Molecular Field Constants Research Articles

Магнитные свойства Rb-=SUB=-2-=/SUB=-KFeF-=SUB=-6-=/SUB=-

The static magnetic properties of the Rb2KFeF6 single crystal in the temperature range T=1.8-300 K in magnetic fields H up to 90 kOe are investigated. At T>1.8 K the crystal is not magnetically ordered, however, the behavior of the inverse susceptibility chi-1(T) indicates a negative paramagnetic Curie temperature Theta of ~0.8 K. This is consistent with the analysis of the magnetization curve M(H) by replacing the external field with an effective Heff field with a negative molecular field constant.

On the anhysteretic magnetization of soft magnetic materials

Electrical steels are still the materials of choice for large-scale transformers and most electric motors. Yet, they may present a nonhomogeneous magnetic nature which prevents describing accurately their anhysteretic magnetization with the Langevin-Weiss model. Although interpolation and extrapolation methods may be used to model any anhysteretic curve, a simple and physically-based model would be of great value for fundamental and applied research. Inspired in the law of partial volumes for gas mixtures, we proposed a law of partial magnetizations for magnetic mixtures. In a two-component system, the model leads to the double Langevin-Weiss function. We also introduced a graphical method and a fitting approach to analyze and model anhysteretic magnetization curves. A semi-log magnetization derivative plot is central to this end. We validated our strategy through well-motivated examples using published data on soft magnets. The single Langevin-Weiss function provided an accurate description of the magnetization of isotropic and anisotropic magnetically homogeneous materials: a soft ferrite and a nanocrystalline alloy, respectively. For modelling a magnetization transverse to the material’s preferred direction, the key is to allow a negative molecular field constant. The double Langevin-Weiss function was suitable for less homogeneous materials, such as a grain-oriented electrical steel magnetized along the rolling direction and a non-oriented electrical steel. Moreover, a highly-grain-oriented electrical steel magnetized transverse to the rolling direction, which exhibits a constricted hysteresis loop, could be modeled in excellent agreement with data. The key for the latter, has been to allow an antiparallel arrangement of the mean magnetization of both components.

On the modelling of the anhysteretic magnetization of homogeneous soft magnetic materials

The analysis and optimization of devices with soft magnetic cores, such as inductive sensors and electric machines, rely on a simple and precise modelling of their nonlinear anhysteretic magnetization. The Langevin-Weiss equation of state has the advantages of being physically-based and capable of accurately describing isotropic materials. In fact, it has even been adopted as the backbone of the popular Jiles-Atherton model to describe magnetic hysteresis. However, many studies show the difficulty of retrieving the modelling parameters given an experimental anhysteretic curve, for which stochastic optimization methods are generally used.In this work, we present a simple and deterministic method for finding the parameters of the Langevin-Weiss model: the saturation magnetization, the temperature dependent a parameter, and the molecular field constants. To this end, we optimize a problem with a nonlinear solver where the fitting variables are instrinsically bounded. We validated the approach by analyzing three widely used soft magnets; a grain-oriented silicon steel, a Mn-Zn soft ferrite, and a Fe-based nanocrystalline alloy with induced anisotropy.We demonstrate that, contrary to what has previously been assumed, the Langevin-Weiss function can provide a good description of the anhysteretic magnetization of any homogeneous material, even materials with strong transverse uniaxial anisotropy. The key, which seems to have been overlooked, is to allow the Weiss molecular field to be negative.

Electronic structure and magnetic exchange interactions in Zn diluted CuFe2O4 magneto-ceramics

