Ground-state phase diagrams of Ising metamagnet in a mixed longitudinal and transverse magnetic field

The ground-state magnetic properties of a two-sublattice Ising metamagnet in a mixed longitudinal and transverse magnetic field are studied within the effective-field theory. A parameter j₂=J₂/J₁ is introduced, which reflects the strength ratio of spin coupling between adjacent planes and in each plane. In addition to the second-order transition lines, the first-order transition lines are also presented, since the ground-state energy can be calculated numerically. The ground-state phase diagrams in h_x–h_z are presented. The results show that when j₂<0 the phase transition of the system is always first-order for h_x<2.751, and when −1000?j₂<0 it is always second-order for h_x>4.36. For the given h_x (0<h_x<14.71), the longitudinal critical magnetic field increases as j₂ decreases. The reentrant phenomenon occurs in the range of j₂<−11.89, h_x>14.71. There is no fourth-order critical point in the phase diagrams given by using EFT as found by using mean field theory (MFT).     

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.     

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).     

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.     

Critical properties of the biaxial Ising model with both the longitudinal crystal field and the transverse dilution crystal field

Within the effective field theory (EFT), the critical properties of the biaxial Ising model with both longitudinal crystal field and transverse dilution crystal field are investigated for a simple cubic lattice. The tricritical point (TCP) and its trajectory are discussed in T-D_x and T-D_z space. A new phenomenon of two TCPs is found in T-D_x space. There exists a second-order line between two first-order lines, separated by two TCPs. The change of dilution concentration leads to a complex relation of the trajectory of the TCP. The degenerate patterns at the ground state appear by changing the longitudinal crystal field. The range of the ordered phase for transition lines labelled as a positive or (negative) value of D_x/J becomes larger or (smaller) with the decrease of t_x in T-D_z space. Some results have not been revealed in previous works.     

Magnetic and magnetocaloric results of magnetic field-induced transitions in La1−xCexMn2Si2 (x=0.35 and 0.45) compounds

The La_1−xCe_xMn₂Si₂ compounds (x=0.35 and 0.45) exhibit an antiferromagnetic-ferromagnetic transition caused by the changes in distance between Mn atoms due to temperature changes. A field-induced transition from antiferromagnetic state to ferromagnetic state at a critical field, which decreases with increase in temperature, can also be induced by applying a magnetic field. In this paper our aim is to study the magnetization and magnetocaloric effect, close to transition temperatures. Our subsidiary aim is to examine the temperature dependence of critical field and ferromagnetic fraction of compounds. The variation of magnetocaloric effect with temperature is correlated with the ferromagnetic-antiferromagnetic phase coexistence. Our final aim is to examine the harmony between magnetocaloric effect values calculated both by the Maxwell theory and by the Landau theory.     

Magnetic anisotropy of Tb1−xGdxMn6Sn6 compounds

Magnetization curves of Tb_1−xGd_xMn₆Sn₆ compounds (0?x?1) have been measured for aligned powder samples in the temperature range 4.2–300 K in pulsed magnetic fields up to 30 T. Temperature and concentration dependences of the magnetocrystalline anisotropy constants K₁ and K₂ and concentration dependence of the temperature of spontaneous spin-reorientation transition have been determined. Using these data, we estimated the contribution of the manganese and terbium atoms to the magnetic anisotropy of Tb_1−xGd_xMn₆Sn₆ and analyzed the origin of the appearance of field-induced first-order magnetic phase transition in these compounds.     

Magnetic properties of MnCr2O4 nanoparticle

The exchange interactions and the magnetic exchange energies are calculated by using the mean field theory and the probability law of Zn_1−xMn_xCr₂O₄ nanoparticles. The high-temperature series expansions have been applied in the spinels Zn_1−xMn_xCr₂O₄ systems, combined with the Padé approximants method, to determine the magnetic phase diagram, i.e. T_C versus dilution x. The critical exponent associated with the magnetic susceptibility (γ) is deduced. The obtained value of γ is insensitive to the dilution ratio x and may be compared with other theoretical results based on the 3D Heisenberg model.     

