The magnetic properties of one-dimensional spin-1 ferromagnetic Heisenberg model in a magnetic field within Callen approximation

The effect of magnetic field h on the magnetic properties of the one-dimensional spin-1 ferromagnetic Heisenberg model is studied by the double-time Green’s function method. The magnetization and susceptibility are obtained within the Callen approximation. The zero-field susceptibility is as a decreasing function of the temperature T. The magnetization m increases in the whole field region, but the susceptibility maximum χ(T_m) decreases. The position T_m of the susceptibility maximum is both solved analytically and fits well to be a power law T_m∼h^γ at low fields and to be linear increasing at high fields. The height χ(T_m) decreases as a power law χ(T_m)∼h^−β with h increasing. The exponents (γ,β) obtained in our results agree with the other theoretical results. Our results are roughly in agreement with the results obtained in the experiment of Ni(OH)(NO₃)H₂O.     

Study of magnetoelectric coupling effect in the hexagonal ferroelectromagnet

Soft-mode theory based on Diffour model for ferroelectric subsystem, and mean-field theory as well as Heisenberg model for antiferromagnetic subsystem are utilized to investigate the magnetoelectric coupling effect in a hexagonal ferroelectromagnet, in which the ferroelectric and antiferromagnetic orders spontaneously coexist below a certain temperature. An anomaly of polarization at the magnetic transition temperature is ascribed to the effect of magnetoelectric coupling. The magnetic excitation has also been studied by spin-wave theory over the three-sublattice model. It is demonstrated that role of magnetoelectric coupling effect is not only related with the strength of magnetoelectric coupling but also special spin lattice structure. Our results show the magnetic specific heat induced by magnetic excitation experiences a suppression by the magnetoelectric coupling.     

Distinction of spin-glass freezing from superparamagnetic blocking

Experimental results on Eu_xSr_1?xS provide clear evidence for a cooperative phenomenon at the spin-glass transition, as distinguished from ordinary thermal blocking of superparamagnetic clusters. Only below the percolation threshold x_p = 0.13 can single-clusters aspects be separated clearly (superparamagnetic regime). In the spin-glass regime for x >x_p, susceptibility and remanent magnetization are studied near the freezing temperature in dependence on temperature, magnetic field and observation time. The anomalous slow relaxations of the remanent magnetization, which follow a power-law, exhibit a strong variation just near T_f0, the transition temperature deduced from static magnetization measurements. In addition, T_f values derived from ac-_χ measurements are distinctly frequency dependent; the frequency variation decreases towards low frequencies and seems to saturate near the T_f0 value. The strong sensitivity of _χ(T_f) to even small applied fields can be represented by a universal function independent of concentration. All these results emphasize the importance of the interactions among the spin clusters of spin glasses which are partially frustrated.     

Memory effect in the triglycine sulphate crystal polarized not parallel to the ferroelectric axis

The experimental results concerning the electric susceptibility χ₂₂ of the triglycine sulphate (TGS) crystal polarized not parallel to the ferroelectric axis at different temperatures have been shown. The process of partial rejuvenation in the ferroelectric phase has been presented. It has been found that the temperature changes of the slope correspond to step-wise changes of a pyroelectric coefficient p=dP/dT (P=P₂, P₃), where P₂ and P₃ are the longitudinal and transverse polarizations, respectively. An interpretation of temperature dependences of P₂ and P₃ as well as χ₂₂ of the triglycine sulphate ferroelectric previously exposed to a prolonged transverse electric field has been proposed. It has been concluded that the number of elementary cells containing molecules in metastable states depends on temperature in such a way that some kind of memory effect can be observed.     

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.     

