Angular dependence of coercivity of grains in nanocrystalline permanent magnets

In this paper magnetization remanence curves were studied for nanocrystalline Pr8Fe87B5, Pr12Fe82B6 and Pr15Fe77B8. Initially the sample was at remanence following saturation along z-axis. After rotating the magnet by 5n degrees （n=0, 1, ..., 18） a field H was applied along z-axis and then decreased to zero, and the remanence Jr^n was measured as a function of H. The curves were compared with those calculated based on the nucleation of reverse domain model and domain wall pinning model. The latter model succeeds in simulation much better than the former, and it is concluded that the magnetization reversal is dominated by domain wall pinning for all the samples. The nucleation mechanism contribution, while remains small, increases with the increase of Pr content.     

Microstructure of precipitation hardened cobalt rare earth permanent magnets

A transmission electron microscope study of several precipitation hardened cobalt rare earth magnets has been undertaken. The magnets were in peak aged condition and varied in the chemical composition. The studies reveal a fine cellular microstructure. The shape and size of cells depend on the heat treatment and alloying elements. The cell interiors consist of at least two plate-shaped 17:2 phases and are surrounded by a 5:1 boundary phase. The replacement of zirconium with hafnium does not alter the cellular morphology and also leads to a high coercivity. The coercive force is strongly influenced by the shape and size of the cellular structure as well as by the lattice misfit between the 5:1 and 17:2 phases. The influence of the microstructure on the coercivity is discussed.     

Angular dependence of the coercive field in sintered Fe77Nd15B8 magnets

The intrinsic nucleation and instability fields of uniaxial single domain particles are determined including the effects of the second anistropy constant and of oblique applied magnetic fields. The theoretical results for the angular dependences of the nucleation and pinning fields are compared with the angular dependence of the coercive field as measured for oriented sinter magnets of composition Fe₇₇Nd₁₅B₈. The experimental results are compatible with the assumption that at room temperature the coercive field in Fe₇₇Nd₁₅B₈ is determined by a nucleation mechanism.     

Coercivity of precipitation hardened cobalt rare earth 17:2 permanent magnets

The influence of the microstructure on the coercivity has been investigated by means of transmission electron microscopy. It is shown that a thin coherent (CoCu)₅Sm-cell boumdary phase, separating cells of 17:2-crystal structure, acts as a pinning centre for magnetic domain walls. The attractive interaction force is interpreted in terms of a micromagnetic theory for domain wall pinning. The coercive force is determined by the domain wall energy gradient and by the magnetoelastic coupling energy between domain wall stresses and lattice deformation strains. The calculated coercive force due to the lattice mismatch, originated by the cellular coherent precipitation structure, is comparable to the experimentally obtained values.     

Angular dependence of coercivity in Pr---Fe---B sintered magnets

Hysteresis loops were measured for varying angles of the applied field at different temperatures in oriented sintered magnets of compositions Fe₇₅Pr₁₇B₈ and Fe₅₃Pr₁₇B₃₀. While at elevated temperatures the coercive field increases monotonically with the angle of the applied field, a minimum in the angular dependence is found below room temperature. The temperature dependence of coercivity for the field applied parallel and with an angle of 45° to the alignment direction is well described by a nucleation model in the whole temperature range. The results are compared to Fe---Nd---B magnets, showing that the occurrence of a minimum in the angular dependence is related to the ratio of the experimental to the theoretical coercive fields.     

Rare earth permanent magnets prepared by hot deformation process

Hot deformation is one of the primary methods for fabricating anisotropic rare earth permanent magnets. Firstly,rapidly quenched powder flakes with a nanocrystal structure are condensed into fully dense isotropic precursors using the hot-pressing process. The prepared isotropic precursors are then hot-deformed to produce high-anisotropy uniaxial bulk rare earth permanent magnets and a highly textured structure is produced via this process. The resulting magnets possess many advantages such as near-net-shape, outstanding corrosion resistance, and ultrafine-grain structure. The influence of the preparation parameters utilized in the hot-pressing and deformation processes on the magnetic properties and microstructure of the permanent magnets are systemically summarized in this report. As a near-net-shape technique, the hot deformation process has notable advantages with regard to the production of irregular shapes, especially for radially oriented ringshaped magnets with high length-diameter ratios or thin walls. The difficulties associated with the fabrication of crack-free,homogeneous, and non-decentered ring-shaped magnets are substantially resolved through an emphasis on mold design,adjustment of deformation parameters, and application of theoretical simulation. Considering the characteristics of hotdeformed magnets which include grain shape and size, anisotropic distribution of intergranular phases, etc., investigation and improvement of the mechanical and electric properties, in addition to thermal stability, with the objective of improving the application of hot-deformed magnets or ring-shaped magnets, is of practical significance.     

