T. Ukai

Ferromagnetic Anisotropy Energies of Ni and Fe Metals –Band Model–

The ferromagnetic anisotropy energies of Ni and Fe metals are calculated based on the differences between the crystal energies with the different directions of the spontaneous magnetization. These crystal energies are calculated by taking into account the variations of the spin-orbit interaction and the magnitude of the spontaneous magnetization, on the basis of the energy bands of ferromagnetic Ni and Fe metals, where the redistribution of the conduction electrons for each direction of the spontaneous magnetization is also taken into account. The obtained results are in agreement with the experimental results. The doubly degenerate energy levels in the energy bands, intersecting the Fermi level, produce the dominant contributions to the anisotropy energy. In Ni metal the temperature dependence of the anisotropy constants can be explained by the temperature variation of the Fermi level, and for Fe metal it can be explained in consideration of the decrease of the exchange splitting.

Ferromagnetic Anisotropy Energies of Co Metal and Co Alloys –Band Model–

The ferromagnetic anisotropy energy of H. C. P. Co metal is calculated by the use of the energy bands of ferromagnetic Co metal given by Ishida. The doubly degenerate energy levels along [0001] axis on the Brillouin zone produce the contributions to make c -axis to be the easy axis. The other doubly degenerate energy levels and the approaching energy levels produce the contributions to make c -plane to be the easy direction. It is shown that at 0 K, c -axis is the easy axis, and when the temperature is raised and the exchange splitting decreases, c -plane becomes the easy direction. The anisotropy energies of Co alloys including 1 at% of Fe and Ni metal are also calculated. The obtained results are in agreement with the experimental results.

Anisotropy energies for Y2Fe14B and Nd2Fe14B

The approximate d bands for Y2Fe14B and Nd2Fe14B are formulated by Deegan’s prescription and the formulas of Slater and Koster. The electronic energies of these crystals with the spin directions [001], [100], [101], and [110] are calculated by Gilat and Raubenheimer’s method. The experimental result of the anisotropy energy for Y2Fe14B is analyzed with use of these calculated results by introducing the differences of the number of d electrons for these four states. In Nd2Fe14B the same differences of the number of d electrons are introduced and the contribution to the anisotropy energy due to 4f electrons is deduced. This contribution is analyzed by the use of the crystalline field potential (the localized model) and the band model with d‐f elements derived by Lendi. The obtained results are considered to be reasonable.

SDW state for Cr metal and dilute Cr‐V and Cr‐Mn alloys

The approximate d bands for Cr metal in antiferromagnetic SDW state are formulated in the tight binding approximation. It is shown that the antiferromagnetic SDW state with the periodicity extending to 21 times the lattice constant has the minimum electronic energy by using these energy bands. The d bands for Cr metal in SDW state including the spin‐orbit interaction are also formulated, and stable spin configuration is investigated by comparing the free energy calculated by these energy bands. It is found that the longitudinal SDW state is stable in low temperatures, and spin flip takes place between 100 and 150 K near 4.428 d electrons per atom. Some inspection is done about the various magnetic states for dilute Cr‐V and Cr‐Mn alloys, and good explanation is obtained for the experimental results.

Ferromagnetic Anisotropy Energy of Double Hexagonal Co-Fe Alloy

The energy bands for d electrons in the double hexagonal structure are calculated in the tight binding approximation, including the spinorbit interaction. The anisotropy constants for the double hexagonal Co-Fe alloy are calculated on the basis of these energy bands. The easy axis is in the c -plane. These obtained results are in agreement with the experimental results. It is shown that the energy bands for the double hexagonal structure there exist the double degenerate energy levels along [0001] axis in the Brillouin zone but these energy levels do not intersect the Fermi level in this alloy, and some approaching energy levels apart from the [0001] axis intersect the Fermi level and produce the contributions to make the easy axis to be in the c -plane.

On the orbital moment of Co in YCo5

Abstract The experimental result of the orbital and spin moments for Co in YCo 5 is analyzed by the use of the approximate d bands for YCo 5 . The calculation of the anistropy constants K u1 and K u2 is worked out. Finally, the contributions to the anistropy constants due to 3d bands of Co I , those of Co II , those of Co I and Co II , and 3d and 4d bands of Co I , Co II and Y are discussed.

Calculation of anisotropy constants

Abstract Accurate calculation is made for the anistropy constants for Ni, Co and Fe metals by using Gilat and Raubenheimers method in d band model. The obtained result is in agreement with the experimental result. Additionally, the anisotropy constants for Ni-based alloys, Co-based alloys and Gd metal are calculated.

Anisotropy energy of Y2Fe14B, Y2Co14B, Y2Fe14−xCoxB, and La2Co14B

The anisotropy energies of Y2Fe14B, Y2Co14B, Y2Fe14−xCoxB, and La2Co14B are discussed with reference to the band model. The energy bands exclusive and inclusive of the p bands in B are formulated in consideration of the spin‐orbit interaction and exchange splitting. The anisotropy constant K1 is estimated through the difference between the calculated electronic energies with the magnetization parallel to [001] and [100]. In Y2Fe14B, the calculated K1 is much the same as the experimental result, and in Y2Co14B, it agrees with the experimental result. In Y2Fe14−xCoxB, the calculated K1 inclusive of the p bands in B is much the same as the experimental result. Finally, the anisotropy energy of La2Co14B is discussed by taking into account the 4f bands just above the Fermi level.The anisotropy energies of Y{sub 2}Fe{sub 14}B, Y{sub 2}Co{sub 14}B, Y{sub 2}Fe{sub 14{minus}{ital x}}Co{sub {ital x}}B, and La{sub 2}Co{sub 14}B are discussed with reference to the band model. The energy bands exclusive and inclusive of the {ital p} bands in B are formulated in consideration of the spin-orbit interaction and exchange splitting. The anisotropy constant {ital K}{sub 1} is estimated through the difference between the calculated electronic energies with the magnetization parallel to (001) and (100). In Y{sub 2}Fe{sub 14}B, the calculated {ital K}{sub 1} is much the same as the experimental result, and in Y{sub 2}Co{sub 14}B, it agrees with the experimental result. In Y{sub 2}Fe{sub 14{minus}{ital x}}Co{sub {ital x}}B, the calculated {ital K}{sub 1} inclusive of the {ital p} bands in B is much the same as the experimental result. Finally, the anisotropy energy of La{sub 2}Co{sub 14}B is discussed by taking into account the 4{ital f} bands just above the Fermi level.

A band theory of magnetic structure of α-and β-manganese

Abstract Based on the Hubbard-like Hamiltonian, a tight binding calculation was made to determine both the magnetic moments and their directions on 29 atoms in the symmetric unit cell of the antiferromagnetic α-Mn metal. The densities of the local magnetic moments and the local densities of states were also calculated.

On the magnetic structure of noncollinear γ‐Fe70Mn30

The approximate d bands for a noncollinear γ‐FeMn alloy are formulated by using Deegan’s method and the formulas of Slater and Koster, and by taking into account the exchange interaction terms to produce the multi‐spin‐density‐wave state. The electronic energies for the noncollinear γ‐Fe70Mn30 alloy with the spin directions parallel to [100], [110], and [111] are calculated and the anisotropy energy is determined. It is seen that the state with the spin direction [111] becomes the lowest and the multi‐spin‐density‐wave state is realized in it. For other noncollinear γ‐FeMn alloys some discussions are given on the magnetic structure for them. Additionally, the anisotropy energies for noncollinear and collinear γ‐FeMn alloys are discussed in detail.