Sol–gel derived nanocrystalline multiferroic BiFeO3 and R (R=Er and Tm) doped therein: Magnetic phase transitions and enhancement of magnetic properties

Nanocrystalline BiFeO₃ and rare earth ion doped BiFeO₃ (Bi_0.9R_0.1FeO₃, R=Er and Tm) were prepared by sol–gel method. Rietveld analysis of the X-ray diffractograms of the samples revealed that small amount of impurity phase of Bi₂Fe₄O₉ was formed together with the desired phase. In the thermal variation of magnetic mass susceptibility (χ_m) of the samples, one sharp transition below T_M (T_M∼100 K, 50 K and 30 K for BiFeO₃, Bi_0.9Er_0.1FeO₃ and Bi_0.9Tm_0.1FeO₃, respectively) was observed, which clearly hint the change of the domination of the ferromagnetic exchange interaction over the usual antiferromagnetic exchange interaction. Also, static magnetization (M) and susceptibility of each doped sample have been drastically enhanced compared to that of BiFeO₃. The values of χ_m and M measured at different temperatures confirmed that the magnetic behavior of the doped systems has been dominated by the paramagnetic/ferromagnetic clusters below ∼T_M. Another phase transition were observed in the χ_m vs. T curve of the samples at relatively higher temperature T_B (∼260 K for BiFeO₃, ∼220 K for Bi_0.9Er_0.1FeO₃ and ∼180 K for Bi_0.9Tm_0.1FeO₃), which may be attributed to the charge ordering transition. Ferroelectric hysteresis loops of the samples observed at 100 Hz confirmed the presence of ferroelectric ordering of the samples. Measured values of dielectric constants at 1 kHz of each sample in presence and absence of magnetic field confirmed a substantial magnetoelectric coupling of all the samples.     

Theory of the reciprocal susceptibility of the trigonal boracites and the experiment scheme

Landau theory is used to describe the ferroelectric trigonal phase of Boracites. The temperature dependence of the principal reciprocal susceptibility is obtained. The calculated result shows that at the Curie temperature T_c, the spontaneous polarization jumps. The component of the principal reciprocal susceptibility perpendicular to polarization jumps but the component parallel to polarization does not. A possible experimental scheme for the measurement of the principal reciprocal susceptibility components is presented.     

Magnetic properties and EPR spectra of [Cu(L-arginine)2](NO3)2·3H2O

Magnetic and EPR data have been collected for complex [Cu(L-Arg)₂](NO₃)₂·3H₂O (Arg=arginine). Magnetic susceptibility χ in the temperature range 2-160 K, and a magnetization isotherm at T=2.29(1) K with magnetic fields between 0 and 9 T were measured. The observed variation of χT with T indicates predominant antiferromagnetic interactions between Cu(II) ions coupled in 1D chains along the b axis. Fitting a molecular field model to the susceptibility data allows to evaluate g=2.10(1) for the average g-factor and J=−0.42(6) cm⁻¹ for the nearest neighbor exchange coupling (defined as H_ex=-∑J_ijS_i·S_j). This coupling is assigned to syn-anti equatorial-apical carboxylate bridges connecting Cu(II) ion neighbors at 5.682 Å, with a total bond length of 6.989 Å and is consistent with the magnetization isotherm results. It is discussed and compared with couplings observed in other compounds with similar exchange bridges. EPR spectra at 9.77 were obtained in powder samples and at 9.77 and at 34.1 GHz in the three orthogonal planes of single crystals. At both microwave frequencies, and for all magnetic field orientations a single signal arising from the collapse due to exchange interaction of resonances corresponding to two rotated Cu(II) sites is observed. From the EPR results the molecular g-tensors corresponding to the two copper sites in the unit cell were evaluated, allowing an estimated lower limit |J |>0.1 cm⁻¹ for the exchange interaction between Cu(II) neighbors, consistent with the magnetic measurements. The observed angular variation of the line width is attributed to dipolar coupling between Cu(II) ions in the lattice.     

On the anisotropic Heisenberg chain

High-temperature expansions are derived for the specific heat and the _χzz element of the susceptibility tensor for a linear chain of spins $\text{1}\text{2}$ with anisotropic nearest-neighbour interactions. (The coupling constants J₁, J₂ and J₃ are chosen to be different.) Use is made of exact results of the XY model, a first-order perturbation calculation in J₃, a high-temperature expansion for the transverse susceptibility _χxx of the anisotropic XY model and the high-temperature expansion for the isotropic Heisenberg chain. Some characteristic features of deviations from the case of axial symmetry in the coupling constants are discussed.     

