The heavy rare earth elements crystallize into hexagonally close packed (h.c.p.) structures and share a common outer electronic configuration, differing only in the number of 4f electrons they have. These chemically inert 4f electrons set up localized magnetic moments, which are coupled via an indirect exchange interaction involving the conduction electrons. This leads to the formation of a wide variety of magnetic structures, the periodicities of which are often incommensurate with the underlying crystal lattice. Such incommensurate ordering is associated with a 'webbed' topology of the momentum space surface separating the occupied and unoccupied electron states (the Fermi surface). The shape of this surface-and hence the magnetic structure-for the heavy rare earth elements is known to depend on the ratio of the interplanar spacing c and the interatomic, intraplanar spacing a of the h.c.p. lattice. A theoretical understanding of this problem is, however, far from complete. Here, using gadolinium as a prototype for all the heavy rare earth elements, we generate a unified magnetic phase diagram, which unequivocally links the magnetic structures of the heavy rare earths to their lattice parameters. In addition to verifying the importance of the c/a ratio, we find that the atomic unit cell volume plays a separate, distinct role in determining the magnetic properties: we show that the trend from ferromagnetism to incommensurate ordering as atomic number increases is connected to the concomitant decrease in unit cell volume. This volume decrease occurs because of the so-called lanthanide contraction, where the addition of electrons to the poorly shielding 4f orbitals leads to an increase in effective nuclear charge and, correspondingly, a decrease in ionic radii.

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.

We describe an ab initio theory of finite temperature magnetism in strongly-correlated electron systems. The formalism is based on spin density functional theory, with a self-interaction corrected local spin density approximation (SIC-LSDA). The self-interaction correction is implemented locally, within the KKR multiplescattering method. Thermally induced magnetic fluctuations are treated using a meanfield 'disordered local moment' (DLM) approach and at no stage is there a fitting to an effective Heisenberg model. We apply the theory to the 3d transition metal oxides, where our calculations reproduce the experimental ordering tendencies, as well as the qualitative trend in ordering temperatures. We find a large insulating gap in the paramagnetic state which hardly changes with the onset of magnetic order.