Effective Magnetic Anisotropy Constant Research Articles

Magnetostrictive strain-sensitivity synergy for laser-beam powder bed fusion processed Fe81Ga19 alloys by magnetic field annealing

Magnetostrictive Fe–Ga alloys have been demonstrated potentialities for numerous applications, whereas, suffering a tradeoff between large magnetostrictive strain and high sensitivity. Herein, bulk polycrystalline Fe81Ga19 alloys were prepared by laser-beam powder bed fusion (LPBF) and then annealed in magnetic field for manipulating the comprehensive magnetostrictive properties. Results indicate that <001> oriented grains are developed in the LPBF-prepared Fe81Ga19 alloys due to high temperature gradient. After magnetic field annealing (MFA), the magnetic domains within the alloys gradually transformed into well-arranged stripe domains, especially, flat and smooth 90° domains were established in the alloys annealed at 2600 ​Oe. As a result, the induced <001> orientation grains and 90° domains contributed to an improved effective magnetic anisotropy constant (57.053 ​kJ/m3), leading to an enhanced magnetostrictive strain of 92 ​ppm. Moreover, the MFA-treated alloys also displayed enhanced magnetostrictive sensitivity (0.097 ​ppm/Oe) owing to the smooth domain structures and low dislocation densities, demonstrating a fruitful strain-sensitivity synergy. In addition, good magnetostrictive dynamic response and enhanced compressive yield strength were also observed for the prepared alloys. This work demonstrates that LPBF and MFA might be an attractive strategy to resolve the tradeoff between strain and sensitivity, providing a basis for the preparation of high-performance magnetostrictive materials.

Bi-magnetic Mn3O4@Ni core–shell binary superparticles: Self-assembly preparation and magnetic behaviors

Binary superparticles formed by self-assembling two different types of nanoparticles may utilize the synergistic interactions and create advanced multifunctional materials. Bi-magnetic superparticles with a core–shell structure have unique properties due to their specific spatial configurations. Herein, we built Mn3O4@Ni core–shell binary superparticles via an emulsion self-assembly technique. The superparticles are generated with a spherical morphology, and have a typical average size of about 240 nm. By altering the ratio of the two magnetic nanoparticles, the thickness of Ni shells can be adjusted. Oleic acid ligands are crucial for the formation of core–shell structure. Magnetic analysis suggests that core–shell superparticles display dual-phase magnetic interactions, contrasting with the single-phase magnetic behaviors of commonly core–shell magnetic nanoparticles. The calculation on the effective magnetic anisotropy constants indicates that the presence of Ni shell layers reduces the dipole interactions among the Mn3O4 core particles. Due to the presence of Ni nanoparticle shells, the blocking temperature of Mn3O4 is reduced, while the Curie temperature of Mn3O4 is independent on Ni content. Tunable magnetic properties can be achieved by modulating the Ni nanoparticle shell thickness. This study offers insights for the development of core–shell superparticles with varied magnetic characteristics.

Exploring the impact of non-magnetic ion Mg2+ into M- type Ba0.5Ca0.5Fe12-xO19 (x = 0.0, 0.1 and 0.2) hexaferrites on structural, magnetic and magnetocaloric effect properties

