Law Of Approach To Saturation Research Articles

Effect of α-Fe₂O₃ Phase on the Magnetic Interactions in Nickel Ferrite (NiFe₂O₄) Nanoparticles.

We report on the effect of α-Fe₂O₃ phase in the magnetic properties and magnetic interactions in nickel ferrite (NiFe₂O₄-NFO) nanoparticles synthesized by co-precipitation method. Structural analysis confirms the formation of the cubic inverse spinel phase without any impurities for the NFO sample annealed in air at 650 °C. When the annealing temperature is increased to 750 °C and 850 °C, α-Fe₂O₃ impurity phase is formed along with the parent NFO phase. Raman spectra recorded at room temperature (RT) confirm the presence of pure NFO phase for the sample annealed at 650 °C, and presence of α-Fe₂O₃ phase is observed in the samples annealed at 750 °C and 850 °C. Saturation magnetization values at RT for the NFO samples annealed at 650 °C, 750 °C and 850 °C are 34 emu/g, 19 emu/g and 28 emu/g respectively. Zero Field Cooled (ZFC) and Field Cooled (FC) measurement reveals the super-paramagnetic behavior along with competing magnetic interactions in all the samples. For the NFO sample annealed at 750 °C and 850 °C, a drop in ZFC magnetization and a small kink in FC magnetization observed around 245 K indicate the presence of a Morin transition (TM) from the α-Fe₂O₃ phase. Anisotropy constants were calculated for all the samples using the law of approach to saturation (LAS) method. The magnetocrystalline anisotropy energy distribution function for the NFO samples annealed at 750 °C and 850 °C exhibit broad peak due to the random distribution of spins associated with different particle size.

Control of structural and magnetic characteristics of cobalt ferrite by post-calcination mechanical milling

The possibility to control the structural parameters of nanostructured spinel cobalt ferrite paves the way to prepare the ferrite with the anticipated magnetic properties for broad applications. This study is aimed at elucidating the correlation between structural parameters and magnetic properties of cobalt ferrite nanoparticles subjected to post-calcination high-energy ball milling. The milling energy was predicted at four different levels, using the standard collision model. The samples produced were characterized by X-ray diffraction (XRD), Fourier transform-infrared spectroscopy (FTIR), X-ray photoelectron spectroscopy (XPS), field emission scanning electron microscopy (FESEM), high-resolution transmission electron microscopy (HRTEM) and vibrating sample magnetometry (VSM). Both FTIR studies and Rietveld refinement of the XRD data shows re-distribution of cations in the spinel structure, induced by a critical level of milling energy. Also, the presence of the three ionization peaks, Co−2p, Fe−2p and O−1s, revealed by XPS confirms the formation of spinel ferrite structure in the cobalt ferrite nanoparticle. The maximum energy products (BH)max of the sample milled under high level ball milling energy was 2.18 MGOe which is almost 5 times higher than that of the un-milled calcined sample. Additionally, the magnetic anisotropy constant was calculated by the Law of Approach to Saturation (LAS) method and indicates a direct correlation between lattice strain and coercivity of samples.

Tuning the magnetic properties of a ferrimagnet

Magnetic properties of manganese ferrite doped with lanthanum and gadolinium having compositional formula MnRExFe2−xO4 (where RE = La3+, Gd3+ and x = 0.02, 0.04, 0.06, 0.08, 0.10) synthesized by co-precipitation method have been investigated. The compositional variation of the magnetic properties for each rare earth ion was studied individually first. Then, the variation of the magnetic properties with the substitution of the two different ion having different magnetic moments was compared. Saturation magnetization of non-magnetic ion (La3+) substituted MnFe2O4 was found to be superior to that of magnetic ion (Gd3+) substituted MnFe2O4. The observed result was explained in terms of Neel’s theory of ferrimagnetism, distribution of cations and magnetic moment of the associated cations. Law of approach to saturation (LAS) was adopted to investigate the dependency of magnetization on the applied field. A strong dependence of magnetic property on the distribution of cations which is specific to the particular rare earth ion was revealed in the present study.

