The magnetocrystalline anisotropy energy (MAE) for fcc Ni and bcc Fe is calculated as the difference of single particle energy eigenvalue sums using a tight-binding model. For nickel we predict a MAE of -0.15 eV and the wrong easy axis, for iron we find a MAE of -0.7 eV with the easy axis in agreement with experiment. Our results compare favorably with previously reported first-principles calculations based on density functional theory and the local spin density approximation. The inclusion of an orbital polarization correction improves the magnitude of the MAE for iron, but fails to bring the result for nickel closer to the experimental value. The outstanding feature of our calculations is the careful handling of the necessary Brillouin zone integrals. Linear interpolation schemes and methods based on Fermi surface smearing were used and analyzed. An alternative method of calculating the MAE based on the torque on a magnetic moment centered on an atom is found to be equivalent to the calculation of the MAE in terms of energy differences. / Graduation date: 1999

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