Local density calculations with self-interaction-corrected core states are reported for the transition-metal ferromagnets Fe, Co, and Ni. The hyperfine field matrix elements have been computed. Good agreement with measurements is obtained for Co, whereas for Fe and Ni the discrepancy between local density theory and experiment remains also in the self-interaction-corrected calculation. Possible changes in the core states due to relativistic exchange corrections are also discussed and found to be of minor importance.

A Reply to the Comment by Gernot Stollhoff, Andrzej Oleś, and Volker Heine.Received 21 April 1995DOI:https://doi.org/10.1103/PhysRevLett.76.856©1996 American Physical Society

Relationship between the Coulomb integral U and the stoner parameter I - Reply (vol 76, pg 856, 1996)

A theoretical and experimental study of the electronic and magnetic structure of Fe2P1-xSix is performed. A hexagonal-orthorhombic crystal structure transition occurs with increasing Si substitution. The latter crystal structure is extremely complex with six inequivalent Fe sites. The magnetic moments, as obtained by our electronic structure calculations, vary substantially between the different sites, from 0.7 mu B to 2.6 mu B. The latter value is one of the largest Fe moments ever found. The estimated hyperfine fields are in fair agreement with Mossbauer data. For this compound it is found that the hyperfine field cannot be assumed to be proportional to the spin magnetic moment when the majority spin band is saturated. This is explained in terms of a hybridization mechanism between the Fe 3d and 4s states, which results in a 4s valence electron contribution that may be large and of either sign.

First principles electronic structure calculations for the itinerant 5f ferromagnet US are presented. At ambient conditions the computed moments agree well with neutron data. As a function of pressure, this magnetization is found to be relatively stable down to volume compressions well over 10%. On further increase in pressure the moment decreases drastically.

A Mössbauer spectroscopic study of orthorhombic Fe2P1−xSi x withx ≤ 0.35 was performed. A large spread in magnetic hyperfine fields was found at the six Fe positions ranging from 10–26 T at 4.2 K. Small rearrangements in the crystal positions as compared to the hexagonal phase cause large changes in the magnetic field. Large changes in Fe magnetic moments have also been obtained in a spin-polarized LMTO band calculation performed on orthorhombic Fe2P as compared to a similar calculation of hexagonal Fe2P.

A systematic ab initio electronic-structure study of the late transition-metal--cerium compounds forming in the cubic Laves-phase structure, and of those cerium compounds (${\mathrm{CeRh}}_{3}$, ${\mathrm{CePd}}_{3}$, and ${\mathrm{CePt}}_{3}$) forming in the ${\mathrm{AuCu}}_{3}$ structure, is performed using the local-density approximation. Magnetic and cohesive properties are shown to be crucially dependent on the treatment of the cerium 4f electron. In all cases investigated (except for the palladium and platinum compounds) our calculations favor a picture with delocalized 4f electrons. Photoemission data for the strongly 4f-4d hybridized ${\mathrm{CeRh}}_{3}$ system is discussed and shown to have a substantial itinerant 4f character. Calculations for some fictitious ${\mathrm{AuCu}}_{3}$ compounds Ce${\mathit{A}}_{3}$, where A is a 4d element preceding Rh or a 5d element preceding Pt, are also presented. This is done in order to elucidate how the position of the cerium 4f band, relative to the Fermi level, changes when such a series of compounds is traversed. The hybridization between the cerium 4f states and the transition-metal d states is shown to vary in a systematic way, which, together with the filling of the transition-metal d band, can explain the position of the 4f band. The calculated 4f position is compared with data from inverse photoemission spectroscopy. Especially the anomalous position of the 4${\mathit{f}}^{1}$ peak, previously found in bremsstrahlung isochromat spectroscopy experiments for ${\mathrm{CeRh}}_{3}$, is found to fit into the calculated trend in a consistent manner.

We summarize recent attempts to calculate the contributions to the spin and orbital magnetization densities of transition metals and actinide compounds. Emphasis is placed on the relative signs of both the local and the diffuse spin moments and the orbital contributions to the moments. Examples include Fe, Co, Ni, actinide transition metal intermetallic compounds and uranium NaCl-type monochalcogenides.