Magnetic study of phase separation and charge ordering in La1−xSrxMnO3 near x=0.5

We have investigated the magnetic phase diagram of polycrystalline and single-crystal La_1−xSr_xMnO₃ near 0.46≤x≤0.50. It turns out that for x<0.48, the polycrystalline material is ferromagnetic (FM), but for x≥0.48, incipient charge ordering takes place along with antiferromagnetism. At x=0.48, the ferromagnetic-antiferromagnetic phase transition in ceramics occurs at less than 85 kOe but requires significantly larger field for increasing x. These observations are in contrast to what is found in the single crystals, which are all FM.     

Critical properties of a random transverse crystal field Ising model with bond dilution

Within effective field theory (EFT), the critical properties of a random transverse crystal field Ising model with bond dilution are studied on a square lattice. Under both weak and strong bond dilution conditions, we consider three cases (α = 0,±0.5) of a transverse crystal field ratio, obtaining global phase diagrams in T−D _x space for changes in the random transverse crystal field concentration. The phase diagrams obtained for a weak bond dilution are very similar in shape to those of pure bond but with decreases in corresponding ordered phases and critical values. However, the phase diagrams for a strong bond dilution exhibit varieties, including a change in reentrant phenomenon, the occurrence of transverse crystal field degeneration, and the opposite direction crossover of temperature peak value.     

The magnetic state of diamagnetically diluted antiferromagnetic cobalt and nickel monoxide

The nearest neighbour J₁(x) and the next-neighbour super-exchange J₂(x) interactions are evaluated by using the mean field theory for Mg1−xBxO (B=Co and Ni) systems. The magnetic energy E(x) is obtained. A magnetic phase diagram of the Mg1−xBxO (B=Co and Ni) solid solutions with 0?x?1 is drawn by high-temperature series expansions (HTSE) combined with the Padé approximants method (PA). The critical exponents associated with the magnetic susceptibility (γ) and with the correlation length (ν) are deduced in order phase.     

The large low-field magnetic entropy changes in Ni43Mn46Sn11−xSbx alloys

A series of Ni₄₃Mn₄₆Sn_11−xSb_x (x=0, 1, and 3) alloys were prepared by an arc melting method. The martensitic transition shifts to higher temperature with the increasing Sb content. The isothermal magnetization curves and Arrott plots around martensitic transition temperatures show a typical metamagnetic behavior. Under a low applied magnetic field of 10 kOe, large magnetic entropy changes around the martensitic transition temperature are 10.4, 8.9, and 7.3 J/kg K, for x=0, 1, and 3, respectively. The origin of the large magnetic entropy changes and potential application for Ni₄₃Mn₄₆Sn_11−xSb_x alloys as working substances in magnetic refrigeration are discussed.     

The influence of magnetoelastic interaction on structural phase transitions in cubic ferromagnetics

In the framework of the Landau theory of phase transitions, the influence of the magnetoelastic interaction on structural transitions in cubic ferromagnetics with a positive first magnetic anisotropy constant is analyzed. It is shown that structural transitions are not accompanied by a reorientation of magnetization in this case. The phase diagrams of such ferromagnetics either contain a termination point of the structural transition or a critical point in which the first-order transition is replaced by a second-order one. Magnetoelastic interaction also leads to the appearance of an interval of the ferromagnetic parameters in which a coupled first-order structural-magnetic transition exists. The phase T?x diagram for Heusler Ni_2+x Mn_1?x Ga alloys is calculated, which is in good agreement with the experimental phase diagram of these alloys.     

The effective-field theory studies of critical phenomena in a mixed spin-1 and spin-2 Ising model on honeycomb and square lattices

An effective-field theory with correlations has been used to study critical behaviors of a mixed spin-1 and spin-2 Ising system on a honeycomb and square lattices in the absence and presence of a longitudinal magnetic field. The ground-state phase diagram of the model is obtained in the longitudinal magnetic field (h) and a single-ion potential or crystal-field interaction (Δ) plane. The thermal behavior of the sublattice magnetizations of the system are investigated to characterize the nature of (continuous and discontinuous) of the phase transitions and obtain the phase transition temperature. The phase diagrams are presented in the (Δ/|J|, k_BT/|J|) plane. The susceptibility, internal energy and specific heat of the system are numerically examined and some interesting phenomena in these quantities are found due to the absence and presence of the applied longitudinal magnetic field. Moreover, the system undergoes second- and first-order phase transition; hence, the system gives a tricritical point. The system also exhibits reentrant behavior.     