Static critical behavior of 3D frustrated Heisenberg model on stacked triangular lattice with variable interlayer exchange coupling

Several Monte Carlo algorithms are used to examine the critical behavior of the 3D frustrated Heisenberg model on stacked triangular lattice with variable interlayer exchange coupling for values of the interlayer-to-intralayer exchange ratio R = |′/J| in the interval between 0.01 and 1.0. A finite-size scaling technique is used to calculate the static magnetic and chiral critical exponents α (specific heat), γ and γ_k (susceptibility), β and β_k(magnetization), ν and ν_k(correlation length), and the Fisher exponent η. It is shown that 3D frustrated Heisenberg models on stacked triangular lattice with R > 0.05 constitute a new universality class of critical behavior. At lower R, a crossover from 3D to 2D critical behavior is observed.     

Quantum Monte Carlo simulation of the ferroelectric or ferrielectric nanowire with core shell morphology

By using the Quantum Monte Carlo simulation; the electric properties of a nanowire, consisting of a ferroelectric core of spin-1/2 surrounded by a ferroelectric shell of spin-1/2 with ferro- or anti-ferroelectric interfacial coupling have been studied within the framework of the Transverse Ising Model (TIM). We have examined the effects of the shell coupling J_s, the interfacial coupling J_Int, the transverse field Ω, and the temperature T on the hysteresis behavior and on the electric properties of the system. The remanent polarization and the coercive field as a function of the transverse field and the temperature are examined. A number of characteristic behavior have been found such as the appearance of triple hysteresis loops for appropriate values of the system parameters.     

Anisotropic magnetization and susceptibility of Ba2Zn2Fe12O22 (Zn2Y)

The anisotropy of the magnetization and the susceptibility of the hexagonal ferrite Ba₂Zn₂Fe₁₂O₂₂ have been determined experimentally between 5 K and T_r = 367 K. The susceptibility is ascribed to the paraprocess. The measurements confirm for the first time the basic concept of the model for the anisotropy of the magnetization proposed by Callen and Callen.     

The large anisotropy of the magnetic and transport properties in the Ba5Co5ClO13 single crystal

In this Letter, the single crystals of Ba₅Co₅ClO₁₃ were grown by the flux method successfully. Their structure, magnetic and transport properties were studied. A large anisotropy of the magnetic and transport properties has been detected in this compound. Below the TN∼108 K, the magnetic susceptibility exhibits an antiferromagnetic peak in χc and an upturn transition in χab. We suggest that this behavior is consistent with the competition of the ferromagnetic (FM) intra-blocks coupling and antiferromagnetic (AFM) inter-blocks coupling in this compound. The temperature dependence of the resistivity displays a hump in ρab and a kink in ρc around TN, suggesting the strong coupling between the transport and magnetic properties. Above and below the transition, the transport properties in ab plane follow the three-dimensional (3D) variable range hopping (VRH) mechanism.     

Magnetoelectric coupling in RMn2O5 multiferroic: a Monte Carlo simulation

Magnetoelectric coupling in RMn₂O₅ (with R?=?non magnetic) multiferroics have been studied using the Monte Carlo simulation. The variation of magnetization and the polarization of RMn₂O₅ multiferroic have been determined. The system undergoes a magnetic transition at T_N and a further reduction of the temperature leads to a ferroelectric transition at T_C?<_? T_N depending on the coupling strength. Magnetic and ferroelectric hysteresis loops are obtained for several temperatures values. Variation of polarization with the external magnetic field of RMn₂O₅ has been given. Variation of polarization and magnetization with the electric field of RMn₂O₅ has been obtained.     

Second harmonic generation in generalized Thue-Morse ferroelectric superlattices

In this paper the second harmonic generation (SHG) in generalized Thue-Morse (GTM(m, n)) ferroelectric superlattices is studied. Under the small-signal approximation, the SHG spectra in both real and reciprocal spaces are investigated. It is found that: (1) only when the structure parameters l, l_A, and l_B are all chosen to be proper, can SHG in GTM(m, n) ferroelectric superlattices be generated; (2) for Family A of generalized Thue-Morse, GTM(m, 1) ferroelectric systems, with the increase of parameter m, the intense peaks of SHG concentrate on the long wavelength (the fundamental beam (FB) wavelength is within ), but for Family B of generalized Thue-Morse, GTM(1, n) ferroelectric superlattices, with the increase of parameter n, the intense peaks of SHG concentrate on the middle wavelength ; and (3) for GTM(m, 1) ferroelectric superlattices, the bigger the m, the stronger the relative integral intensity (RII) of SHG would be, but for GTM(1, n) ferroelectric systems, the bigger the n, the weaker the RII of SHG would be.     

