Modeling the Magnetic Properties of La0.62Er0.05Ba0.33Fe0.2Mn0.8O3: Mean-Field Study and Bean Rodbell Model

The Brillouin function, the phase transition and the related magnetic properties in La0.62Er0.05Ba0.33Fe0.2Mn0.8O3 perovskite have been studied using Bean-Rodbell model. The Brillouin function allows determining the total momentum J and the mean filed exchange parameter λ of the perovskite. The mean-filed equation draws the system to second order phase transition. These constants were used to stimulate the experimental isotherms M (H, T) by meanfield theory. The predicted results are compared to the available experimental data. It is noted that a good agreement has been found, with minor discrepancies, between theoretical and experimental data.

Магнитные свойства легированных натрием композитов типа фуллерен-терморасширенный графит

The magnetic properties (field range H = 0–50 kOe, temperature range T = 3–300 K), and structural features of a sodium-doped carbon composite material based on fullerene C_60 and thermally exfoliated graphite (TEG) are studied. The material is obtained with different ratios of the components by sintering at a pressure of 7 GPa and T = 600°C, at which it is found that significant amorphization of the crystal lattice of the initial C_60 occurs. The dia-, para-, and ferromagnetic components ( M _D, M _PM, and M _FM) were separated from the total magnetic moment of the samples under study. It is found that a sodium dopant has no effect on the magnetic properties of the composite. Analysis of the M _PM( H ) field dependences by using the Brillouin function for the fullerene-containing sample (i.e., without TEG) makes it possible to determine the quantum number of the total angular momentum of paramagnetic (PM) centers. Its value is found to be J = 1, which corresponds to elementary magnetic moment μ_PM = 2μ_B of a PM center. The concentration of PM centers is estimated at the level of N _PM ≈ (2–5) × 10^18 g^–1 for most samples, including the material without TEG. The introduction of TEG into the initial composition and an increase in its proportion in the composite leads to a strong increase in the magnetic moment, which is explained by an increase in both the J value and the concentration of PM centers.

Inverse Brillouin Function and Demonstration of Its Application

The Brillouin function arises in the quantum theory of paramagnetic materials, where it describes the dependence of the magnetization on the externally applied magnetic field and on the temperature of the system. There is no closed form exact analytical expression for the inverse Brillouin function, however, there have been several approximations proposed. In this work, we first compare relative errors and simplicity of several approximations for the inverse Brillouin function. Next, we demonstrate the application of the inverse Brillouin function by determining the Hamiltonian of the system using the simulation data of the magnetization dependence on the temperature. Then we compare the Hamiltonian that was used to set up the simulation with the Hamiltonian determined from the magnetization temperature dependence and an approximation to the inverse Brillouin function. We found that some of the approximations for the inverse Brillouin function can be used to accurately predict the Hamiltonian of the system given the magnetization dependence on temperature.

Characterizing Defects Induced by Irradiation Damage in 6H-SiC

There are many methods describing defects induced by ion implantation, but none are capable of describing it quantitatively. In order to solve this problem, we studied the magnetic change of silicon carbide (SiC) after ion implantation, and found that even if the implantation intensity and defects were increased, we found that all samples have the same paramagnetic background. In this paper, we use the paramagnetic characteristics shown by part of the defects to characterize the degree of defects. We studied how to characterize the concentration of the defect, using the Brillouin function to fit the data, validated the experimental results and analyzed the relationship between paramagnetic center concentration and defects.

Probing the magnetic superexchange couplings between terminal CuII ions in heterotrinuclear bis(oxamidato) type complexes

The reaction of one equivalent of [n-Bu4N]2[Ni(opboR2)] with two equivalents of [Cu(pmdta)(X)2] afforded the heterotrinuclear CuIINiIICuII containing bis(oxamidato) type complexes [Cu2Ni(opboR2)(pmdta)2]X2 (R = Me, X = NO3 – (1); R = Et, X = ClO4 – (2); R = n-Pr, X = NO3 – (3); opboR2 = o-phenylenebis(NR-substituted oxamidato); pmdta = N,N,N’,N”,N”-pentamethyldiethylenetriamine). The identities of the heterotrinuclear complexes 1–3 were established by IR spectroscopy, elemental analysis and single-crystal X-ray diffraction studies, which revealed the cationic complex fragments [Cu2Ni(opboR2)(pmdta)2]2+ as not involved in any further intermolecular interactions. As a consequence thereof, the complexes 1–3 possess terminal paramagnetic [Cu(pmdta)]2+ fragments separated by [NiII(opboR2)]2– bridging units representing diamagnetic S Ni = 0 states. The magnetic field dependence of the magnetization M(H) of 1–3 at T = 1.8 K has been determined and is shown to be highly reproducible with the Brillouin function for an ideal paramagnetic spin = 1/2 system, verifying experimentally that no magnetic superexchange couplings exists between the terminal paramagnetic [Cu(pmdta)]2+ fragments. Susceptibility measurements versus temperature of 1–3 between 1.8–300 K were performed to reinforce the statement of the absence of magnetic superexchange couplings in these three heterotrinuclear complexes.

Approximations for Brillouin and its reverse function

Purpose The mathematical complexity of the BJ(x) Brillouin function makes it unsuitable for most calculations and its application difficult for computer programming in magnetism. Here, its approximation with the tanh function is proposed to ease the mathematical operations for most cases. The approximation works with good accuracy, acceptable in practical calculations. This approximation has already formed the foundation of the “hyperbolic model” in magnetism for the study of hysteretic phenomena. The reversal of the Brillouin function is an important but difficult mathematical problem for practical purposes. Here, a proposal has been put forward for an easy approximation using an analytical expression. This provides a good workable solution for the BJ(x)−1 function dependent on J, the angular momentum quantum number of the material used. The proposed approximation is applicable within the working range of practical applications. The paper aims to discuss these issues. Design/methodology/approach The multi-variant Brillouin function is closely approximated by the tanh function to ease calculations. Its mathematically unsolved reversed function is approximated by a simple analytical expression with a good working accuracy. Findings The Brillouin function and its reversal can be approximated for practical users mostly for professionals working in Magnetism. Research limitations/implications Most if not all practical problems in Magnetism can be solved within the limitations of the two approximations. Practical implications Both proposed functions can ease the mathematical problems faced by researchers and other users in Magnetism. Social implications Ease the frustration of most users working in the field of Magnetism. Originality/value The application of the tanh function for replacing the Brillouin function led to the creation of the hyperbolic model of hysteresis. To the author's knowledge, the reverse function was mathematically only solved in 2015 with a vastly complicated mathematics, and is hardly suitable for practical calculations in Magnetism. The proposed simple expression can be very useful for theorists and experimental scientists.

Conductivities of zinc oxide by finite block spins

In the current work, we have demonstrated the phase of ZnO by reference to block theory, in which the phase may be considered to show a paramagnetic ordering between block spins, which in turn comprise random spins that have a majority of individual spins in a given direction. By making use of the Curie–Weiss law of block spins for zinc oxide, we obtained the susceptibility for the lower approximation of the Brillouin function and calculated the resistivity. The resistivity of ZnO mainly stems from spin glass-like disorders according to our analysis.