Dynamic magnetic hysteresis behavior and dynamic phase transition in the spin-1 Blume-Capel model

The nature (time variation) of response magnetization m(wt) of the spin-1 Blume-Capel model in the presence of a periodically varying external magnetic field h(wt) is studied by employing the effective-field theory (EFT) with correlations as well as the Glauber-type stochastic dynamics. We determine the time variations of m(wt) and h(wt) for various temperatures, and investigate the dynamic magnetic hysteresis behavior. We also investigate the temperature dependence of the dynamic magnetization, hysteresis loop area and correlation near the transition point in order to characterize the nature (first- or second-order) of the dynamic transitions as well as obtain the dynamic phase transition temperatures. The hysteresis loops are obtained for different reduced temperatures and we find that the areas of the loops are decreasing with the increasing of the reduced temperatures. We also present the dynamic phase diagrams and compare the results of the EFT with the results of the dynamic mean-field approximation. The phase diagrams exhibit many dynamic critical points, such as tricritical (•), zero-temperature critical (Z), triple (TP) and multicritical (A) points. According to values of Hamiltonian parameters, besides the paramagnetic (P), ferromagnetic (F) fundamental phases, one coexistence or mixed phase region, (F+P) and the reentrant behavior exist in the system. The results are in good agreement with some experimental and theoretical results.     

The possibility of re-entrant phenomena induced by a transverse field in ultra-thin transverse Ising films

The phase diagrams and temperature dependences of magnetizations in ultra-thin transverse Ising thin films are studied by the use of both the effective-field theory with correlations (EFT) and the mean-field theory (MFA). Novel features, such as the possibility of re-entrant phenomena, are obtained for the magnetic properties in such systems with a zero transverse field at the surfaces, when the EFT is applied to them, although such features could not be found from the use of the MFA. When the transverse field at the surfaces takes a finite value, however, the re-entrant phenomena could not be found from the both formulations of the EFT and the MFA. Similar phenomena are then obtained in the phase diagrams by using the MFA and the EFT.     

Spin glass-like behavior,giant magnetocaloric and giant magnetoresistance effect in PrPb manganites

The Pr_1−xPb_xMnO₃ (x=0.1–0.5) perovskites have been fabricated by solid-state reaction. The X-ray diffraction patterns show that the samples are of single phase with orthorhombic structure. The field-cooled (FC) and zero-field-cooled (ZFC) thermomagnetic curves measured at low field and low temperatures exhibit the spin glass-like state. The Curie temperature of samples increased with increase in Pb content. The maximum magnetic entropy change |ΔS_m|_max reaches the giant values of 3.91 and 3.68 J/kg K for quite low magnetic field change of 1.35 T for the samples x=0.1 and 0.4, respectively. The resistance measurements show that there is insulator–metal phase transition on the R(T) curves for samples with x?0.3. The giant magnetoresistance effect is also observed for all samples studied.     

Phase boundary between uniaxial and planar ferromagnets in layered perovskite manganite La2−2xSr1+2xMn2O7 (0.313⩽x⩽0.350)

We have examined magnetizations as a function of temperature and magnetic field in layered perovskite manganites La_2−2xSr_1+2xMn₂O₇ single crystals (x=0.313, 0.315, 0.318, 0.320 and 0.350) in order to determine the phase boundary between two ferromagnets (one is an uniaxial ferromagnet whose easy axis is parallel to the c-axis and the other is a planar ferromagnet whose easy axis is within the ab-plane) and following results are obtained: (i) all the present manganites exhibit magnetic transitions from a ferromagnet to a paramagnet at 76, 107, 116, 120 and 125 K for x=0.313, 0.315, 0.318, 0.320 and 0.350, respectively; (ii) for x=0.318, 0.320 and 0.350, the magnetic structure is a planar ferromagnet below Curie temperature; (iii) for x=0.313 and 0.315, the magnetic structure changes from an uniaxial to a planar ferromagnet at 66 and 85 K, respectively. From the results described above we have constructed the magnetic phase diagram of layered perovskite manganite La_2−2xSr_1+2xMn₂O₇ (0.313?x?0.350).