The Mg substituted Ba-Ca Hexaferrites Ba0.5Ca0.5Fe12-xMgxO19 (BCFMO) (x = 0.0, 0.1 and 0.2) were prepared through the conventional ceramic technology. The microstructure, morphology, magnetic and magnetocaloric Effect (MCE) of all samples were investigated by XRD, SEM, EDX and BS1 and BS2 magnetometer. XRD analysis revealed the formation of Magnetoplumbite structure with P63/mmc space group and minor secondary phase R-3 m and having crystallites in the range of 121–108 nm. The XRD refinement indicates a preference for Mg2+ ions to occupy the octahedral 12k site. SEM analysis showed the presence of the hexagonal shape for all products. The saturation magnetization Ms decreases from 69.77 to 65.55 emu/g and the coercive field Hc increases from 1.29 to 3.54 kOe with the increase in Mg concentration. The increase of Hc with increasing Mg concentration is attributed to the reduction in crystallite sizes. Additionally, the magnetocrystalline anisotropy parameters (obtained by the "Law of Approach to Saturation method") such as the anisotropy field (Ha) and the effective magnetic anisotropy constant (Keff) were found to be 16.59–24.18 kOe and 5.15–6.94 105 emu/cm for x = 0.0–0.2, respectively.The MFC-MZFC curves for all compounds show a paramagnetic (PM) to ferromagnetic (FM) phase transition at the Curie Temperature TC. Doping with Mg2+ in BCFO lowers the Curie temperature TC down to T ∼700 K. The maximum entropy (-ΔSmmax) (x = 0.1) and the corresponding RCPmax (x = 0.2) at 5 T are found to be 1.80 J.kg-1.K-1 and 114.29 J.kg-1 respectively. The above results demontrate that the samples have great potential for permanent magnets and guide for the Magnetocaloric Effect (MCE) applications.

Effect of moringa oleifera with pure and Zn-doped Mn and Ni nanoferrites for hyperthermia applications

Nanoferrites like spinel manganese ferrite (MnFe2O4) and inverse spinel nickel ferrite (NiFe2O4) have an efficient heating deportment to the destruction of neoplasm. The incorporation of Moringa oleifera (MO) leaf extracts with magnetic nanoparticles as heat mediators is an effective approach for treating magnetic hyperthermia. This study investigated the potential heating behavior of bare, Zn-doped MnFe2O4 and NiFe2O4 nanoparticles (NPs) with Moringa oleifera leaf extracts as magnetic hyperthermia agents. High-resolution transmission electron microscopy showed the spherical-like morphology of MnFe2O4 NPs with no impurities in the EDX spectra. X-ray diffraction spectra confirmed the cubic spinel and inverse spinel structure for MnFe2O4 and NiFe2O4 NPs, respectively. Magnetic properties of the prepared nanoferrites exhibit low coercivity values (in the range of 13–18 Oe representing superparamagnetic behavior. Further, the binding energies of the prepared nanoferrites were revealed by X-ray photoelectron spectroscopy. The effective magnetic anisotropy constant (Keff) was calculated to be around 3.9–5.9 kJ/m3 by electron spin resonance. An increased specific surface area (120.69 m2/g) and wider porosity (17.053 nm) were observed for MnFe2O4/MO NPs through Brunauer-Emmett-Teller (BET) analysis. Thermal properties were investigated by measuring the effective specific absorption rate in an alternating magnetic field ranging from 23 to 31 * 10−9 W/g Oe2 Hz. Results indicated that the green synthesized MnFe2O4/MO NPs are promising agents for magnetic hyperthermia applications in cancer therapy.

Composite magnetic properties of cobalt ferrite nanoparticles embedded in bacterial nanocellulose of different porosity levels

A simple and novel strategy for tuning the macroporous structure of bacterial nanocellulose allows for embedding nanoparticles on the template. Here, cobalt ferrite nanoparticles were co-precipitated in-situ at two templates with different porosities. Different analytical techniques like SEM, XRD, TGA, and PPMS allow for characterizing the properties of the prepared magnetic nanocomposites. After eight months of aging at room conditions, lyophilized bacterial nanocellulose preserved the macroporous structure (porosity ∼ 46%). However, rehydration and re-lyophilization of the cellulose decrease the template porosity (∼8%). The cobalt ferrite nanoparticles, growth on high and low macroporous templates, were single-crystalline and microstrain-free. The nanoparticle's shape and mean size do not change with the porosity of the template, but the cluster size does. However, the differences in porosity on templates allow tuning the nanoparticle concentration and then its magnetic interactions (in high macroporous near 63%, and low about 43%) in the nanocomposites. Magnetic data confirm the influence of the template porosity on the magnetic particle concentration. The magnetic behavior as a temperature function (effective magnetic anisotropy constant, coercive force, and reduced remanence) is dependent on the template porosity. These dissimilarities were correlated with cluster size variations, where the differences in the aggregation modify the magnetic dipolar interactions among particles.