Tailoring of microstructure, magnetic properties and charge carrier dynamics of YIG nanoparticles by Gd doping

Effect of gadolinium doping on growth mechanism, microstructure, magnetic properties and conductivity relaxation behavior of sol-gel prepared yttrium iron garnet (YIG) nanoparticles is studied in detail. Rietveld microstructural analysis of XRD data confirms the growth of single phase nanocrystalline YIG. Gd doping created oxygen vacancies inside the system which played an important role in controlling transport properties. Switching field distribution (S.F.D.) and Law of Approach to saturation (L.A.S.) techniques were adapted to analyze magnetic properties which delineate an improvement of coercivity and anisotropy constant. Impedance spectroscopy revealed the grain contributions only to the conduction process and frequency dependent conductivity follows universal power law. Harviliak-Negami (H.N.) formalism was adapted to analyze the modulus data in the frequency domain. Scaling of conductivity and electrical modulus data established that the conduction and relaxation process are temperature and composition independent. Non-Debye type correlative motion of charge carriers was established via analysis of decay function of electric field ϕ(t) inside the material which was described by Kohlrausch-Williams-Watts (K.W.W.) function. Improvements of magnetic and electrical properties in the prepared system can be beneficial for different applications.

Law of Approach to Saturation in Mn–Zn Ferrite Nanoparticles

In this paper, the law of approach to saturation (LAS) was applied to a series of Mn–Zn ferrite nanoparticles with compositional formula Mn1−xZnxFe2O4 where x = 0, 0.1, 0.2, 0.3, 0.4 and 0.5 to study the dependence of magnetization, M, on the applied magnetic field, H. Using the statistical parameters, the field range was chosen. The dependence of magnetization on the applied field was studied based upon the output of the statistical parameters for the curve fitted using different forms of LAS, namely, $M=M_{s}\left [ 1-\frac {a}{H}-\frac {b}{H^{2}} \right ]+kH$ , $M=M_{s}\left [ 1-\frac {a}{H}-\frac {b}{H^{2}} \right ], M=M_{s}\left [ 1-\frac {b}{H^{2}} \right ]$ and $ M=M_{s}\left (1- \frac {1}{15}\frac {{H_{A}^{2}}}{H^{\frac {1}{2}}\left (H^{\frac {3}{2}}+H_{R}^{\frac {3}{2}} \right )} \right )+k H$ . A critical examination on the output parameters resulted from fitting into different equations, indicates the dependency of magnetization on the applied field as a characteristic of the composition of Mn–Zn ferrites. The statistical parameters, along with physically meaningful fitted parameters, provide knowledge on dependency of magnetization of different compositions of Mn–Zn ferrites over different regions of applied field.

Systematic study of Ce3+ on the structural and magnetic properties of Cu nanosized ferrites for potential applications

Ce3+ substituted Cu-spinel nanoferrites CuCexFe2−xO4 (x = 0.00, 0.02, 0.04, 0.06, 0.08 and 0.10) were synthesized via sol–gel self-combustion hybrid route. Single phase spinel ferrite of Cu nanoferrites were examined using X-ray diffraction (XRD) analysis whereas the multiphase structure was observed as Ce contents increased from x = 0.06. Field emission scanning electron microscopy (FESEM), Thermogravimetric and differential thermal analysis (TGA and DTA) and Fourier transform infrared spectroscopy (FTIR) were used to find out the morphology phase and metal stretching vibrations of Ce3+ substituted nanocrystalline ferrites. The crystallite size was increased and found in the range of 25–91 nm. The agglomerations in Cu ferrite samples increase as the Ce3+ concentration increases. The magnetic properties such as remanence, saturation magnetization, coercivity, Bohr magneton and magnetocrystalline anisotropy constant (K) were determined using M−H loops recorded from a vibrating sample magnetometer (VSM). Saturation magnetization, remanence and coercivity are increased as the Ce3+ contents increase in Cu nanocrystalline samples. Moreover, law of approach to saturation (LoA) was used to calculate the maximum value of saturation for Ce-doped Cu nanoferrites. The soft magnetic behaviour of the Cu nanoferrite is observed as compared to the samples substituted with the increased Ce contents in Cu nanocrystalline ferrite. Bohr magneton and magnetocrystalline anisotropy are found to increase with the substitution of rare earth Ce3+ contents in Cu spinel nanocrystalline ferrite. Ce-doped Cu nanocrystalline ferrites with excellent properties may be suitable for potential applications in sensing, security, switching, core, multilayer chip inductor, biomedical and microwave absorption applications.