We report a detailed study on the electronic structure and temperature (1.9K≤T≤900K) dependence of magnetization in Zn diluted cuprospinel [Cu1−xZnxFe2O4 (0≤x≤0.6)]. The electronic structure determined from the x-ray photoelectron spectroscopy and Rietveld analysis of the x-ray diffraction patterns reveals the structure to be (Cu(1−x)/5ZnxFe4(1−x)/5)A [Cu4(1−x)/5Fe2−4(1−x)/5]BO4. Beyond a specific dilution limit (0.05≤xp≤0.1), a sudden phase-change from tetragonal (I41/amd) to cubic (Fd3m) is noticed with an alteration in the A–O–A (3.29%) bond angle and A–O bond length (0.67%). Our analysis shows that all these compounds order ferrimagnetically below the Néel temperature (TFN) due to dissimilar site-specific magnitudes of spins, yet, they undergo a second transition at low temperatures T1∼66K with asymptotic Curie temperature TA(=C/χ0) as high as −547.2K for the undoped case. Dilution with Zn cause quadratic decay (b2x2+b1x+yo) of the ferrimagnetic ordering temperature from 743 K to 370.5 K for x=0 and 0.6, respectively. On the contrary, a significant increase in the saturation magnetization (MS) was observed with increasing x until the critical composition xc∼0.4 beyond which MS decreases continuously (MS=1.64μB and 4.73μB for x=0 and 0.4, respectively). From the temperature dependence of inverse paramagnetic susceptibility [χ−1(T>TFN)] data and Néel’s expression for ferrimagnets, we evaluated the molecular field constants and exchange interactions (J) between the tetrahedral A- and octahedral B-sites. A systematic compositional dependence of this analysis yields that JAB (∼25kB for x=0) is the dominant exchange interaction in comparison to JBB and JAA; however, JAB decreases significantly with increasing the composition (JAB∼−5.5kB for x=0.6). The isothermal magnetization data and law of approach to saturation analysis reveals that the investigated system possesses very high anisotropy field HK ≥5.5kOe with cubic anisotropy constant K1≥1.6×106erg/cc at xc.

Effect of annealing temperature on structural and magnetic properties of Co2TiO4 ceramics prepared by sol-gel method

In this paper, polycrystalline Co2TiO4 ceramics have been synthesized using a sol-gel process followed by annealing at different temperatures. The lattice size and the average grain size of the samples increases with rise in annealing temperature. The temperature-dependent inverse paramagnetic susceptibilities recorded under zero-field-cooling condition have been fitted according to the Néel's expression for ferrimagnets. Subsequently, the molecular field constants and the corresponding exchange constants have been calculated. The fitting result shows that the magnetic interaction in the system becomes weaker as the annealing temperature rises. In addition, negative magnetization is observed during field-cooling process. The higher annealing temperature is beneficial to the growth of tetrahedral sublattice, leading to a decrease on compensation temperature. Furthermore, magnetization hysteresis loops for all the samples demonstrate the crucial role of grain size on the magnetic properties.

Size-dependent structural, magnetic, and optical properties of MnCo2O4 nanocrystallites

Finite-size (d = 5.4–112 nm) and surface effects on the structural, optical, and magnetic properties of ferrimagnetic inverse-spinel MnCo2O4 are reported. For d ≥ 87 nm, partial tetragonal distortion of the inverse spinel-lattice was observed. The Curie temperature TC of MnCo2O4 nanostructures, as determined by dc-magnetic susceptibility (χ) measurements, follows a finite-size scaling relation TC(d) = TC(∞)[1−(ξ0/d)λ] with a shift exponent λ = 0.75 ± 0.15 and microscopic correlation length ξ0 = 1.4 ± 0.3 nm, which is consistent with the mean field theory. For T > TC, χ(T) fits Néel's expression for the two-sublattice model with antiferromagnetic molecular field (exchange) constants NBB ∼ 85.16 (JBB ∼ 2.94 × 10−22 J), NAB ∼ 110.96 (JAB ∼ 1.91 × 10−22 J), and NAA ∼ 43.8 (JAA ∼ 1.13 × 10−22 J) and asymptotic Curie temperature Ta ∼ 717.63 K. The optical energy bandgap Eg, evaluated from the Kubelka-Munk function ([F(R∞)ℏω]2 = C2(ℏω - Eg)) is blueshifted to 2.4 eV (d ∼ 5.4 nm) from 1.73 eV (d ∼ 112 nm) due to the quantum confinement and non-stoichiometry. The role of tetragonal distortion and grain-size-effects in the intensity of crystal field transitions and variation in the magnetic ordering are further discussed and compared with Co3O4 nanostructures.

Reentrant spin-glass behavior and bipolar exchange-bias effect in “Sn” substituted cobalt-orthotitanate