Hyperthermia of Magnetically Soft-Soft Core-Shell Ferrite Nanoparticles

Magnetically soft-soft MnFe2O4-Fe3O4 core-shell nanoparticles were synthesized through a seed-mediated method using the organometallic decomposition of metal acetyl acetonates. Two sets of core-shell nanoparticles (S1 and S2) of similar core sizes of 5.0 nm and different shell thicknesses (4.1 nm for S1 and 5.7 nm for S2) were obtained by changing the number of nucleating sites. Magnetic measurements were conducted on the nanoparticles at low and room temperatures to study the shell thickness and temperature dependence of the magnetic properties. Interestingly, both core-shell nanoparticles showed similar saturation magnetization, revealing the ineffective role of the shell thickness. In addition, the coercivity in both samples displayed similar temperature dependencies and magnitudes. Signatures of spin glass (SG) like behavior were observed from the field-cooled temperature-dependent magnetization measurements. It was suggested to be due to interface spin freezing. We observed a slight and non-monotonic temperature-dependent exchange bias in both samples with slightly higher values for S2. The effective magnetic anisotropy constant was calculated to be slightly larger in S2 than that in S1. The magnetothermal efficiency of the chitosan-coated nanoparticles was determined by measuring the specific absorption rate (SAR) under an alternating magnetic field (AMF) at 200-350 G field strengths and frequencies (495.25-167.30 kHz). The S2 nanoparticles displayed larger SAR values than the S1 nanoparticles at all field parameters. A maximum SAR value of 356.5 W/g was obtained for S2 at 495.25 kHz and 350 G for the 1 mg/mL nanoparticle concentration of ferrogel. We attributed this behavior to the larger interface SG regions in S2, which mediated the interaction between the core and shell and thus provided indirect exchange coupling between the core and shell phases. The SAR values of the core-shell nanoparticles roughly agreed with the predictions of the linear response theory. The concentration of the nanoparticles was found to affect heat conversion to a great extent. The in vitro treatment of the MDA-MB-231 human breast cancer cell line and HT-29 human colorectal cancer cell was conducted at selected frequencies and field strengths to evaluate the efficiency of the nanoparticles in killing cancer cells. The cellular cytotoxicity was estimated using flow cytometry and an MTT assay at 0 and 24 h after treatment with the AMF. The cells subjected to a 45 min treatment of the AMF (384.50 kHz and 350 G) showed a remarkable decrease in cell viability. The enhanced SAR values of the core-shell nanoparticles compared to the seeds with the most enhancement in S2 is an indication of the potential for tailoring nanoparticle structures and hence their magnetic properties for effective heat generation.

Evaluation of effective magnetic anisotropy constant of magnetic nanoparticles from coercive field of AC magnetization curve

Magnetic nanoparticles (MNPs) have been widely studied for use in biomedical application with the magnetic anisotropy constant K playing an important role in determining the performance. We estimated K near room temperature from the coercive field Hc of an AC magnetization (M–H) curve. First, we performed numerical simulation of the AC M–H curve of immobilized MNPs and clarified the dependencies of Hc on the MNP parameters and excitation conditions. Based on the simulation result, we obtained an analytical expression for Hc that was more general and included the previously obtained expression; and in addition, it could be applied to an MNP sample with a core-size distribution. Next, we measured the AC M–H curves of two commercial MNP samples and determined the dependencies of Hc on the amplitude and frequency of the excitation field. The dependencies agreed reasonably well with the analytical results. The K value was evaluated to obtain the best fit between the measured and analytical Hc, and the obtained K values were consistent with those estimated using other methods. The temperature dependence of K near room temperature was also determined. The present method will provide a useful tool to estimate the K value of MNPs.

