Ground state phase diagrams and the tricritical behaviors of Ising metamagnet in both external longitudinal and transverse field

The ground state magnetic properties of a two-sublattice Ising metamegnet in both external longitudinal and transverse fields are studied within the mean-field approach. A parameter α=(Z₁J₁+Z₂J₂)/(Z₁J₁−Z₂J₂) which reflects the strength ratio of spin coupling in the plane and in adjacent planes is introduced. The ground state energy, the longitudinal staggered magnetization, the longitudinal total magnetization and the transverse total magnetization are calculated. The ground state phase diagrams in Ω−h and Ω−α plane are presented. The results show that when Ω is given, the longitudinal critical magnetic field increases when α decreases; the phase transition changes always from first order to second order with increase in the longitudinal magnetic field h or decrease in α. The reentrant phenomenon occurs in the range α?−0.66, Ω?0.21, h?0.78.     

Magnetic properties of Ising metamagnet in both external longitudinal and transverse fields

The phase diagrams of a two-sublattice Ising metamagnet at finite temperature in a mixed longitudinal field and a transverse magnetic field are investigated by the use of an effective-field theory (EFT) with correlations. In addition to the second-order transition lines, the first-order transition lines are also presented in the phase diagrams, since the Gibbs free energy can be calculated numerically. The results show that there is no fourth-order critical line in the phase diagrams given by using EFT as found by using mean-field theory (MFT). The tricritical lines and their projection in the t−h_x plane obtained by using EFT are also quite different from those by using MFT. Only one type of phase diagram is obtained by using EFT while three kinds of phase diagrams are obtained by using MFT, which indicates that only the first kind of phase diagrams obtained by using MFT is reliable. Furthermore, it is shown that the region of first-order transitions increases as the transverse magnetic field h_x decreases.     

An effective-field study of Ising metamagnet in an external field

The phase diagrams and magnetization curves of a two-sublattice Ising metamagnet at finite temperature with longitudinal crystal field H are investigated by the use of an effective-field theory (EFT) with correlations. In addition to the second-order transition lines, the first-order transition lines are also presented, since a method to calculate the Gibbs free energy numerically at finite temperature within EFT is found in this work. The results show that there is no fourth-order critical point or reentrant phenomenon in the phase diagrams given by using EFT as found by using mean-field theory (MFT).     

The phase diagrams of a spin-1 transverse Ising model

The phase diagrams of the spin-1 transverse Ising model with the presence of a crystal field is investigated by using an effective-field theory (EFT). We give a method to calculate the Gibbs free energy numerically at finite temperature within the EFT. The first-order transition lines are obtained by comparing the Gibbs free energy. The phase diagrams and the Gibbs free energy are also compared with those given using the mean-field theory (MFT).     

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.     

Phase transitions and multicritical points in the mixed spin-3/2 and spin-2 Ising model with different single-ion anisotropies

The phase diagram of mixed spin-3/2 and spin-2 Ising ferromagnetic model with different single-ion anisotropies is investigated by the use of a mean-field theory based on the Bogoliubov inequality for the Gibbs free energy. Global phase diagrams are obtained in the temperature-anisotropy plane. In particular, by changing values of the single-ion anisotropies, several different types of phase diagrams of first-order transition between two ordered phases, are studied in detail. A variety of multicritical points such as tricritical points, isolated critical points, and triple points are obtained.     

Sequence of the phase transitions in a two-dimensional ferromagnet with competing one-ion and exchange anisotropies

The phase states of a two-dimensional ferromagnet system with anisotropic exchange interaction have been investigated for various relations between the material constants. It is shown that the competition between the exchange and the one-ion anisotropies, and the account of the magnetodipolar and the magnetoelastic interactions lead to the sequence of the phase transitions. The explicit solutions of the dispersion equation have been found in the homogeneous phase states.     

