Multicritical Dynamic Phase Diagrams and Dynamic Hysteresis Loops in a Mixed Spin-2 and Spin-5/2 Ising Ferrimagnetic System with Repulsive Biquadratic Coupling: Glauber Dynamic Approach

The stationary states of the kinetic mixed spin-2 and spin-5/2 Ising ferrimagnetic system with repulsive biquadratic coupling are examined within a mean-field approach under the presence of a time varying (sinusoidal) magnetic field. We employ Glauber-type stochastic dynamics to construct a set of coupled mean-field dynamic equations, and we solve these equations to find the phases in the system. We also investigate the thermal behavior of the dynamic order parameters to characterize the nature (continuous or discontinuous) of the dynamic phase transitions (DPTs) and obtain the DPT points. The phase diagrams are presented in the reduced magnetic field amplitude and reduced temperature plane, and a comparison is made with the results of other kinetic mixed spin systems. We also study the behavior of the dynamic magnetic hysteresis and investigate the effects of the frequency on hysteresis properties, and we find the results are in good agreement with some previous theoretical and experimental works.     

A Green＇s function model for ferromagnetism and spin excitations of （Ga,Mn）As diluted magnetic semiconductors

We study (Ga, Mn)As diluted magnetic semiconductors in terms of the Ruderman--Kittel--Kasuya--Yosida quantum spin model in Green's function approach. Random distributions of the magnetic atoms are treated by using an analytical average of magnetic configurations. Average magnetic moments and spin excitation spectra as functions of temperature can be obtained by solving self-consistent equations, and the Curie temperature T_C is given explicitly. T_C is proportional to magnetic atomic concentration, and there exists a maximum for T_C as a function of carrier concentration. Applied to (Ga, Mn)As, the theoretical results are consistent with experiment and the experimental T_C can be obtained with reasonable parameters. This modelling can also be applied to other diluted magnetic semiconductors.     

On the concentration dependence of wings of spectra of spin correlation functions of diluted Heisenberg paramagnets

Singular points of the autocorrelation function on the imaginary time axis that is averaged over the location of spins in the magnetically dilute spin lattice with isotropic spin–spin interaction at a high temperature have been studied. For the autocorrelation function in the approximation of the self-consistent fluctuating local field, nonlinear integral equations have been proposed which reflect the separation of the inhomogeneous spin systems into close spins and other spins. The coordinates of the nearest singular points have been determined in terms of the radius of convergence of the expansion in powers of time, the coefficients of which have been calculated from recurrence equations. It has been shown that the coordinates of singular points and, consequently, the wings of the autocorrelation function spectrum at strong magnetic dilution are determined by the modulation of the local field by the nearest pairs of spins leading to its logarithmic concentration dependence.     

Isotropic nuclear magnetic resonance shifts in low-spin iron(III) porphyrin and hemin systems

Calculations, based on the t ₂ ⁵ (single vacancy) configuration including spin-orbit coupling, have been carried out to evaluate the magnetic susceptibility anisotropies in low-spin iron(III) heme proteins. The results have been used to assess the importance of second order Zeeman effects and thermal population of excited states when evaluating dipolar nuclear magnetic resonance shifts in such systems. The temperature dependencies predicted by the theory are discussed in light of experimental data in the literature.     

Monte carlo simulation of magnetization and coercivity of free magnetic clusters

Based on Monte Carlo method, the oscillatory behaviour of the average magnetic moment as a function of the cluster sizes and the temperature dependences of magnetic moment with different sizes have been studied. It is found that the oscillations superimposed on the decreasing moment are associated with not only the geometrical structure effects but also the thermal fluctuation. The hystereses and thermal coercivities for free clusters with zero and finite uniaxial anisotropies have been calculated. The simulated thermal dependence of the coercivity is consistent with the experimental result, but does not fit the T^α law in the whole temperature range. It is evident that an easy magnetization direction and an anisotropy resulting from the spin configurations exist in the free clusters with the pure exchange interaction, which is also proved by the natural angle and energy distribution of clusters. A systematic theoretical analysis is also made to establish the relationship between natural angle and coercivity.     

A simple approximation for Ising spin models

A simple method is introduced for Ising spin systems based on the correlated molecular-field theory. Here, we consider an interacting triple in the mean field of its surrounding lattice points taking into account the product of three spins in the cluster. The present results for Curie temperature are compared to the mean-field theory(MFT), Bethe–Peierls–Weiss(BPW) approach, and self-consistent correlated field(SCCF) approximation, respectively. A procedure of triangular clusters is investigated that yields very distinguishable improvement of the critical temperature, as well.     