Temperature Dependence of Magnetization, Anisotropy, and Hyperfine Fields of NiFe2–xYbxO4($x = 0$ , 0.05, 0.075)

Nickel ferrite (NiFe 2 O 4 ), an inverse spinel in which the tetrahedral (A) sites are occupied by Fe3+ ions and the octahedral (B) sites are occupied by Fe3+ and Ni2+ ions, can be represented as Fe A 3+ Ni B 2+ Fe B 3+ O 4 2− [1-3]. The cation distribution and the resulting magnetic properties are reported to be quite interesting in rare-earth doped nickel ferrite due to the absence of center of symmetry [2, 3]. Kamala Bharathi et al. have reported that, substitution of Fe3+ by Dy3+ ion in NiFe 2 O 4 causes development of magnetocapacitance, leads to ferroelectricity and affects several other properties [3]. These materials play an important role in applications (spintronic memory cell, high frequency devices etc) [4]. There are no reports on thermal behavior of magnetic anisotropy in the rare earth substituted Ni ferrites. Understanding these behaviors will be useful in novel applications such as heat-assisted magnetic recording [4, 5]. In the present work, the temperature dependence of magnetic anisotropy and hyperfine fields of NiFe 2−x Yb x O 4 (x = 0, 0.05, 0.075) are reported. All the samples were prepared by solid state reaction. The materials are found to have formed in inverse spinel structure, from the powder XRD patterns. Rietveld refinement carried out on the XRD patterns revealed that Yb3+ ions occupy the B site and the lattice is found to be expanded with the introduction of Yb3+. The lattice constants are 8.3415(1) A (reported value is 8.34 A [1]), 8.3436(0) A and 8.3463(5) A for x = 0, 0.05 and 0.075 compounds respectively. Magnetization was measured at 5 K, 100 K, 200 K, and 300 K and the magnetization was observed to decrease with x. This is attributed to substitution of Fe3+ by Yb3+ in the B-site. The saturation magnetization values, at all the measured temperatures obtained through Honda plots are given in Table 1. The moments calculated using Hund's rule (assuming that Yb3+ and Fe3+ moments are parallel) are 2.82 μ B /f.u., 2.76 μ B /f.u. and 2.71 μ B /f.u. for x = 0, 0.05 and 0.075 compounds respectively. The experimental values are less in comparison with the calculated moments. In NiFe 2 O 4 , this difference is in accordance with the reported literature [1-3]. At each temperature, M-H data were fitted to the law of approach to saturation (LAS) [1, 6] and K1(T), the first order magnetocrystalline anisotropy constant at a temperature T, was obtained from LAS. At any given temperature, the observed increase in K1 of x = 0.05 and 0.075 compared with x = 0, is explained on the basis of single-ion model i.e. localized divalent ions in the octahedral site. The temperature dependence of K1 of cubic systems was investigated by plotting ln K1(T) vs ln M(T). The slopes of the straight line obtained are 7.5, 12.5 and 11.44 for x = 0, 0.05 and 0.075 respectively. This can be compared with the value of 10 proposed for magnetic anisotropy in cubic systems [1, 6]. The deviation of the exponent is explained on the extent of localization of the divalent ion.

