J. Trygg

Ab initio calculation of molecular field interactions in rare‐earth transition‐metal intermetallics (invited)

The interaction, KRM, between the rare‐earth 4f moment and the transition‐metal 3d moments in rare‐earth transition‐metal intermetallics is shown to depend upon the R‐5d moment, which is due to 3d–5d hybridization, and local 4f–5d exchange integrals. Both the R‐5d moment and KRM may be calculated ab initio from the local spin‐density approximation to density functional theory in self‐consistent energy‐band calculations with the localized 4f‐moments fixed at their Russel–Saunders values. Detailed examples are given for the RFe2 (R=Gd−Yb) series. The exchange integrals are similar to those entering into the density functional version of Stoner theory and their energy dependence must be treated carefully. The calculated local exchange integrals are shown to be related to the molecular fields derived from spin Hamiltonians, hence to the spin‐wave spectra. Reasonable agreement with values of the molecular fields extracted from inelastic neutron scattering and high field susceptibility measurements is obtained.

Density functional theory of molecular fields in R-M systems

Abstract In the local spin density approximation to the density functional theory the interaction, K RM , between the rare-earth 4f moment and local 4f-5d exchange integrals. Detailed examples are given for the RFe 2 (R=Gd-Yb) series. The calculated local exchange integrals are shown to be energy dependent and are then related to the molecular fields.

Ab initio calculation of the magnetism in GdFe12

Abstract Electronic structure calculations by means of the LMTO-ASA method have been performed for the hypothetical rare earth-transition metal compound GdFe 12 with the ThMn 12 structure. The R-4f magnetic moments were obtained from the standard Russel-Saunders scheme but the radial 4f spin density was otherwise part of the self-consistent band calculation. The influence of localized 4f magnetism upon the conduction band magnetism is found to give noticeable changes in the local moments of the iron. The presence of the 4f spin moment is found to induce a redistribution of the conduction electron spin moment between the rare earth and iron sites while the total conduction moment remains practically constant.

Theory of the Curie temperatures of the rare earth metals

Abstract The curie temperatures of the rare earth metals have been calculated ab initio using the local pin density approximation. The exchange splitting of the 5d-states depends upon local 4f-5d exchange integrals, κ 415d , which are calculated ab initio in the local spin density approximation. The Curie temperatures may then be obtained without use of adjustable parameters but are calculated to be too high by a factors of two to three if normal itinerant electron mean field theory is used. We have found that it is necessary allow for disordered local 5d moments above T c and to calculate the local susceptibility. When the local fluctuation contribution to the Landau Parameter, A , is included the Curie temperatures are actually reduced to below those measured.

ORBITAL PARAMAGNETISM IN METALLIC SYSTEMS WITH LARGE ANGULAR MOMENTA

We demonstrate that the field induced spin and orbital moments in paramagnetic metals in general are parallel, since the Zeeman energy overcomes the spin-orbit energy that is in favor of an antiparallel arrangement when the electronic shell is less than half-filled. In the early actinides, however, the spin-orbit energy becomes sufficiently strong to approach the border where the moments can couple antiparallel. This results in peculiar magnetic states for α-Pu and some uranium compounds, where the spin moments are antiparallel to the applied field and the magnetic response dominated by the orbital character, and consequently these systems display unusual spin densities and magnetic form factors.

Surface layer relaxation for Be(101̄0): theory

Abstract We predict an inwards surface relaxation of the (1010) surface of Be. The surface layer relaxes inwards with 25% of the inter planar distance, a rather large value. However, the corresponding change of nearest-neighbour interatomic distances is smaller, of the order 2–6%. We show that the relaxation is correlated with a pronounced surface state in the vicinity of the Fermi level. By following the inward relaxation of the surface layer, we show that the total energy is lowered mainly due to the one-particle energy. The most preferable termination of the Be(1010) surface is shown to be the so-called A termination. Also, the termination of the Be(0001) is investigated and we conclude that the hcp termination is preferable compared to the fcc termination.

Theoretical aspects of the 4f-localization at the surface of α-Ce

Electronic structure calculations, based on density functional theory, demonstrate that the surface of α-Ce is spin and orbitally polarized and very similar to that obtained from a calculation for bulk γ-Ce. In contrast, the lower lying layers do not deviate from characteristics associated with bulk α-Ce. These results imply that the surface of α-Ce is γ-like. This is consistent with photoemission experiments and the calculations provide a theoretical complement to the these data. In addition to confirming the picture given by the photoemission data, we demonstrate that it is only the topmost layer of Ce atoms which have electronic properties which deviate from the bulk. This in turn shows that the chemical bonding of the surface atoms is very different compared to the bulk atoms. Our finding that it is only the topmost layer of α-Ce which deviates from bulk behaviour can probably be verified experimentally.

Enhancement of orbital magnetism at surfaces: Co on Cu(100) (abstract)

By combining MCXD experiments with first principles electronic structure calculations, we demonstrate that the orbital contribution to magnetism can be strongly enhanced at surfaces. This effect is illustrated for Co grown on a Cu(100) surface. The MCXD measurements were performed using the SX 700 plane gratingmonochromators at BESSY. The Co films were evaporated and characterized in situ, for their cleanness, thickness (1.6–50 ML), and structural order. For a film thickness up to 2.2 ML, measurements of the ac MCXD susceptibility response at a fixed photon energy allowed one to measure the critical temperature,Tc, of the films and their critical properties were characterized in situ. For several samples the MCXD response as a function of the x‐ray incidence angle was investigated as well. This allows one to quantify and correct saturation effects that can occur in the measurements. Data were taken in a temperature range between 40 and 350 K, and for many samples measurements were performed at several reduced temperatures,T/Tc. The first layer of Co on the Cu(100) surface shows an enhanced orbital moment, in contrast to the subsequent layers where the orbital moment is bulklike. The lowering of the symmetry, the enhanced spin moment, and the increased value of the density of states at the Fermi level are factors that combine to give the observed enhancements.

Field-induced magnetism in actinide systems

Abstract We demonstrate that the field-induced spin and orbital moments in paramagnetic metals in general are parallel, regardless of the filling of the electronic shell. The early actinides, however, approach the border where the moments go antiparallel. This results in peculiar magnetic states for α-Pu and some uranium compounds, where the spin moments are antiparallel to the applied field and the magnetic response is dominated by the orbital contribution, and consequently these systems display unusual spin densities and magnetic form factors.

Giant surface layer relaxation for Be (1010)

Abstract We predict a giant surface relaxation of the (10 1 0) surface of Be. The surface layer relaxes inwards with 25%, which we show is due to a pronounced surface state close to the Fermi level. We also predict that the (10 1 0) surface at Be is terminated such that the surface has 8 nearest neighbours (A termination).