Improved magnetic anisotropy of Co-based multilayer film with nitrogen dopant

Modulating the magnetic anisotropy of ferromagnetic thin films is crucial for constructing high-density and energy efficient magnetic memory devices. Ta/W(N)/Co/Pt multilayers were deposited on silicon substrates by magnetron sputtering at room temperature. The influences of N dopant on the magnetic anisotropy of the multilayers were investigated by preparing the sample with N incorporation. The results indicate that when sputtering W target with only argon gas (Ar), Ta/W/Co/Pt sample shows in-plane magnetic anisotropy (IMA). When sputtering W target at a different amount of N2 and Ar atmosphere, it can induce perpendicular magnetic anisotropy (PMA) for proper N-doped Ta/W(N)/Co/Pt sample. When the gas flow ratio of Ar:N2 is 16:6, the effective magnetic anisotropy constant reach its maximum value of 1.68 × 105 J·m−3, which enhanced by about 400% than our past works (annealing treatment is necessary to induce PMA in Pt/Co/MgO system). X-ray diffraction (XRD) and X-ray reflection (XRR) results demonstrate that N dopants can effectively promote the formation of β-W phase and reduce the roughness of W(N)/Co interface, which are beneficial for PMA. X-ray electron spectroscopy (XPS) analysis reveals that N doping redistributes Co charges, nitrogen ions participate in electron allocation of Co and attract some electrons of Co to form orbital hybridization between Co 3d and N 2p. This may be another important reason for the PMA formation.

Robust perpendicular magnetic anisotropy of Co3Sn2S2 phase in sulfur deficient sputtered thin films

Perpendicular magnetic anisotropy (PMA) in magnetic thin films is a fundamental key feature in the design of spintronic devices. As one of magnetic Weyl semimetals, ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ has been studied for its large anomalous Hall effect (AHE), uniaxial crystalline magnetic anisotropy, and half metallicity. In this study, we investigated the effect of off-stoichiometric composition on the PMA and AHE of ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{x}$ thin films fabricated by the sputtering technique. The prepared thin films have off-stoichiometric S compositions $x$ of 1.54 (S poor) and 3.27 (S rich) as well as the nearly stoichiometric one of 2.02. In addition to the ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ phase, the segregated Co metal is found to contribute to the measured magnetization in the S-poor and S-rich films. The coercive field of perpendicular magnetization in all the films is much larger than that in the ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ bulk crystals despite the fact that effective perpendicular magnetic anisotropy constants (${K}_{\mathrm{u}}^{\mathrm{eff}}$) between the prepared films are significantly different. In addition, the ${K}_{\mathrm{u}}^{\mathrm{eff}}$ values of two samples with $x=2.02$ and 2.22 are comparable to those of the bulk crystals. In contrast to the isotropic magnetization behavior in the S-rich film, the S-poor film holds the PMA feature. This result means that the PMA is more robust in the S-poor film than in the S-rich film. For the electrical transport properties, a large tangent of Hall angle of about 0.2 is observed for both the nearly stoichiometric and the S-poor films. This large tangent of Hall angle demonstrates that the Weyl feature of ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ phase is well maintained even in the S-poor thin films as well as the nearly stoichiometric films although the amount of Co segregation in both S-poor and S-rich films is similar. Our findings on the influence of off-stoichiometry on the PMA and AHE are beneficial to design magnetic devices incorporated with the Weyl features of ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$.

Perpendicular magnetic anisotropy and its electrical control in FeNiB ultrathin films

We study the perpendicular magnetic anisotropy in (Fe100−xNix)80B20 (FeNiB) films with various Ni contents. Perpendicularly magnetized films are achieved when the Ni content is in the range of 30 at. %–70 at. %. An effective perpendicular magnetic anisotropy (PMA) constant of 1.1× 105 J/m3 is achieved for the (Fe50Ni50)80B20 film. We also fabricate magnetic tunnel junction devices containing FeNiB films, and electrical measurements show that a tunneling magnetoresistance ratio of more than 20% can be achieved for devices having an orthogonal magnetization configuration. The PMA of the FeNiB film clearly changes by varying the bias voltage applied along the FeNiB/MgO junction, and a voltage-controlled magnetic anisotropy (VCMA) efficiency of over 30 fJ/Vm is demonstrated. From systematic investigations, there is no clear correlation between PMA and VCMA efficiency in the FeNiB/MgO junction. These experimental results should facilitate the development of energy-efficient magnetic random-access memory.