Effect of Mn substitution on the cation distribution and temperature dependence of magnetic anisotropy constant in Co1−xMnxFe2O4 (0.0≤x≤0.4) ferrites

Abstract The effect of Mn substitution on temperature dependent magnetic properties of Mn substituted cobalt ferrite, i.e., Co1−xMnxFe2O4 (x=0.0–0.4), prepared by a ceramic method has been investigated. X-ray diffraction (XRD) analysis reveals that all samples posses a single phase cubic spinel structure. The lattice constant determined from XRD increases with Mn substitution whereas the bulk density of the samples decreases. Mossbauer results reveal that Co, Fe and Mn ions are distributed over the tetrahedral (A) and octahedral (B) sites for the prepared samples. Hysteresis loops yield a saturation magnetization (Ms) and coercive field (Hc) that vary significantly with temperature and Mn content (x). The temperature dependence of the magnetization obtained for μoH=5 T presents a maximum at 175 K which is also dependent on the value of x. The high field regimes of the hysteresis loops are modeled using the Law of Approach to Saturation (LAS) to determine the first-order cubic anisotropy coefficient (K1). It has been found that the anisotropy of these materials increases significantly with decreasing temperature. However, below 175 K, the shape of the anisotropy energy function changes significantly causing a first-order magnetization process (FOMP) at higher fields, which also prevents the magnetization to saturate even under a maximum applied field of 5 T. In general, the anisotropy coefficient decreases with increasing Mn substitution at a given temperature, which could be explained in terms of the site occupancy of the Mn2+ substituent in the cubic spinel lattice.

Magnetic behavior of nickel–bismuth ferrite synthesized by a combined sol–gel/thermal method

The bulk NiFe2−xBixO4 ferrites with various Bi3+ concentration (x=0, 0.1, 0.15) were synthesized via sol–gel procedure, starting from nickel, bismuth and iron nitrate powders, followed by the conventional thermal treatment. The structural and magnetic properties of the as-prepared ferrites were studied by means of X-ray diffraction, alternating gradient force magnetometry and Faraday balance. The anisotropy constant was determined by the law of approach to saturation (LAS) model. An increasing Bi3+ concentration in NiFe2−xBixO4 leads to a decrease in the saturation magnetization, Néel temperature and the anisotropy constant of the material.

The Measurement for the Effective Anisotropy Constant of the Nanocomposite Permanent Magnetic Material Nd<sub>2</sub>Fe<sub>14</sub>B/α-Fe

The effective anisotropy constant and the saturation magnetization in nano composite Nd2Fe14B/α-Fe have been calculated by the law of approach to saturation (LATS) method. The applicability of the method has been analyzed. The calculated result shows that the LATS method is suitable for the calculation of the effective anisotropy constant and the saturation magnetization in nano composite permanent magnetic materials.

Silica Encapsulated Ni Nanoparticles: Variation of Optical and Magnetic Properties with Particle Size

Ni nanoparticles embedded in SiO2 matrix were prepared by sol-gel process. The molar percentages of Ni were varied from 2 to 20% of total SiO2 present in the matrix. Transmission electron microscope (TEM) images revealed that particle sizes varied from 8.0-15.7 nm at an annealing temperature of 773 K with variation of concentration. The optical absorption spectra revealed that the surface plasmon resonance (SPR) peak in the UV region of the spectrum shifted with the particle diameter (D) from that at 247.3 nm for D = 8.0 nm to 250.7 nm for D = 15.7 nm. In hysteresis loop measurements the magnetizations (M) of the nanocomposites also increased with higher Ni content in the matrix and did not saturate in the measuring limit of the magnetic filed (H) of 4 KOe. The anhysteric curves for different samples were analyzed with the law of approach to saturation (LAS). The zero field cooled (ZFC) and field cooled (FC) magnetization measurements at 50 Oe showed increasing broadening of the ZFC curve with the higher Ni content. To calculate the average blocking temperature ((T(B a distribution of the blocking temperatures (T(B)) was assumed to initiate theoretical fittings and it was found to be increasing with the Ni concentration in the matrix.