Photoemission spectra and scanning tunneling microscopy (STM) images of the clean Pt3Ti(111) surface are presented. Grazing-emission core-level spectra show that the topmost layer is pure platinum, modified compared with the Pt(111) surface. The Pt 4f levels at the surface are shifted 0.4 eV toward the Fermi level relative to bulk Pt3Ti while the Pt 4f and Ti 2p levels in the bulk are shifted 0.4 and 1.3 eV to higher binding energy relative to pure bulk platinum and titanium, respectively, Tunneling measurements show a surface with only metallic atoms and a small p(2 x 2) buckling. Our observations of molecularly adsorbed CO are not compatible with metallic titanium atoms at the surface and the STM data thus indirectly confirm that only platinum atoms are present in the topmost layer. Linear muffintin-orbital calculations of the bulk band structure and valence-band photoemission spectra reveal highly hybridized electron states between the Pt d and Ti d levels. The calculations give a minor charge transfer from Ti to Pt, 0.37 electrons per Ti atom, but the large core-level shifts reflect the stability of the alloy and the response to the excitation rather than the amount of charge transfer. The observed segregation of platinum to the surface and the altered electronic structure of the topmost layer, due to interaction with the underlying alloy, are in full agreement with earlier conclusions based on low-energy electron-diffraction measurements and on the chemical properties of the surface.

The theoretical analysis of the contributions to the spin and orbital magnetization densities of transition metals, rare earths and actinides is described. Emphasis is placed upon the relative signs of both the local and diffuse spin moments and the orbital contributions to the moments. Examples include Fe, Co, Ni, rare earth and actinide intermetallic compounds and uranium NaCl-type monochalcogenides.

A theory for orbital splitting is derived from a statistical Hartree-Fock (HF) treatment of open shell interactions. In a scaling procedure, where the HF spinpolarization matrix is replaced by the corresponding local spin density matrix, an expression for the orbital splitting is derived which is well suited for implementation in the standard ab initio calculational scheme. Results for Co metal as well as for the itinerant 5f ferromagnet US is presented, which are in good agreement with experiment.

Self-consistent electronic-structure calculations have been performed for the ferromagnetic Laves-phase compound GdCo2 and GdCo2H4. Experimentally, the magnetic moment for GdCo2 is Only a little reduced when the hydride is formed, but the Curie temperature drops from T(c) = 395 K to T(c) = 90 K in the hydride. Using parameters that are calculated ab initio (the susceptibility and the exchange coupling) the Curie temperature is calculated from a simple model and found to agree with experiment for GdCo2. For the hydride, the reduction in T(c) is accounted for, but we calculate the Curie temperature to be slightly too large (157 K). By simply scaling the calculated T(c) for GdCo2 and GdCo2H4 with the de Gennes factor, the Curie temperature for the other heavy rare-earth cobalt compounds and their hydrides are estimated.

We consider how magnetism in itinerant intermetallic systems arises within the local spin density approximation (LSDA) through the concepts of local exchange and hybridization. The delicate interplay between these two mechanisms explains trends in ground state magnetic properties. This is exemplified with the AFe2 (A = 5d transition metal atom) and AnFe2 (An = actinide) series of intermetallic compounds.

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, κ415d, 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 Tc 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.

In the local spin density approximation to the density functional theory the interaction,KRM, between the rare-earth 4f moment and local 4f-5d exchange integrals. Detailed examples are given for the RFe2 (R=Gd-Yb) series. The calculated local exchange integrals are shown to be energy dependent and are then related to the molecular fields.

A semiquantitative discussion of the energy difference between a localized f configuration and the formation of an f band state is given. Density-functional calculations are used to estimate these energy terms for the early actinide metals Pa, U, Np, Pu, and Am. It is concluded that the onset of localization (the critical U/W, U=intra-atomic Coulomb repulsion, W=bandwidth) depends strongly on band filling and I/W (I=Stoner parameter). For an early f metal the critical U/W is almost independent of I/W and much larger than unity.

The electronic structure of CeRh3 Was studied by photoemission and bremsstrahlung isochromate spectroscopy (BIS). An analysis of the spectra, taken at different temperatures, on the basis of the Anderson single-impurity model leads to considerable inconsistencies that mark the limits of applicability of the model. On the other hand, the BIS spectrum of CeRh3 can be well described by the results of a local-density-approximation band-structure calculation. These findings confirm a bandlike character of the 4f states in strongly hybridized Ce systems.

A semiquantitative discussion of the energy difference between a localized f configuration and the formation of an f band state is given. Density-functional calculations are used to estimate these energy terms for the early actinide metals Pa, U, Np, Pu, and Am. It is concluded that the onset of localization (the critical U/W, U=intra-atomic Coulomb repulsion, W=bandwidth) depends strongly on band filling and I/W (I=Stoner parameter). For an early f metal the critical U/W is almost independent of I/W and much larger than unity.