Quantum spin model of a cubic ferromagnet in a magnetic field

The zero temperature phase diagram of a one-dimensional ferromagnet with cubic single ion anisotropy in an external magnetic field is studied. The mean-field approximation and the density-matrix renormalization group method are applied. Two phases at finite magnetic fields are identified: a canted phase with spontaneously broken symmetry and a phase with magnetization along the magnetic field. Both methods predict that the canted phase exists even for the single-ion anisotropy strong enough to destroy the magnetic order at zero magnetic field. In contrast to the mean-field theory, the density-matrix renormalization group predicts a reentrant behavior for the model. The character of the phase transition at finite magnetic field has also been considered and the critical index has been found. Received 9 May 2000 and Received in final form 5 July 2000     

Magnetic properties of a mixed spin- 1/2 and spin- 3/2 transverse Ising model in a longitudinal magnetic field

The mixed spin- 1/2 and spin- 3/2 transverse Ising model in a longitudinal magnetic field is studied within the framework of the effective-field theory with correlations. In this approach the effective-field equations are derived by using a probability distribution method based on the generalized but approximated van der Waerden identities. The total longitudinal and transverse magnetizations, the transverse susceptibility and longitudinal susceptibility and the critical temperatures are obtained. We find a number of interesting phenomena in these quantities, due to the applied transverse field and the longitudinal field.     

Structure and magnetic phase diagram of mixed rare-earth Nd1−xTbxFe10.5Mo1.5 compounds

The structural and magnetic properties of Nd_1−xTb_xFe_10.5Mo_1.5 (x=0$x=0$, 0.2, 0.4, 0.6, 0.8, 1.0) compounds have been investigated by means of X-ray diffraction and magnetic measurements. All the investigated compounds crystallize in the tetragonal ThMn₁₂-type structure with I4/mmm space group. The lattice parameters a, c and the unit-cell volume V decrease with increasing x. The Curie temperatures T_C are almost independent x. There exists a unique spin-reorientation transition for the end compositions of Nd_1−xTb_xFe_10.5Mo_1.5 compounds with x=0$x=0$ and x=1$x=1$, while two spin-reorientation transitions are observed for x=0.2–0.8$x=0.2–0.8$. The room-temperature magnetocrystalline anisotropy of Nd_1−xTb_xFe_10.5Mo_1.5 compounds changes from uniaxial to planar with increasing x content. Based on magnetic measurements, a magnetic phase diagram of Nd_1−xTb_xFe_10.5Mo_1.5 compounds is constructed. By minimizing the magnetocrystalline anisotropy energy, a theoretical magnetic phase diagram for the Nd_1−xTb_xFe_10.5Mo_1.5 system is derived, showing a reasonable agreement with the observations.     

Magnetizations of a nanoparticle described by the transverse Ising model

The characteristic influences of size S, exchange interaction and transverse field on the longitudinal and transverse magnetizations of a ferroelectric small particle described by the transverse Ising model are investigated by the use of the standard mean-field theory. In particular, the longitudinal magnetization of a nanoparticle is strongly affected by the surface situations. The effective exponent β_eff of the longitudinal magnetization is also studied. We find some characteristic phenomena of β_eff, depending on the values of S and the ratios of the physical parameters. In relation of recent investigations, the thermal variations of longitudinal and transverse magnetizations in the nanoparticle, consisting of a ferromagnetic core with size S=3 surrounded by a ferromagnetic surface shell with an antiferromagnetic inter-shell coupling, are examined and some typical ferrimagnetic behaviors are found in them. In relation to these phenomena, the effects of surface dilution on the magnetizations are investigated and some novel features are found in the system with size S=3 surrounded by such a ferromagnetic diluted surface shell.     

Magnetoelastic instability in Ising-like models

The magnetoelastic instability in nanostructured ring-shaped Ising-like spin 1/2 model has been investigated by using the exact diagonalization method. It is found that there exists two critical anisotropy parameters and () in the phase diagram. As the anisotropy parameter , the magnetoelastic transition from dimerized phase to uniform phase is a first order transition with an increase of the lattice spring constant. While for , the transition is continuous. Another critical value divides the different lattice distortion behavior as the anisotropy is strengthened.     

