Value Of Anisotropy Constant Research Articles

Magnetocrystalline anisotropy of iron within limitation of standard band approach

An attempt to get more insight into the ab initio calculations of magnetic anisotropy in ferromagnetic 3 d transition metals is presented. The calculations are performed for bulk crystalline iron. We use the tight-binding Slater-Koster (SK) interpolation scheme for the self-consistent spin-polarized electronic band structure of the LMTO-ASA method. Electronic structure effects produced by the spin-orbit (SO) interaction are studied within the perturbation theory up to fourth-order terms. There is only one adjustable parameter which describes SO coupling. All other parameters in this paper are calculated from first principles. The discrepancy between calculated and experimental values of anisotropy constants is significantly reduced by taking into account the fourth-order corrections alone. The widely discussed numerical precision of the total energy calculations and the local density approximation of the density functional formalism seem to be important. However these are not the only possible deficiencies of the general theoretical framework which are essential for handling the problem of magnetocrystalline anisotropy in itinerant magnets. In this context the possibility of an hitherto unexploited approach to the calculation of the magnetocrystalline anisotropy is indicated.

Magnetic anisotropy investigation in (2 1 0)-oriented Bi-substituted magnetic garnets

Different methods of describing growth- and stress-induced anisotropy are analysed. Two-parameter and quadratic models (generally five parameters) are discussed. A (2 1 0)-oriented epitaxial garnet film was chosen as an example of this analysis. Magnetic anisotropy constants were analyzed using both the traditional FMR technique and a magneto-optical anisometer based on the Faraday effect. The two-parameter model turned out to be incorrect for anisotropy description in such films. Observed differences between the experimental values of anisotropy constants from FMR and magneto-optical methods may be connected to magnetostriction influence on the resonance frequency.

The effect of nonmagnetic inclusions on the easy direction of gadolinium

It is shown that the presence of nonmagnetic inclusions in gadolinium crystals has a significant effect on the first anisotropy constant K1, leading to a variation of easy direction with inclusion content. The observed concentration of hexagonal oxide platelets is sufficient to explain differences in the values of anisotropy constants and easy direction reported by various workers. The authors conclude that the most reliable measurements are those of Corner and Tanner (1976) and Smith et al. (1977) on characterised, high-purity gadolinium crystals produced by solid state electrotransport.

On the Magnetocrystalline Anisotropy of Iron Selenide Fe7Se8

Magnetization measurements along the a -and c -axes of a single crystal of a compound Fe 7 Se 8 have been carried out in magnetic fields up to 92 kOe over the temperature range 4.2° to 300°K, together with magnetic torque measurements on the b c -plane up to 9 kOe. The results of magnetization measurements along the c -axis lead to the magnetocrystalline anisotropy energy of the form, E (θ)=- K 0 |cos θ|+ K 3 cos 2 θ+ K 4 cos 4 θ, the last term being for minor correction. In this expression θ is an angle between magnetization and field direction. The measured values of anisotropy constants K 0 and K 3 at 290°, 77° and 4.2°K are K 0 =0.3×10 6 , 32×10 6 and 65×10 6 erg/cc and K 3 =2.5×10 6 , 18×10 6 and 35×10 6 erg/cc, respectively. From the magnetocrystalline energy mentioned above, it can be shown that the magnetic moment takes a conical distribution around the c -axis at low temperatures. The results of torque measurements on the b c -plane is reproduced by assuming a triad crystal domain structure.

Some Properties of Supported Smallα−Fe2O3Particles Determined with the Mössbauer Effect

M\"ossbauer spectra of ${\mathrm{Fe}}^{57}$ in $\ensuremath{\alpha}\ensuremath{-}{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$ have been measured as a function of particle size and temperature. Bulk $\ensuremath{\alpha}\ensuremath{-}{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$ shows a change in the sign of the quadrupole interaction in going through the Morin transition temperature, 263\ifmmode^\circ\else\textdegree\fi{}K. Analyses of the spectra show that the magnetization vector is in the $c$ plane above the transition temperature and parallel to the $c$ axis below it. In contrast, finely divided $\ensuremath{\alpha}\ensuremath{-}{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$ particles, supported on a high-area silica, do not undergo a Morin transition. The spectra show that the magnetization vector remains perpendicular to the $c$ axis at least down to 10\ifmmode^\circ\else\textdegree\fi{}K. It is evident that the spins are pinned by the surface in small particles. When the particle size is less than 135 \AA{}, the room-temperature spectrum consists only of a quadrupole-split center line corresponding to superparamagnetic $\ensuremath{\alpha}\ensuremath{-}{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$. As the particle size is gradually increased, a 6-line hyperfine spectrum of increasing intensity appears. This transition from superparamagnetic to ferromagnetic behavior, coupled with a measurement of the average particle size by x-ray line broadening, leads to a calculated value of the crystalline anisotropy constant in the $c$ plane of (4.7\ifmmode\pm\else\textpm\fi{}1.1)\ifmmode\times\else\texttimes\fi{}${10}^{4}$ erg per ${\mathrm{cm}}^{3}$. A sample with an average particle size just below that required for ferromagnetic behavior at room temperature, when cooled, displays an increasing fraction of ferromagnetic material as the temperature is decreased. From these data the particle size distribution of the $\ensuremath{\alpha}\ensuremath{-}{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$ is determined. In addition, these data are used to calculate an independent value of the anisotropy constant of (4.1\ifmmode\pm\else\textpm\fi{}1.1)\ifmmode\times\else\texttimes\fi{}${10}^{4}$ erg per ${\mathrm{cm}}^{3}$. Careful measurements on the series of samples with varying particle sizes show that the quadrupole splitting increases from the bulk value of 0.42 mm ${\mathrm{sec}}^{\ensuremath{-}1}$ to a value of 0.98 mm ${\mathrm{sec}}^{\ensuremath{-}1}$ for particles with an undetermined average size of less than 100 \AA{}.

Experimental Determination of the Anisotropy Distribution in Ferromagnetic Powders

A technique to determine the anisotropy distribution in a ferromagnetic powder consisting of uniaxial particles has been developed. This technique can be used for samples with randomly oriented particles as well as with oriented samples. In principle it eliminates incoherent magnetization reversals which led to errors in previous methods. It involves saturating the material in a magnetic field and then making torque measurements at an angle several degrees away from the saturating direction. In these measurements the torque on the specimen as a function of magnetic field is recorded as the field is cycled from zero to a specified field and then reduced to zero. This cycling procedure is continued, gradually increasing the maximum applied field upon subsequent cycles until the magnetic field exceeds the highest anisotropy field of the particles in the distribution. For elongated γ-Fe2O3 particles this technique gives length-to-width distributions which approach those observed by the electron microscope technique. These results are compared to those obtained by remanence measurements which give smaller values of anisotropy constants, indicating the importance of incoherent magnetization reversals, when the remanence is acquired.