Temperature dependence of the coercive force of deformed silicon iron crystals

The temperature dependence of the coercive force of deformed silicon iron (Fe-3.15 Si) crystals was studied. It was shown that the current theories relating coercive force to dislocation density do not explain changes observed in H_c. The latter were attributed to changes in the domain structure whose necessity was proved thermodynamically.     

Research on La–Co-substituted strontium ferrite magnets for high intrinsic coercive force

M-type strontium ferrites with substitution of Sr²⁺ by rare-earth La³⁺, and a little amount of Fe³⁺ by Co²⁺ according to the formula Sr_1−xLa_xFe_12−xCo_xO₁₉, are prepared by the ceramic process. Effects of the substituted amount of La³⁺ and Co²⁺ on structure and magnetic properties of Sr_1−xLa_xFe_12−xCo_xO₁₉ compounds have systematically been investigated by X-ray diffraction (XRD), vibrating sample magnetometer (VSM) and B–H hysteresis curve measurements. In our results, the suitable amount of La³⁺–Co²⁺ substitution may remarkably increase saturation magnetization. Intrinsic coercive force (H_cj) of Sr ferrite magnets is evidently increased without significant decrease in residual flux density (B_r) by La³⁺–Co²⁺ substitution.     

Optimizing magnetization orientation of permanent magnets for maximal gradient force

The force exercised on a permanent magnet (PM) in a nonuniform field (gradient force) is dependent on the magnetization orientation of the magnet. In this paper, it is shown theoretically that the gradient force is greatest when the magnetization through the magnet, or at least at its surface, is collinear with the external field. The formulae for calculating the force between an axis-symmetric optimal magnet and a coaxial axis-symmetric coil are presented. Using the finite element method (FEM), calculations of the magnetic field distribution of an optimal cylindrical magnet and some its approximations are performed. The forces between these magnets and a pancake coil are computed and compared. For a system consisting of a magnet with a height of 1 unit and a diameter of 2 units and magnetization invariant in field and an annular pancake coil with a diameter of 2.4 units, a thickness of 0.2 units, an inner diameter of 0.4 units and a distance from the magnet of 0.2 units, the force on the optimal magnet was 1.44 times greater than the force on an axially magnetized magnet of the same size and magnetization magnitude. The optimal magnetization may be approximated by magnetization inclined at a constant angle to the axis and by a combination of axially and radially magnetized sections. With magnetization at a constant angle to the axis in the axis plane, the force was greatest when the angle was about 45°, being 1.38-fold compared to the force on an axially magnetized magnet. When the magnet was composed of an axially magnetized cylindrical core and a radially magnetized outer ring, the force was greatest when the volume of the core was approximately equal to the volume of the ring, being 1.26-fold compared to the force on an axially magnetized magnet. The optimal magnet and its approximations also provided a reduced stray field. A short review of methods of the fabrication of permanent magnets (PMs) with a continuous variation of the magnetization orientation and with radial magnetization orientation is given.The results of this study can be used to design linear electromagnetic (micro)actuators.     

The dependence of coercivity on anisotropy field in sintered R-Fe-B permanent magnets

To investigate the dependence of intrinsic coercivity of R-Fe-B permanent magnets (R = rare earths) on the anistropy field of R₂Fe₁₄B, the temperature dependence of the intrinsic coercivity of Pr₁₅Fe₇₇B₈ and Nd₁₅Fe₇₇B₈ have been measured from 4.2 K to the Curie temperature of the magnets. Study of the interrelation between coercivity and anisotropy field by modifying the anisotropy field through atomic replacement in the rare earth sublattice has been also attempted in pseudobinary alloys (Nd_1−xR′_x)₁₅Fe₇₇B₈ with R′ = Tb, Dy and Er. A coercivity versus anisotropy field and composition. The R₁₅Fe₇₇B₈ has been constructed from the observed dependence of the coercivity on both temperature and composition. The role of boundary phases is discussed by comparing R₁₅Fe₇₇B₈ with SmCo₅ magnets.     

Frequency dependence of coercive properties

Significant frequency dependence of domain wall coercive field, due to the widening of the hysteresis loops, was observed based on AC hysteresis curve measurements in epitaxial magnetic garnet films. Domain wall oscillation measurements did not reveal any frequency dependence. The different results of the two measurement methods were analyzed, and the observed frequency dependence was attributed to the inertia of the moving domain walls. It was shown that the real value of the domain wall pinning field cannot be determined by AC hysteresis measurements, even in non-conducting materials.     

Concentration dependence of the Fe moments in rare earth iron compounds

A linear relationhip has been found between the hyperfine fields observed at the various Fe sites in rare earth iron compounds R_xFe_y and the relative number of near neighbour Fe atoms corresponding to these sites. From these results it is concluded that the concentration dependence of the magnitude of the Fe moments in these compounds is largely determined by the local environment.     