Investigation of Magnetic Properties of Magnetic Poly (glycidyl methacrylate) Microspheres: Experimental and Theoretical

Biocompatible magnetic poly (glycidyl methacrylate) microsphere is a novel nanocomposite with a myriad of promising bioapplications. Investigation of their characteristics by experimental analysis methods has also been carried out in the past. However, a survey of the magnetic anisotropy constant has not been mentioned and the influence of the poly (glycidyl methacrylate) polymer matrix on the Fe3O4 magnetite nanoparticles embedded inside has also not been discussed. Moreover, the accurate characterization of the magnetite nanoparticle size distribution remains challenging. In this paper, we present an effective approach was used to solve these problems. First of all, we combine both experiment and theory to estimate the effective magnetic anisotropy constant. Besides that, we implement an accurate method to determine magnetite nanoparticle size distribution in the magnetic poly (glycidyl methacrylate) microspheres composite nanomaterial.

The effect of temperature on parameters of hyperfine interactions and spatial spin-modulated structure in multiferroic BiFeO3

A detailed study of the temperature-dependent evolution of the hyperfine interaction parameters and spatial spin-modulated structure in multiferroic BiFeO3 has been carried out by 57Fe Mössbauer spectroscopy in a wide temperature range, including the temperature of the magnetic phase transition. Temperature dependences of the hyperfine magnetic field distributions, isotropic and anisotropic contributions to hyperfine magnetic fields, quadrupole shift and the anharmonicity parameter were measured. A change in the sign of the effective magnetic anisotropy constant was detected at a temperature T ≈ 330 K. At this temperature, the magnetic anisotropy changes from the “easy axis” to the “easy plane” type.

High heating efficiency of interactive cobalt ferrite nanoparticles

Cobalt ferrite nanoparticles (CFNPs) are emerging as a potential candidate for biomedical applications, such as magnetic hyperthermia therapy (MHT), due to their high saturation magnetisation (M S) and effective magnetic anisotropy constant (K eff) at the nanoscale. For MHT, heating efficiency depends considerably on applied AC magnetic field, particle diameter, and inter-particle interaction. Our study is aimed at developing a superparamagnetic nanosystem based on CFNPs with enhanced specific absorption rate (SAR) for advanced MHT. The CFNPs were synthesised using thermal decomposition of organometallic precursors. Transmission electron microscopy reveals a narrow size distribution of the CFNPs, with average particle sizes of 8 and 11 nm. Magnetic measurements showed high values of M S (~70 emu g−1) and K eff (2–3 × 106 erg cm−3). The ferromagnetic behaviour and strong interaction between particles at room temperature are also observed. Large SAR values of the CFNPs are achieved, which are superior to those reported previously in the literature. The high heating efficiencies of the present CFNPs make them a promising candidate for advanced MHT.

Magnetocrystalline and Surface Anisotropy in CoFe2O4 Nanoparticles.

The effect of the annealing temperature Tann on the magnetic properties of cobalt ferrite nanoparticles embedded in an amorphous silica matrix (CoFe2O4/SiO2), synthesized by a sol-gel auto-combustion method, was investigated by magnetization and AC susceptibility measurements. For samples with 15% w/w nanoparticle concentration, the particle size increases from ~2.5 to ~7 nm, increasing Tann from 700 to 900 °C. The effective magnetic anisotropy constant (Keff) increases with decreasing Tann, due to the increase in the surface contribution. For a 5% w/w sample annealed at 900 °C, Keff is much larger (1.7 × 106 J/m3) than that of the 15% w/w sample (7.5 × 105 J/m3) annealed at 700 °C and showing comparable particle size. This indicates that the effect of the annealing temperature on the anisotropy is not only the control of the particle size but also on the core structure (i.e., cation distribution between the two spinel sublattices and degree of spin canting), strongly affecting the magnetocrystalline anisotropy. The results provide evidence that the magnetic anisotropy comes from a complex balance between core and surface contributions that can be controlled by thermal treatments.