Dynamical theory of thermal spin fluctuations in metallic ferromagnets

A self-consistent dynamical theory of thermal spin fluctuations is developed which describes their spatial correlation. It is based on the functional integral method and utilizes the quadratic representation for the electron free energy in a fluctuating exchange field with renormalized susceptibilities allowing for the interaction of various spin fluctuation modes. Interpolation between the single-site and homogeneous susceptibilities is used, where these susceptibilities are found self-consistently. The average over fluctuations takes account of both long-wavelength and local excitations. A closed system of equations is formed for both unknown quantities: the magnetization and the mean-square exchange field at a site. The basic characteristics of a specific magnet are the density of electron states and the atomic magnetic moment at T=0. A method is proposed for separating the relatively slow thermal-spin fluctuations from the rapid zero-spin fluctuations forming the ground state of the magnets. At T=0 we have a system of equations of mean field theory. The temperature excites thermal spin fluctuations, which are described by taking account of correlation in time and space. The magnetization, susceptibility, magnitude of the spin fluctuations and their distribution over momenta, and the degree of magnetic short-range order in iron are calculated as functions of the temperature in the ferromagnetic and paramagnetic phases, and also at the transition between them, the Curie temperature. Fiz. Tverd. Tela (St. Petersburg) 40, 90–98 (January 1998)     

Tunable in-plane spin orientation in Fe/Si(557) film by step-induced competing magnetic anisotropies

Although the spin-reorientation transition from out-of-plane to in-plane in Fe/Si film is widely reported, the tuning of in-plane spin orientation is not yet well developed. Here, we report the thickness-, temperature- and Cu-adsorptioninduced in-plane spin-reorientation transition processes in Fe/Si(557) film, which can be attributed to the coexistence of two competing step-induced uniaxial magnetic anisotropies, i.e., surface magnetic anisotropy with magnetization easy axis perpendicular to the step and volume magnetic anisotropy with magnetization easy axis parallel to the step. For Fe film thickness smaller than 32 monolayer(ML), the magnitudes of two effects under various temperatures are extracted from the thickness dependence of uniaxial magnetic anisotropy. For Fe film thickness larger than 32 ML, the deviation of experimental results from fitting results is understood by the strain-relief-induced reduction of volume magnetic anisotropy.Additionally, the surface and volume magnetic anisotropies are both greatly reduced after covering Cu capping layer on Fe/Si(557) film while no significant influence of Na Cl capping layer on step-induced magnetic anisotropies is observed.The experimental results reported here provide various practical methods for manipulating in-plane spin orientation of Fe/Si films and improve the understanding of step-induced magnetic anisotropies.     

Dynamic phase transitions in the kinetic mixed spin-1/2 and spin-5/2 Ising model under a time-dependent oscillating magnetic field

We calculate the dynamic phase transition (DPT) temperatures and present the dynamic phase diagrams in the kinetic mixed spin-1/2 and spin-5/2 Ising model under the presence of a time-dependent oscillating external magnetic field. We employ the Glauber transition rates to construct the set of mean-field dynamic equations. The time variation of the average magnetizations and the thermal behavior of the dynamic magnetizations are investigated, extensively. The nature (continuous or discontinuous) of the transitions is characterized by studying the thermal behaviors of the dynamic magnetizations. The DPT points are obtained and the phase diagrams are presented in two different planes. Phase diagrams contain four fundamental phases and three coexistence or mixed phases, which strongly depend on interaction parameters. The phase diagrams are discussed and a comparison is made with the results of the other mixed spin Ising systems.     

Electron spin resonance shift in spin ladder compounds

We analyze the effects of different coupling anisotropies in a spin-1/2 ladder on the electron spin resonance (ESR) shift. Combining a perturbative expression in the anisotropies with density matrix renormalization group computation of the short range correlations at finite temperature, we provide the full temperature and magnetic field evolution of the ESR paramagnetic shift. We show that for well chosen parameters the ESR shift can be in principle used to extract quantitatively the anisotropies and, as an example, discuss the material BPCB.     

Magnetic surfaces

The magnetic ground state, magnetic anisotropies and spin excitations of surfaces, interfaces and ultra-thin films of ferromagnetic 3d-metals are discussed. Enhanced magnetic ground state moments and altered hyperfine fields as predicted by ab initio band calculations have not been conclusively verified by experiments up to now. Future calculations should take into account dipolar fields and the role of interface roughness. Very large magnetic anisotropies are observed at magnetic surfaces and interfaces. In Ni/Cu multilayered films, the superposition of surface and stress-induced anisotropies was used to switch the easy axis of magnetization from the film plane to a perpendicular orientation by a proper choice of the Ni layer thickness. This could be an attractive possibility to develop new magnetic materials for technical applications. The temperature dependence of the spontaneous magnetization at surfaces and in ultra-thin films deviates from the behaviour of bulk material. Size effects as well as surface effects of spin wave excitations are discussed, comparing theoretical and experimental results. The need for more complete theories including surface exchange, surface anisotropy and realistic surface structures is emphasized.     

Softening of spin-wave stiffness near the ferromagnetic phase transition in diluted magnetic semiconductors

Employing the self-consistent Green's function approach, we studied the temperature dependence of the spin-wave stiffness in diluted magnetic semiconductors. Note that the Green's function approach includes the spatial and temperature fluctuations simultaneously which was not possible within conventional Weiss mean-field theory. It is rather interesting that we found the stiffness becomes dramatically softened as the critical temperature is approached, which seems to explain the mysterious sharp drop of magnetization curves in samples within diffusive regime.     

