation degree is enlarged beyond the 2 terms of the conventional Lorentz approximation. By varying some parameters of the model plasma, that is the electric field strength, the magnitude of the excitation cross section and the excitation threshold, the main features of plasmas in inert as well as molecular gases are modelled and the impact of these parameters on the mentioned quantities is analysed. Some of the converged results are compared with results of corresponding Monte Carlo simulations. The approximation degree required to find the converged values of isotropic distribution, main macroscopic quantities and electron distribution in the velocity space (and thus its real anisotropy) is estimated by solving the Boltzmann equation over wide parameter ranges.     

Thermodynamic properties of ferromagnets with uniaxial and biaxial anisotropy

The thermodynamic properties of spin-one Heisenberg ferromagnets with uniaxial and biaxial anisotropy are investigated in the molecular field approximation (MFA) and random phase approximation (RPA). In MFA a full phase diagram comprising three lines of bicritical points, is obtained.Using the standard-basis operator method, the collective excitation spectrum is studied in detail; moreover the softening of the excitations at the phase boundaries is discussed. A self-consistent version of RPA with emphasis on the role of kinematic restrictions with regard to the standard-basis operators is analyzed.Moreover, the phase transitions are considered in the Ising model, where a line of tricritical points occurs, and the planar model, where a line of bicritical points, two lines of tricritical points and a line of triple points, occur.     

Role of inter-site exchange and hybrid interactions in itinerant ferromagnetism

In this work, we study the magnetic properties of itinerant electron systems using the Hubbard-like tight binding Hamiltonian along with inter-site exchange and hybrid interactions. We have used the mean-field approximation to deal with the exchange and hybrid interactions. It is found that hybrid interaction is more effective than exchange interaction for the on-set of ferromagnetic state. We have studied the effect of hybrid interaction on various physical quantities at different temperatures. The effective mass (m*/m) of up spin electrons increases slowly as the temperature decreases but below the critical temperature (T_c), it decreases rapidly. For down spin electrons effective mass increases slowly as the temperature decreases and below T_c, it increases more rapidly. Spectral weight (n/m*) for up spin electrons decreases slowly upto T_c and below T_c, it increases rapidly. For down spin electrons spectral weight decreases slowly upto T_c and below T_c, it decreases rapidly. Our results for both the effective mass and spectral weight are in good agreement with recently observed experimental behaviour in itinerant ferromagnet Ga_1−xMn_xAs [Phys. Rev. Lett. 89 (2002) 097203]. We have also studied variation of the spectral weight and optical absorption with temperature in presence of magnetic field. We found that these two quantities for up spin electrons increase as applied magnetic field increases at all temperatures (∼4T_c). For down spin electrons these two quantities decrease as applied magnetic field increases.     

T=0 phase diagram and nature of domains in ultrathin ferromagnetic films with perpendicular anisotropy

We present the complete zero temperature phase diagram of a model for ultrathin films with perpendicular anisotropy. The whole parameter space of relevant coupling constants is studied in first order anisotropy approximation. Because the ground state is known to be formed by perpendicular stripes separated by Bloch walls, a standard variational approach is used, complemented with specially designed Monte Carlo simulations. We can distinguish four regimes according to the different nature of striped domains: a high anisotropy Ising regime with sharp domain walls, a saturated stripe regime with thicker walls inside which an in-plane component of the magnetization develops, a narrow canted-like regime, characterized by a sinusoidal variation of both the in-plane and the out of plane magnetization components, which upon further decrease of the anisotropy leads to an in-plane ferromagnetic state via a spin reorientation transition (SRT). The nature of domains and walls are described in some detail together with the variation of domain width with anisotropy, for any value of exchange and dipolar interactions. Our results, although strictly valid at T=0, can be valuable for interpreting data on the evolution of domain width at finite temperature, a still largely open problem.     

EPR Investigation of Exchange Interactions Between Neodymium Ions in {[Nd2(α-C4H3OCOO)6(H2O)2]} n

Electron paramagnetic resonance (EPR) of a new compound {[Nd₂(α-C₄H₃OCOO)₆(H₂O)₂]} _n composed of Nd³⁺–Nd³⁺ dimers is reported. The anisotropy parameters of the spin–spin interaction are determined by fitting experimental and simulated spectra in X- and Q-bands. It is shown that the anisotropy of the exchange interaction gives the main contribution to the anisotropy of the spin–spin interaction. The observed anisotropy disagrees with the expected in the model of the isotropic exchange interaction between real spins. A feature of the EPR spectrum not described by the model of the isolated Nd–Nd dimers and reflecting the magnetization transfer between dimers is detected. The magnetization transfer due to both the relaxation transitions and the interdimer interaction is considered.     

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.