We report the co-existence of longitudinal ferrimagnetic behavior with Néel temperature TN ∼ 46.1 K and reentrant transverse spin-glass state at 44.05 K in Tin (Sn) doped cobalt-orthotitanate (Co2TiO4). The ferrimagnetic ordering is resulting from different magnetic moments of Co2+ on the A-sites (3.87 μB) and B-sites (5.069 μB). The magnetic compensation temperature (TCOMP) shifts from 31.74 K to 27.1 K when 40 at. % of “Sn4+” substitutes “Ti4+” at B-sites where the bulk-magnetization of two-sublattices balance each other. For T > TN, the dc-magnetic susceptibility (χdc = M/Hdc) fits well with the Néel's expression for the two-sublattice model with antiferromagnetic molecular field constants NBB ∼ 15.44, NAB ∼ 32.01, and NAA ∼ 20.88. The frequency dependence of ac-magnetic susceptibility χac data follows the Vogel-Fulcher law, and the power-law of critical slowing-down with “zν” = 6.01 suggests the existence of spin-clusters (where “z” and “ν” being dynamic critical-exponent and correlation length of critical-exponent, respectively). This system exhibits unusual hysteresis loops with large bipolar exchange-bias effect (HEB ∼ 13.6 kOe at 7 K) after zero-field cooling process from an un-magnetized state, and a dramatic collapse of remanence (MR) and coercive field (HC) across TCOMP. The possible origins of such anomalous characteristics were discussed.

Co-existence of ferrimagnetism and spin-glass state in the spinel Co2SnO4

The nature of magnetic ordering in the inverted spinel Co2SnO4 = [Co2+][Co2+Sn4+]O4 is investigated by measuring the temperature dependence of its magnetization (M) and ac-susceptibilities (χ′ and χ″) in different magnetic fields (H) using a superconducting quantum interference device magnetometer. The polycrystalline sample with a grain size of 3–5 μm was prepared by the solid-state route and characterized by x-ray diffraction and scanning electron microscopy. Above the ferrimagnetic Néel temperature TN = 41 K, χdc = M/H fits well with the Néel' expression for the two-sublattice model of ferrimagnetism. The ferrimagnetic ordering is suggested to result from different magnetic moments of Co2+ on the A sites (3.87 μB) and B sites (4.16 μB) and antiferromagnetic molecular field constants with magnitudes NAA = 13.6, NBB = 36.8, and NAB = 33.2. The temperature variations of χ′ and χ″ under various dc-bias fields suggest the existence of a spin-glass (SG) phase for T < TSG = 39.1 K in which only the transverse spin components are frozen below TSG. This co-existence of longitudinal ferrimagnetic order below TN = 41 K and transverse SG state below TSG = 39.1 K is suggested to result from the presence of non-magnetic Sn4+ ions on the B sites.

The effect of approximating some molecular integrals in coupled-cluster calculations: fundamental frequencies and rovibrational spectroscopic constants for isotopologues of cyclopropenylidene

The effect of approximating the three- and four-virtual molecular orbital integrals in single and double coupled-cluster theory including a perturbational correction for connected triple excitations [CCSD(T)] is investigated for the calculation of higher-order properties, specifically the calculation of a molecular quartic force field and spectroscopic constants. The approach was proposed previously, but investigated for only second- and lower-order properties. It is shown that the conclusions reached previously are essentially unchanged on moving to higher-order properties. That is, approximating the selected integrals has essentially no effect on the accuracy of CCSD(T) calculations, and the error due to approximating integrals is much smaller than the residual error due to one-particle basis set deficiencies. The advantage of this approach is that it significantly reduces the amount of data needed to perform CCSD(T) calculations, thereby reducing computational requirements associated with input/output operations and message passing in massively parallel, distributed memory algorithms. These savings are particularly important for large basis set calculations where the reduction in data can be as high as three orders of magnitude for ∼1000 unoccupied molecular orbitals. The approach was tested by computing the quartic force field, vibrational frequencies, and spectroscopic constants of cyclopropenylidene and isotopologues. Comparison of our best results with available experimental data shows excellent agreement between theory and experiment. It is hoped that the theoretical spectroscopic data presented herein for cyclopropenylidene and isotopologues is useful in the interpretation of future laboratory experiments and astronomical observations.

Size dependence of the magnetic properties of antiferromagneticCr2O3nanoparticles