Spin-liquid state for two-dimensional Heisenberg antiferromagnets on a kagomé lattice

The magnetic properties of the spin liquid state of the antiferromagnetic Heisenberg model on the kagomé lattice are investigated within the self-consistent mean-field theory. The results show that the spin liquid ground-state energy per site is , which is in very good agreement with the best numerical estimates. The spin structure factor and spin susceptibility are also discussed. Received 1 December 1998 and Received in final form 12 April 1999     

Phase transitions and multidomain states in magnetic nanostructures with competing anisotropies

The evolution of the magnetic states in nanostructures with competing surface and bulk anisotropies was studied under a variation in the applied magnetic field. For spatially uniform magnetic states, the energy functional reduces to the energy of a bulk magnet in which the effective anisotropy depends on the thickness of the ferromagnetic layer. This dependence results in spin reorientation as the nanolayer thickness varies. The lines of first-order phase transitions and the equilibrium parameters of multidomain structures and domains of competing phases were determined. The calculated magnetic phase diagrams are used to analyze magnetic states and to construct magnetization curves.     

Spin configurations in the absence of an external magnetic field in a magnetic bilayer with in-plane cubic or uniaxial anisotropies

The spin configurations in the absence of an external magnetic field have been systematically investigated for a magnetic bilayer system consisting of two ferromagnetic layers separated by a non-magnetic layer with interlayer exchange coupling. Based on a phenomenological model, the conditions for the existence of collinear and non-collinear spin structures were derived for three kinds of magnetic bilayers with different combinations of in-plane cubic and uniaxial anisotropies for the two ferromagnetic layers. The phase diagrams of the spin configurations at zero field were drawn, taking into account the lowest-order anisotropy parameters of both the ferromagnetic layers. The values of the canting angle have been derived analytically and then numerically plotted.     

The mixed spin-1/2 and spin-1 Ising system on a two-layer Bethe lattice

Two layered magnetic Bethe lattice with varying coordination number q is introduced and numerically studied via exact recursion relations within a pairwise approach. The system is influenced by competing interlayer and intralayer nearest-neighbour (NN) coupling interactions and also by the crystal and external magnetic fields. Cases where both layers are ferromagnetic or one is ferro and the other antiferromagnetic are considered. System configurations’ energy calculations are used to devise some ground state phase diagrams that have proven useful for the investigation of the very low temperature behaviour of the model. Analysis of the thermal behaviours of the total magnetization within the model parameters’ space yield interesting phase diagrams which display fascinating properties, in particular the presence of tricritical points. Increasing negative values of the crystal field strength stabilizes the disordered paramagnetic phase and sometimes gives rise to wavy transition lines.     

Magnetoresistance and magnetic ordering fingerprints in hydrogenated graphene

Spin-dependent features in the conductivity of graphene, chemically modified by a random distribution of hydrogen adatoms, are explored theoretically. The spin effects are taken into account using a mean-field self-consistent Hubbard model derived from first-principles calculations. A Kubo transport methodology is used to compute the spin-dependent transport fingerprints of weakly hydrogenated graphene-based systems with realistic sizes. Conductivity responses are obtained for paramagnetic, antiferromagnetic, or ferromagnetic macroscopic states, constructed from the mean-field solutions obtained for small graphene supercells. Magnetoresistance signals up to ～7% are calculated for hydrogen densities around 0.25%. These theoretical results could serve as guidance for experimental observation of induced magnetism in graphene.     

Effects of disorder on ferromagnetism in diluted magnetic semiconductors

We present results of a numerical mean-field treatment of interacting spins and carriers in doped diluted magnetic semiconductors, which takes into account the positional disorder present in these alloy systems. Within our mean-field approximation, disorder enhances the ferromagnetic transition temperature for metallic densities not too far from the metal-insulator transition. Concurrently, the ferromagnetic phase is found to have very unusual temperature dependence of the magnetization as well as specific heat as a result of disorder. Unusual spin and charge transport is implied.     

Electron correlations and many-body techniques in magnetism

Recent progress in the theory of magnetism and electron correlations is reviewed to clarify the theories developed in the last decade and their mutual relations. A historical development of the theory of magnetism is outlined, and the dynamical coherent potential approximation (CPA) which completely takes account of the dynamical spin and charge fluctuations within the single-site approximation is introduced. Both the dynamical effects on various magnetic properties and the many-body band structure are shown to be explained on the same footing. It is shown that the dynamical CPA is equivalent to the other single-site theories of strongly correlated electrons: the many-body CPA, the dynamical mean-field theory (DMFT), and the projection operator method CPA (PM-CPA). These theories are elucidated with use of a common concept of effective medium or coherent potential. The effects of orbital degeneracy and the realistic calculation scheme are discussed with an emphasis on Hund’s rule coupling. Non-local theories of magnetism and electron correlations which go beyond the single-site approximation are presented. They include the molecular dynamics approach to the magnetic short range order, the dynamical cluster methods as a direct extension of the DMFT, and the self-consistent projection operator approach as an extension of the PM-CPA with use of the incremental cluster expansion. The current problems of their approaches and their future perspective are discussed.