A correlation between the two ratios γ/χ(0) and |Jm|/TK in Kondo system

Using the approach based on molecular field calculations for resonant level model; a close relationship between the two ratios γ/χ(0) and |J_m|/T_K is obtained. Where γ represents the electronic contribution in the specific heat, χ(0) is the susceptibility at zero temperature, J_m is the molecular field parameter and T_K is the Kondo temperature.     

First-order phase transition from an antiferromagnetic ferroelectric to a cycloidal multiferroic with weak ferromagnetism during the joint action of applied magnetic and electric fields

The thermodynamics of the phase transition in a perovskite-like multiferroic, in which an antiferromagnetic ferroelectric transforms into a new magnetic state where a spiral spin structure and weak ferromagnetism can coexist in applied magnetic field H, is described. This state forms as a result of a first-order phase transition at a certain temperature (below Néel temperature T _N ), where a helicoidal magnetic structure appears due to the Dzyaloshinskii-Moriya effect. In this case, the axes of electric polarization and the helicoid of magnetic moments are mutually perpendicular and lie in the ab plane, which is normal to principal axis c. Additional electric polarization p, which decreases the total polarization of the ferroelectric P, appears in the ab plane. The effect of applied magnetic and electric fields on the properties of a multiferroic with a helicoidal magnetic structure is described. An alternating electric field is shown to cause a field-linear change in magnetic moment m, whose sign is opposite to the sign of the change of electric field E. The detected hysteretic phenomena that determine the temperature ranges of overheating and supercooling of each phase are explained. A comparison with the experimental data is performed.     

Field dependent susceptibility of the 2D ferromagnet (CH3NH3)2CuCl4 in the paramagnetic phase

The temperature dependence of the ac susceptibility (χ) at constant applied magnetic field was investigated in the paramagnetic region of the quasi-2D ferromagnet (CH₃NH₃)₂CuCl₄. Above the Curie temperature (T_C=8.85 K) a maximum in the χ(T,H) curves was observed at T_m(H). The temperature at the maximum increases with increasing applied field. This anomaly is related to short range fluctuations close the order transition. The behavior of T_m(H) is governed by the gap exponent of the scaling function (Δ=γ+β). We found Δ=2.2±0.1 in very good agreement with the previously known values of γ and β.     

Monte Carlo investigation of phase transitions in the frustrated Heisenberg model on a triangular lattice

The critical properties and phase transitions of the three-dimensional frustrated antiferromagnetic Heisenberg model on a triangular lattice have been investigated using the Monte Carlo method with a replica algorithm. The critical temperature has been determined and the character of the phase transitions has been analyzed using the method of fourth-order Binder cumulants. A second-order phase transition has been found in the three-dimensional frustrated Heisenberg model on a triangular lattice. The static magnetic and chiral critical exponents of the heat capacity α, the susceptibility γ and γ _k , the magnetization β and β _k , the correlation length ν and ν _k , as well as the Fisher exponents η and η _k , have been calculated in terms of the finite-size scaling theory. It has been demonstrated that the three-dimensional frustrated antiferromagnetic Heisenberg model on a triangular lattice forms a new universality class of the critical behavior.     

Short-time dynamic behavior of the two-dimensional square lattice fully frustrated XY model

The short-time dynamic behavior of the two-dimensional fully frustrated XY model on a square lattice with ferromagnetic and antiferromagnetic couplings arranged in a zigzag pattern near the critical temperature is investigated. The Ising-like phase transition temperature T_c and all the static and dynamic critical exponents 2β/ν, ν and z are determined for two definitions of order parameter: the staggered chiral magnetization M_χ and the staggered magnetization M_st. We find that T_c, 2β/ν and z are almost independent of the definition of order parameter: T_c=0.4544(2), 2β/ν=0.265(4) and z=2.24(3) for M_χ while they are 0.4546(2), 0.274(4) and 2.25(3) for M_st, respectively. But ν depends on the definition of order parameter, ν=0.813(13) for M_χ while it is 0.862(16) for M_st.