Magnetic properties of antiferromagnetic (AFM) ${\text{Cr}}_{2}{\text{O}}_{3}$ nanoparticles have been studied as a function of the nanoparticle size. The synthesized nanoparticles present an ellipsoidal shape with the major axis of approximately 170 nm and the minor axis that increases with the synthesis temperature from 30 to 70 nm. By magnetization and electron paramagnetic resonance experiments, we have obtained the parameters that characterize the AFM nanoparticles system. We have found that the N\'eel temperature, ${T}_{N}$, and the spin-flop field, ${H}_{\text{SF}}$, increase with the particle size from ${T}_{N}=288\text{ }\text{K}$ and ${H}_{\text{SF}}(5\text{ }\text{K})=10\text{ }\text{kOe}$ for the smaller nanoparticles and approach the bulk values [${T}_{N}=308\text{ }\text{K}$ and ${H}_{\text{SF}}(5\text{ }\text{K})=60\text{ }\text{kOe}$] for the larger particles. From the experimental results and the molecular-field theory applied to AFM coupled sublattices, we estimated the magnetic anisotropy, $K$, and the molecular-field constant, $\ensuremath{\lambda}$, as a function of the ${\text{Cr}}_{2}{\text{O}}_{3}$ nanoparticle size. When the size is reduced, $\ensuremath{\lambda}$ only diminishes $\ensuremath{\sim}8%$ with respect to its bulk value $(4.9\ifmmode\times\else\texttimes\fi{}{10}^{4}\text{ }{\text{Oe}}^{2}\text{ }\text{g}/\text{erg})$; instead, $K$ decreases more than an order of magnitude from $K=3.8\ifmmode\times\else\texttimes\fi{}{10}^{4}$ to $8.7\ifmmode\times\else\texttimes\fi{}{10}^{2}\text{ }\text{erg}/\text{g}$. We analyzed the results on the basis of a core shell model where the nanoparticle internal order consists of an antiferromagnetically ordered core and a disordered surface shell, which presents a frustrated magnetic state.

The susceptibilities and molecular-field constants of rare-earth compounds from mean-field theory

The mean-field theory is employed in present work to study the validity conditions for a popular formula which is widely used to calculate the susceptibilities of rare-earth compounds and their molecular-field constants from known transition temperatures [Proc. R. Soc. Lond. 276A (1963) 19; Phys. Rev. 163 (1967) 444]. To facilitate the theoretical analysis, we consider a special system, CeTe 2, whose magnetic behavior below T N is mainly governed by the lowest crystal-field (CF) Kramers doublet according to our recent theoretical studies. We find that, when the external field and the localized moment are both considerably weak, the formula can be safely used, but, when their magnitudes are appreciable with respect to temperature, one has to include the both terms in the Hamiltonian and perform the calculations self-consistently in order to calculate the susceptibility accurately; and to reflect the intrinsic magnetic properties of a system, the external field must be very weak in experimental measurements or theoretical calculations. Finally, we propose an alternative approach to determine the exchange constant from the known transition temperature, or vice versa.

Magnetic susceptibility and spin-lattice interactions inU1−xPuxO2single crystals

Single crystals of mixed uranium-plutonium dioxides have been grown by means of a chemical vapor transport reaction and characterized by x-ray diffraction on bulk and powdered single crystals. Magnetization and susceptibility data were taken using a commercial superconducting quantum interference device. Characteristic ordering temperatures have been determined as well as paramagnetic Curie temperatures and effective magnetic moments. Departures of the reciprocal susceptibility as a function of temperature from linearity have been treated in detail based on a model of vibronic interactions introduced to explain the gross features of susceptibility measurements on thorium-diluted ${\mathrm{UO}}_{2}$ [Sasaki and Obata, J. Phys. Soc. Jpn. 28, 1157 (1970)]. The influence of spin-lattice interactions causes a certain shape of the observed $1/\ensuremath{\chi}$ vs T curves from which we are able to suggest different mechanisms for the interactions as a function of the constituent's concentrations. From our susceptibility measurements characteristic parameters have been calculated using a model of tetragonal vibrational modes of the oxygen cage surrounding each uranium ion. These include specific coupling parameters G, mode characteristic temperatures ${T}_{\ensuremath{\omega}},$ and molecular-field constants $\ensuremath{\lambda}.$

Magnetic Properties of Layer-Type Compounds TlGdS2and TlGdSe2

Ternary thallinm lanthanide dichalcogenides TILnX2 (X = S, Se, or Te; Ln = lanthanide, except Ce and Pr) crystallize in the rhombohedral structure of α-NaFeO 2 type (R3m). Their crystal lattice consists of the layers of Ln 3 + ions separated by three layers of the non-magnetic ions (-Ln-X-Tl-X-Ln-). The magnetization was measured in the field range 0-14 T. The molecular field constants λm were estimated by fitting the Brillouin function to the experimental magnetization plots. The difference between the λ m values for the thallium gadolinium sulphide and the selenide corresponds to the different character of Gd-S and Gd—Se bonds and gives rise to the different J 1 and J2 exchange integrals.

