We present a first-principles theory of the variation of magnetic anisotropy, K, with temperature, T, in metallic ferromagnets. It is based on relativistic electronic structure theory and calculation of magnetic torque. Thermally induced local moment magnetic fluctuations are described within the relativistic generalization of the disordered local moment theory from which the T dependence of the magnetization, m, is found. We apply the theory to a uniaxial magnetic material with tetragonal crystal symmetry, L1 0-ordered FePd, and find its uniaxial K consistent with a magnetic easy axis perpendicular to the Fe/ Pd layers for all m and proportional to m 2 for a broad range of values of m. This is the same trend that we have previously found in L1 0-ordered FePt and which agrees with experiment. We also study a magnetically soft cubic magnet, the Fe 50 Pt 50 solid solution, and find that its small magnetic anisotropy constant K 1 rapidly diminishes from 8 eV to zero. K 1 evolves from being proportional to m 7 at low T to m 4 near the Curie temperature. The accounts of both the tetragonal and cubic itinerant electron magnets differ from those extracted from single ion anisotropy models and instead receive clear interpretations in terms of two ion anisotropic exchange.

Using a first-principles, relativistic electronic structure theory of finite temperature metallic magnetism, we investigate the variation of magnetic anisotropy K with magnetization M in metallic ferromagnets. We apply the theory to the high uniaxial K material, L1(0)-ordered FePt, and find its magnetic easy axis perpendicular to the Fe/Pt layers for all M and K to be proportional to M2 for a broad range of values of M. For small M, near the Curie temperature, the calculations pick out the easy axis for the onset of magnetic order. Our ab initio results for this important magnetic material agree well with recent experimental measurements, whereas the single-ion anisotropy model fails to give the correct qualitative behavior.

From the basis of ab initio electronic structure calculations which include the effects of thermally excited magnetic fluctuations, we predict Mn-stabilized cubic zirconia to be ferromagnetic above 500 K. We find this material, which is well known both as an imitation diamond and as a catalyst, to be half-metallic with the majority and minority spin Mn impurity states lying in zirconia's wide gap. The Mn concentration can exceed 40%. The high-Tc ferromagnetism is robust to oxygen vacancy defects and to how the Mn impurities are distributed on the Zr fcc sublattice. We propose this ceramic as a promising future spintronics material.

The magnetocrystalline anisotropy (MCA) of bulk and thick films of FePt is calculated from a 'first-principles' theory. The starting point is a description from electronic density functional theory for systems of interacting electrons moving in lattices of ions. Relativistic effects such as spin-orbit coupling are included. FePt readily transforms into a CuAu-type (L1 0) ordered phase and this coincides with the material's high anisotropy. Here we describe how to calculate the MCA of a partially ordered alloy and to extract its dependence on the long range chemical order parameter η. We present calculations of the MCA of FePt as a function of η and find excellent agreement with the experimental data of Okamoto et al (2002 Phys. Rev. B 66 024413) and others with respect to the magnetic easy axis, the magnitude of the MCA and its trend with decreasing η. We also study the paramagnetic phase of the ordered alloy using the 'disordered local moment' picture of metallic magnetism at finite temperatures. We calculate a Curie temperature of 935 K in reasonable agreement with experiment (710 K) and find the easy axis for the onset of ferromagnetic order to coincide with the magnetic easy axis found at low temperatures.

The electron energy-loss near-edge structure ͑ELNES͒ at the O K edge has been studied in yttria-stabilized zirconia ͑YSZ͒. The electronic structure of YSZ for compositions between 3 and 15 mol % Y 2 O 3 has been computed using a pseudopotential-based technique to calculate the local relaxations near the O vacancies. The results showed phase transition from the tetragonal to cubic YSZ at 10 mol % of Y 2 O 3 , reproducing experimental observations. Using the relaxed defect geometry, calculation of the ELNES was carried out using the full-potential linear muffin-tin orbital method. The results show very good agreement with the experimental O K-edge signal, demonstrating the power of using ELNES to probe the stabilization mechanism in doped metal oxides.

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