High magnetic performance in Al‐substituted BaFe 12 O 19 by a wet chemical process

A wet chemical process has prepared Al-substituted barium ferrite nanoparticles BaFe11AlO19. Structural and magnetic properties of BaFe11AlO19 powers were characterized with an X-ray diffractometer, a vibrating sample magnetometer, and a Mössbauer spectroscopy. The results of X-ray diffraction measurements showed that the BaFe11AlO19 had an M-type hexagonal structure with lattice parameters a0=5.871, c0=23.190 Å and X-ray density ρx=5.194 g/cm3. The particle size was 37 nm. Mössbauer spectra of BaFe11AlO19 measured at various absorber temperatures of 15–800 K. Its Curie temperature is found to be 700 ± 5 K. The average hyperfine field Hhf(T) of the BaFe11AlO19 shows a temperature dependence of [Hhf(T)-Hhf(0)]/Hhf(0)=-0.34(T/TC)5/2-0.05(T/TC)3/2 for T/TC<0.7, indicative of spin-wave excitation. The anisotropy fields HA was 21.2 kOe and anisotropy constant K1 was 2.86 × 106 erg/cm3 at room temperature, as determined the law of approach to saturation (LAS). The saturation magnetization was 44.3 emu/g and the coercivity was 7.56 kOe. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

졸겔법에 의한 Ba-ferrite분말의 제조 및 자기적 특성 연구

BaFe<TEX>$_{12}$</TEX> O<TEX>$_{19}$</TEX> 분말을 sol-gel법을 이용하여 제조하였다. X-선 회절분석결과 hexagonal 결정구조를 갖으며 격자상수 a와 c는 a=5.822, c=23.215 <TEX>$\AA$</TEX>으로 분석되었다 뫼스바우어 분광기 실험을 통해 Curie온도는 780<TEX>$\pm$</TEX>3K 임을 확인할 수 있었으며, 4f<TEX>$_2$</TEX>, 2a. 4f<TEX>$_1$</TEX>, 12k, 2b의 5-site에 해당하는 각각의 이성질체이동값이 상온에서 0.26, 0.24, 0.15, 0.25, 0.24 mm/s로서 Fe<TEX>$^{3+}$</TEX> 의 상태로 존재함을 알 수 있었다. 접근의 법칙(Law of approach to saturation)에 의해 결정자기 이방성 에너지 H<TEX>$_{A}$</TEX> 와 결정자기 이방성 상수 <TEX>$K_1$</TEX>를 계산하였으며 95<TEX>$0^{\circ}C$</TEX>에서 열처리한 바륨페라이트의 경우 <TEX>$K_1$</TEX> = 2.5 <TEX>${\times}$</TEX> <TEX>$10^{6}erg/cm^3$</TEX> 그리고 H<TEX>$_{A}$</TEX> = 14 kOe 값을 가졌다. M-type hexagonal BaFe<TEX>$\sub$</TEX>12/O<TEX>$\sub$</TEX>19/ ferrite powder was prepared by sol-gel process. The M-type hexagonal structure with <TEX>${\alpha}$</TEX> = 5.882 and c = 23.215 <TEX>${\AA}$</TEX> and its Curie temperature T<TEX>$\sub$</TEX>C/ was determined 780<TEX>${\pm}$</TEX>3 K. The isomer shifts of ,4f<TEX>$_2$</TEX>, 2a. 4f<TEX>$_1$</TEX>, 12k, and 2b were indicated 0.26, 0.24, 0.15, 0.25, and 0.24 mm/s, therefore, the valence states of the Fe ions were ferric (Fe<TEX>$\^$</TEX>3+/). By the law of approach to saturation (LAS), the effective anisotropy field H<TEX>$\sub$</TEX>A/ and crystalline anisotropy constant K<TEX>$_1$</TEX> were estimated. The value of K<TEX>$_1$</TEX> and H<TEX>$\sub$</TEX>A/ were K<TEX>$_1$</TEX> = 2.5<TEX>${\times}$</TEX>10<TEX>$\^6/erg/cm^3$</TEX> and H<TEX>$\sub$</TEX>A/ = 14 kOe, respectively.