The possibility of two compensation points in a ferrimagnetic mixed spin-1 and spin-3/2 Ising system using Bethe lattice approach

We give an exact formulation of a mixed spin-1 and spin-3/2 Ising model on the Bethe lattice, which shows ferrimagnetism and compensation points. The model incorporates antiferromagnetic nearest-neighbor interaction which is relevant to describe ferrimagnetism. The influence of two sublattice crystal fields, D_A and D_B, on compensation points is studied in detail. For certain crystal-field values, the single or double compensation temperature may occur in the present system.     

Effect of the transverse field on the site-diluted Ising model in a longitudinal random field

Phase diagrams and magnetization curves of a diluted spin-3/2 transverse Ising model in a random field on honeycomb lattices are investigated by the use of an effective-field theory with correlations. The tricritical point is found in the system, in contrast to the corresponding spin-1/2 Ising counterpart. The possible reentrant phenomena displayed by the system due to the competition effects that occur for appropriate ranges of the random and transverse fields are investigated.     

Effective-field theory on the kinetic Ising model

As an analytical method, the effective-field theory (EFT) is used to study the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field. The effective-field equations of motion of the average magnetization are given for the square lattice (Z=4) and the simple cubic lattice (Z=6), respectively. The dynamic order parameter, the hysteresis loop area and the dynamic correlation are calculated. In the field amplitude h₀/ZJ-temperature T/ZJ plane, the phase boundary separating the dynamic ordered and the disordered phase has been drawn, and the dynamical tricritical point has been observed. We also make the compare results of EFT with that given by using the mean field theory (MFT).     

A generalized spin ladder in a magnetic field

We study the phase diagram of coupled spin-1/2 chains with bilinear and (chiral) three-spin exchange interactions in a magnetic field. The model is soluble on a one-parametric line in the space of coupling constants connecting the limiting cases of a single and two decoupled Heisenberg chains with nearest neighbour exchange only. We give a complete classification of the low-energy properties of the integrable system and introduce a numerical method which allows to study the possible phases of spin ladder systems away from the soluble line in a magnetic field. Received 17 November 1998 and Received in final form 22 January 1999     

Novel massive ground states of spin chains in a magnetic field

Novel massive quantum states appearing in spin chains under a strong magnetic field are discussed. These states lead to plateaus in magnetization curves. When the systems are axially symmetric and the field is applied parallel to the symmetry-axis, the phenomena are analogous to metal-insulator transitions. Striking features of the plateau phenomena - exactness and rationality - are explained as consequences the commensurability condition to the underlying lattice. The effects of the planar anisotropy are also discussed in detail. Received: 16 February 1998 / Revised: 20 April 1998 / Accepted: 30 April 1998     

Comprehensive theory for reduction of products of spin operators

We present a comprehensive theory that reduces the total power of products of spin operators. This theory improves the previous one [P.J. Jensen, F. Aguilera-Granja, Phys. Lett. A 269 (2000) 158] in two aspects. One is that for the set of spin operators S⁺, S⁻, Sz, a new method is suggested where the expansion coefficients in the reduction formula can be solved from linear equations. This new method is of direct physical meaning and is easier to handle. The other is that we show a method to reduce the products of another set of spin operators Sx, Sy, Sz. For this set of operators, the use of permutation regulation of x→y, y→z and z→x can save much time in obtaining some reduction formula. The present comprehensive theory enables one to deal more easily with the decoupling problems in Green' function theory where the set of either S⁺, S⁻, Sz or Sx, Sy, Sz operators is used.     

The phase diagrams and compensation behaviors of mixed spin Blume-Capel model in a trimodal magnetic field

The phase diagrams and compensation behaviors of mixed spin-1/2 and spin-1 Blume-Capel model in a trimodal magnetic field are investigated in the framework of the effective field theory on simple cubic lattice. The change of negative crystal field and trimodal concentration can affect the TCP, the second-order phase and the magnetic field degeneration at ground state in T-H space. In T-D space, the trajectory of the TCP takes on the acre curve and there exist the two TCPs under certain condition. In addition to giving one or two compensation temperature points in M-T space, the mixed spin Blume-Capel model also provides one or two novel compensation magnetic field points in M-H space. Some results are not revealed in previous works.