On the inclusion theory of coercive force

Randomly distributed spherical inclusions are considered in the derivation of an expression for the coercive force of a ferromagnetic single crystal, containing two magnetic domains separated by a single Bloch wall.     

The coercive field of sintered and melt-spun NdFeB magnets

The magnetic hysteresis loops have been investigated in the temperature range between 4.2 and 575 K for aligned sintered permanent magnets of nominal composition Nd₁₅Fe₇₇B₈ and for isotropic melt-spun ribbons of composition Nd₁₅Fe₇₆B₉. The measured temperature and field dependence of the coercive field is analysed within the framework of theoretical results for nucleation fields of the ideal Nd₂Fe₁₄B matrix and, of disturbed surface regions of Nd₂Fe₁₄B grains. Furthermore the pinning of domain walls at thin soft magnetic grain boundary phases is considered for the high temperature range. It is concluded that for both types of NdFeB magnets the relevant magnetic hardening mechanisms at lower temperatures are nucleation processes in magnetically inhomogeneous regions whereas at higher temperatures the pinning of domain walls at grain boundaries predominates. The critical temperature where the change of nucleation hardening to pinning hardening occurs depends sensitivity on the crystal anisotropy, the grain boundary microstructure and the macroscopic grain- and multi phase arrangements.     

Angular momentum and temperature dependence of fission barriers with a realistic force

Angular distributions and excitation functions were measured for 30 2⁺ resonances in the³⁹K(p,p₀) and₃₉K(p, α⁰) reactions. Partial reduced widths have been extracted for three proton channels; the relative signs of the reduced width amplitudes for two of these channels were also determined. Reduced widths are generally consistent with a Gaussian distribution for the reduced width amplitudes, but the amplitudes themselves are not. These data represent the first measurement of correlation coefficients in an entrance channel and suggest that the large correlations previously observed in exit channels are generic features of this mass region.     

Hysteresis and rotational hysteresis of textured polycrystalline magnets

A system of magnetic particles with uniaxial anisotropy is considered. The orientation of the particles is described by a distribution function, representing the texture by a single integer n. In each particle, two elementary processes of the magnetization reversal of the particles are taken into account, the coherent rotation of the magnetization and the pinning of domain walls. In the framework of this model the hysteresis loops including minor loops and virgin curves and the rotational hysteresis are computed, where arbitrarv angles between the texture axis and the external field are taken into consideration.     

Field dependence of the elastic constantsc 11 andc 33 of paramagnetic rare earth metals

An earlier theory for the magnetic field dependence of the elastic constantsc ₁₁ andc ₃₃ of paramagnets of hcp structure is extended in three different ways. First, the effect of the principal axial crystal-field term on the energy eigenstates of each magnetic ion is taken into account. Secondly, a field-dependent part of having its origin in the homogeneous strains is shown to yield a contribution toc ₁₁ andc ₃₃ similar in form to the other contributions. Finally, a contribution toc ₁₁ andc ₃₃ coming from the part of the magnetoelastic interaction linear in the strains evaluated in second order perturbation theory is calculated. This second order contribution is large and may predominate over the other contributions in certain cases. All three effects lead to correction terms to the earlier theory varying as (1/T). This temperature variation is too weak, however, to explain the apparent temperature dependence of the magnetoelastic coupling constants measured by Salama, Melcher and Donoho for terbium and by Kale, Donoho, Pinatti and Ferreira for dysprosium. The unexpectedly strong temperature dependence deduced from their measurements is discussed in the light of the present extensions to the theory, suspicion falling on the susceptibility functions _z (T) and (T) that enter the analysis of the data.     

Theory of thermal remagnetization of permanent magnets

A self-consistent mean-field theory explaining the thermal remagnetization (TR) of polycrystalline permanent magnets is given. The influence of the environment of a grain is treated by an inclusion approximation, relating the field inside the grain to the local field outside by means of an internal demagnetization factor n. For the switching fields and the fluctuations of the local fields around the mean field, Gaussian distributions of widths σ_s, and σ_f, respectively, are assumed. The isothermal hysteresis curve, the recoil curves, and the TR dependent on the model parameters n, σ_s, and σ_f are calculated. Furthermore, the influence of the initial temperature and the strong dependence of the TR on the demagnetization factor of the sample are studied, and it is shown that for reasonable parameter sets TR effects up to 100% are possible. The theoretical results correspond well with the experimental situation.     

Angular dependence of X-ray photoelectrons

The intensity of X-ray induced photoelectrons has been measured in function of the emission angle relative to the surface of solid samples. The angular