Preparation and Magnetic Properties of Fe0.7Co0.3–SiO2 Granular Alloy Solid

The Fe 0.7 Co 0.3 -SiO 2 granular alloy solid has been prepared using a sol-gel method, and investigated by X-ray diffraction (XRD), transmission electron microscopy (TEM) and vibrating sample magnetometer (VSM). The effective magnetic anisotropy K E has been measured by the law of approach to saturation (LATS). The evolution of the magnetic properties for the granular alloy solid during reducing is described and explained by means of particle size distribution and superparamagnetic behaviour. When the measuring temperature changes from 100 to 800 K, the variations of saturation magnetization, effective magnetic anisotropy and coercivity of the Fe 0.7 Co 0.3 -SiO 2 granular solid are much smaller than those of existing magnetic recording media. The Fe 0.7 Co 0.3 -SiO 2 granular alloy solid has a potential for application in high density magnetic recording media, which can be used in a wide temperature range.

Magnetic anisotropy and coercivity of ultrafine iron particles

Ultrafine iron particles are characterized by X-ray diffraction (XRD) and transmission electron microscopy (TEM). Using the law of approach to saturation (LATS), effective magnetic anisotropy is obtained at different temperatures. K E increases with the decrease of temperature, and decreases with the thickening of the surface oxide layer. The temperature dependence of coercivity has been investigated.

Studies on the magnetic viscosity and the magnetic anisotropy of γ-Fe 2 O 3 powders

O3 powders, acicular γ-Fe2O3, and CoFe–γ-Fe2O3 powders are prepared by different methods. Particle shapes and mean particle sizes of samples are determined by transmission electron microscopy (TEM). Magnetic parameters are measured by a vibrating sample magnetometer (VSM) at different temperatures. Effective magnetic anisotropy constants KE of granular γ-Fe2O3 powders at different temperatures are obtained by using the law of approach to saturation (LATS). KE values of acicular γ-Fe2O3 and CoFe–γ-Fe2O3 powders are measured by a magnetotorquemeter. It is found for the first time that the variation tendency of KE with temperature for granular γ-Fe2O3 is about the same as that of shape magnetic anisotropy Ksh. Fluctuation field Hf and activation volume Vf of samples are measured. A theoretical expression of Vf is derived. For granular γ-Fe2O3 powders, calculated activation volumes are consistent with experimental ones at different temperatures. But as for acicular γ-Fe2O3 powders, calculated activation volumes are larger than experimental ones. Experimental results show that magnetization reversal of granular γ-Fe2O3 at different temperatures is close to homogeneous rotation.

Studies on the Magnetic Anisotropy and the Coercivity of Granular γ-Fe2O3 Powders

The granular γ-Fe2O3 powders are prepared. The particle shapes and mean particle sizes of the samples are determined by Transmission Electron Microscopy (TEM). Using Extracting Sample Magnetometer (ESM) and Vibrating Sample Magnetometer (VSM), the magnetic parameters are measured at different temperatures. By the Law of Approach to Saturation (LATS), the effective magnetic anisotropy constants KE of granular γ-Fe2O3 powders at different temperatures are obtained. By using the mixed-coercivity model, a good explanation is given to the temperature dependence of the coercivity for granular γ-Fe2O3. It is found experimentally, for the first time, that the variation tendency of KE with temperature for granular γ-Fe2O3 is about the same as that of the shape magnetic anisotropy Ksh, and that the magnetization reversal process of granular γ-Fe2O3 is close to uniform rotation at different temperatures.

Correlation between the inhomogeneity and the magnetic anisotropy in polycrystalline ferromagnetic materials

The application of the law of approach to saturation (LAS) to a great variety of ferromagnetic materials gives as a result a general correlation between the inhomogeneity parameter A and the anisotropy field H A , of the form H A = A n ( n ≈ 1.4). Deviations of the data from this correlation are explained in terms of the metallurgical state of the material. The application of the LAS to mixed crystal series gives the concentration dependence of A( x) and H A( x). Unusually high H A values are explained by taking into account spin freezing effects. The increase of A( x) and H A( x) on approaching a critical concentration supports the appearance of mictomagnetism.