Estimation of the effective magnetic anisotropy constant of multi-core based magnetic nanoparticles from the temperature dependence of the coercive field

We estimated the effective magnetic anisotropy constant K of magnetic nanoparticles (MNPs) from the temperature dependence of the coercive field Hc of the M–H curve for use in biosensing applications. For this purpose, a previous analytical expression for Hc was extended so that it can be applied to nanoparticles with a size distribution. Using the extended expression for Hc, we estimated the K value of multi-core based MNP sample that consists of crystalline aggregates of elementary particles. We prepared three MNP samples. One is Resovist, in which elementary particles and aggregates are mixed. The Resovist sample was magnetically divided into two fractions called MS1 and MS3, which included mainly aggregates and elementary particles, respectively. We discuss the K value of elementary particles and aggregates from the comparison among the three samples. It is suggested that the K value of the aggregates is much smaller than that of the elementary particles. The temperature dependence of K of the aggregates is also discussed.

Interfacial Perpendicular Magnetic Anisotropy in Magnetic Tunnel Junctions Comprising CoFeB with FeNiSiB Layers

Controlling ferromagnetic thickness (t) and properties such as saturation magnetization (Ms) and effective magnetic anisotropy constant (Keff) has been regarded as critical for the performance of magnetic tunnel junctions (MTJs) with interfacial perpendicular magnetic anisotropy. Here, we report the effects of hybridizing a CoFeB layer with a FeNiSiB layer as part of a magnetic free layer structure. We deposited thin film stacks by magnetron sputtering on Si wafers with thermal oxides and carried out post-deposition heat treatment at 300 °C for 1 h in a vacuum under a magnetic field. We found that Ms and Keff could be tuned by adding a layer of amorphous FeNiSiB. While the Ms and Keff values were modified, the tunneling magnetoresistance (TMR) ratios of the MTJs were maintained, even though the CoFeB thickness was decreased by half. Moreover, an asymmetric bias voltage dependence of TMR was suppressed in the MTJs with FeNiSiB/CoFeB hybrid free layers due to improvements in the interface quality between the CoFeB/MgO interfaces.

Effect of reaction temperature on electrical and magnetic properties of chemically synthesized MnS nanocrystals

In the present work, MnS nanocrystals have been synthesized using a wet chemical technique with three different precursor reaction temperatures in the range of 55 °C–75 °C. The high precision LCR measuring instrument was used to study the dielectric and electrical properties of the MnS nanocrystals in terms of complex dielectric constant, complex impedance, complex electric modulus, and AC electrical conductivity. The effects of grains and grain boundaries on the dielectric relaxation and the electrical conduction mechanism of the material have been investigated with the frequency (50 Hz–5 MHz) of the applied field at different temperatures (323 K–473 K). The dielectric measurements have confirmed the presence of dipolar and interfacial polarization in the structure. The dielectric constant and loss tangent were found to decrease with the increasing reaction temperature. The complex impedance and the electric modulus investigation revealed the presence of a non-Debye type of relaxation in the samples. The Cole-Cole plot and the conductivity studies have confirmed a typical NTCR behavior in the as-synthesized MnS nanocrystals. The activation energy calculated from the Arrhenius equation was found to be 0.27 eV, 0.34 eV, and 0.38 eV for the samples synthesized at 55 °C, 65 °C and 75 °C respectively. VSM measurements revealed that the saturation magnetization increase and coercivity decrease with the increasing reaction temperature. Furthermore, the effective magnetic anisotropy constant, the particle volume, and the relaxation time of the MnS nanocrystals were estimated. The magnetic measurements confirmed that all the samples exhibit paramagnetic behavior.

Effect of bilayer repeats on magnetic properties of Au-buffered Co/Ni multilayers with perpendicular magnetic anisotropy

Abstract The effect of bilayer repeats (N) on the static and dynamic magnetic properties of Co/Ni multilayers was investigated. The effective perpendicular magnetic anisotropy constant of multilayers drops from 1.08 × 10 6 erg/cm3 to 0.78 × 10 6 erg/cm3 with N increasing from 5 to 11. For Co/Ni multilayers with N ≤ 7 , sharp magnetization switching was observed. In contrast, Co/Ni multilayers with N ≥ 9 have a long tail in the hysteresis loop. Ferromagnetic resonance measurements show that intrinsic Gilbert damping changes from 0.021 to 0.016 with increase in N and is inversely proportional to N. This study provides a deep understanding and effective control of magnetic properties of Co/Ni multilayers for spintronics devices.