Ferrimagnetic-like behavior of ZnMn 2As 2

The magnetic susceptibility of a single crystal of the magnetic semiconductor ZnMn 2As 2 has been investigated in the paramagnetic region for the first time. It is shown that this compound behaves as a ferrimagnet with two magnetic sublattices. The molecular field constants and effective moment values are determined for the Mn ions in two different crystallographic positions, corresponding to tetrahedral and octahedral coordinations by the As ions, respectively.

Calculation of the paramagnetic susceptibility and specific heat in UGa 2 and UPd 2Al 3 from ab initio crystal field theory

In the framework of the self-interaction corrected local density approximation, ab initio calculations have been carried out to obtain crystal field parameters for the paramagnetic state of UGa 2 and UPd 2Al 3. In two sets of calculations localized 5f states with occupation two and three, respectively, have been assumed. Using these parameters and adjusted anisotropic molecular field constants, the paramagnetic susceptibility for both compounds and the Schottky contribution to the specific heat in UPd 2Al 3 have been obtained by crystal field model calculations. Very good agreement between theoretical and experimental data is found for 5f 2 occupation in UGa 2. For UPd 2Al 3, the 5f 2 assumption yields qualitatively reasonable results as well, but it does not explain the T = 50 K maximum in the experimental data.

Magnetic properties of Cr-Mn austenitic stainless steels

The magnetic susceptibility x of three Cr-Mn austenitic stainless steels was measured as a function of temperature in the range 5–400 K. All specimens showed a characteristic susceptibility maximum. The temperature of the maximum and especially the curve shape depend strongly on specimen composition and metallurgical conditions (as-quenched, deformed). Because no significant field dependence appeared, the susceptibility maximum was identified as the antiferromagnetic Néel temperature. x;( T) measurements above T N were fitted to a modified Curie-Weiss equation. Comparison between measurements and generalized-molecular-field-theory predictions allowed us to identify the magnetic structure as that of a first-type antiferromagnet with fcc crystal structure. The atomic magnetic moment and the molecular-field coefficients depend strongly not only on composition, but also on metallurgical prehistory, that is, on the degree of the applied mechanical deformation and heat treatment. Mainly, manganese affected the antiferromagnetic interactions, while chromium affected the ferromagnetic. Mn and Fe contributed the most to the effective atomic moment. Measurements on mechanically deformed specimens show a structure sensitivity of the molecular-field constants. This could be interpreted consistently in terms of lattice-parameter changes. The apparent structure sensitivity of the effective atomic moment can be attributed to changes in matrix composition caused by precipitation.

Thermodynamic and magnetic properties of HoRh 2Si 2: A comparison between experiments and calculations in a crystal field model

The origin of two peaks observed in the magnetization and the heat capacity curves of HoRh 2Si 2 is investigated. The thermodynamic and the magnetic properties of this compound are calculated using a Hamiltonian including crystal field and isotropic exchange interaction terms which are comparable in magnitude. Two components (parallel and perpendicular to the c-axis) of the magnetization are evaluated by the molecular field approximation. The two peaks in the magnetization and the heat capacity can be reproduced by choosing appropriate values for crystal field parameters and molecular field constant. The lower transition temperature corresponds to the temperature at which the perpendicular component of the magnetization disappears, and the higher one, to that at which the parallel component of the magnetization disappears.

EPR in LiHoF 4 with a far infrared laser

A low-temperature FIR spectrometer was used for measuring EPR of LiHoF 4 in the field range 0–7 T, frequency range 150–1600 GHz. Zero field splittings and g-values for the lowest four energy levels are presented. Two sets of hyperfine lines were observed, corresponding to Δ m N = 0 and Δ m N = −1, each set with line spacings according to A h = 1.57 GHz . The exchange part of the molecular field constant is determined and compared to results from previous experiments.

Measurements of the complete magnetic moment vector in single crystals of PrAl2and NdAl2

Magnetisation measurements parallel and perpendicular to the applied field are reported for single crystals of ferromagnetic NdAl2 and PrAl2 in the range 4.2-200K and for magnetic fields up to 8.00 T applied in the (100) direction and directions near to (110) and (111). A quantitative description of the magnetisation is given in terms of a two-dimensional molecular field theory using two crystal-field parameters and the molecular field constant. Below the Curie temperature a satisfactory agreement between theory and experiment is obtained.

A method for the calculation of the magnetization of random high anisotropy amorphous materials

We introduce a procedure for the calculation of the magnetization distribution for a random anisotropy amorphous ferromagnetic material using a steepest descent method. The technique is applied to several anisotropy distributions, and the magnetization of each is presented as a function of temperature for realistic values of molecular field constant and anisotropy.