Structural and magnetic properties of Gd–Zn substituted M-type Ba–Sr hexaferrites by sol-gel auto-combustion method

This work is report on Gd–Zn substituted M-type Ba–Sr hexaferrites with Ba0.5Sr0.5-xGdxFe12.0-xZnxO19 (0.0 ≤ x ≤ 0.4) by sol-gel auto-combustion method. X-ray diffractometer (XRD), Fourier transformer infrared (FTIR) spectroscopy, scanning electron microscopy (SEM), X-ray Photoelectron Spectroscopy (XPS) and Quantum Design measurement system (SQUID) were used to characterize M-type Ba–Sr hexaferrites. The results of X-ray patterns showed that the single M-type hexaferrite phase can be obtained when x = 0.00–0.20, however the impurity phase (α-Fe2O3) was observed for the hexaferrites with Gd–Zn content (x) ≥ 0.30. FT-IR frequency bands in the range (581–592) cm−1 and (431–442) cm−1 corresponded to the formation of tetrahedral and octahedral clusters of metal oxides in the hexaferrites, respectively. XPS survey showed that hexagonal crystal structure was formed completely, which was correlated closely with the results of XRD patterns and FT-IR spectra. SEM revealed the shape of the hexagonal plate. Measurements of the magnetization versus the field M(H) of Ba0.5Sr0.5-xGdxFe12.0-xZnxO19 (0.0 ≤ x ≤ 0.4) hexaferrites were conducted at 5 and 300 K. Zero field cooling (ZFC) and field cooled (FC) measurement data did not show blocking temperature peak, indicating the ferrimagnetic behavior of prepared hexaferrites. Moreover, at low temperatures a spin glass behavior was observed. The squareness ratio (Mr/Ms) indicated the uniaxial anisotropy for various hexaferrites. The deduced values of saturation magnetization (Ms), the magneton number (nB) and the effective magnetic anisotropy constant (Keff) decreased, whereas the values of the anisotropy fields (Ha) and the coercive field (Hc) increased with increasing Gd–Zn content at both 5 and 300 K.

Calculating temperature-dependent properties of Nd2Fe14B permanent magnets by atomistic spin model simulations

Temperature-dependent magnetic properties of Nd$_2$Fe$_{14}$B permanent magnets, i.e., saturation magnetization $M_\text{s}(T)$, effective magnetic anisotropy constants $K_i^\text{eff}(T)$ ($i=1,2,3$), domain wall width $\delta_w(T)$, and exchange stiffness constant $A_\text{e}(T)$, are calculated by using \textit{ab-initio} informed atomistic spin model simulations. We construct the atomistic spin model Hamiltonian for Nd$_2$Fe$_{14}$B by using the Heisenberg exchange of Fe$-$Fe and Fe$-$Nd atomic pairs, the uniaxial single-ion anisotropy of Fe atoms, and the crystal-field energy of Nd ions which is approximately expanded into an energy formula featured by second, fourth, and sixth-order phenomenological anisotropy constants. After applying a temperature rescaling strategy, we show that the calculated Curie temperature, spin-reorientation phenomenon, $M_\text{s}(T)$, $\delta_w(T)$, and $K_i^\text{eff}(T)$ agree well with the experimental results. $A_\text{e}(T)$ is estimated through a general continuum description of the domain wall profile by mapping atomistic magnetic moments to the macroscopic magnetization. $A_\text{e}$ is found to decrease more slowly than $K_1^\text{eff}$ with increasing temperature, and approximately scale with normalized magnetization as $A_\text{e}(T) \sim m^{1.2}$. This work provokes a scale bridge between \textit{ab-initio} calculations and temperature-dependent micromagnetic simulations of Nd-Fe-B permanent magnets.