M. S. S. Brooks

3d-5d band magnetism in rare earth-transition metal intermetallics: total and partial magnetic moments of the RFe2 (R=Gd-Yb) Laves phase compounds

The magnetic moments of the RFe2 (R=Gd-Yb) Laves phase compounds have been calculated. Agreement with published measured values for single crystals is excellent. The R 4f magnetic moments were obtained from the standard Russell-Saunders scheme but the radial 4f spin density was otherwise part of the self-consistent density functional calculation. The influence of the localized 4f magnetism upon the conduction band magnetism is examined in detail and exchange interactions extracted. The site- and angular-momentum-resolved contributions to the total conduction bands magnetic moments are calculated and shown to obey an approximate sum rule which conserves the total conduction band moment, despite the change of 4f moment, across the series.

3d-5d band magnetism in rare earth transition metal intermetallics: LuFe2

Self-consistent energy band calculations for LuFe2 are reported. LuFe2 is found to order magnetically according to the Stoner criterion and the calculated moment is 2.85 mu B/formula unit in agreement with experiment. Spin-orbit coupling was included in the calculation and the spin and induced orbital contributions to the moment at the Fe site also found to be in agreement with experiment. The total moment is calculated to include a contribution of -0.41 mu B at the Lu site, which as yet has not been observed. The mechanism responsible for the ferrimagnetic alignment of the 3d and 5d spin densities is investigated in detail, and the Lu-5d moment related to 3d-5d hybridisation.

Rare-earth transition-metal intermetallics

Abstract The combination of itinerant transition metal (M = Fe) and localized rare-earth (R = Gd-Y) magnetism in RFe 2 compounds has been investigated in self-consistent energy band calculations. The computed and measured total moments are in good agreement for all cases where single crystal data are available. We find, however, that there is a significant contribution to the moment from the R-5d partial moments coupled antiparallel to the Fe-3d moment which results from 3d–5d hybridization. The R-4f moments interact with the conduction band system solely by local exchange interactions, which are calculated ab initio from density functional theory. A sum rule for the total 3d + 5d moment is shown to be obeyed and the effective ferrimagnetic exchange interaction between rare-earth and transition-metal moments is discussed. Finally, the spin wave spectra of these materials are evaluated in terms of a model arising from these calculations.

Chemical bonding and magnetism in 3d-5f intermetallics

The authors report self-consistent energy band calculations for UFe2 and UCo2 in four approximations: both semi-relativistic and fully relativistic for the paramagnetic ground states; both spin-polarised and spin-polarised with spin-orbit coupling included self consistently for the ferromagnetic ground state of UFe2. They compare ab initio calculated and measured lattice constants, bulk moduli, linear specific heat coefficients, pressure dependence of the magnetic moment and magnetic form factor. UCo2 is found to be an enhanced paramagnet and UFe2 an itinerant ferromagnet with a magnetic moment due mainly to the iron moments. However, the magnetism on the uranium sites is unusual in that they calculate both spin and orbital contributions to the moment that are large, antiparallel and almost equal.

Measurement of anisotropy constant in US with polarized neutrons (invited)

Uranium compounds can have an anisotropy that is considerably greater than that found in rare‐earth compounds. Early estimates of K1 in ferromagnetic US (Tc = 178 K), for example, were that K1 ≳ 108 erg/cm3. We have re‐examined this cubic material and determined K1 in the range of reduced moment (μ/μ0) from 0.1 < (μ/μ0) < 0.7 and find that it varies logarithmically over almost three orders of magnitude. The highest measured K1 is 2 × 108 erg/cm3 at (μ/μ0) = 0.7, but an extrapolation, which we anticipate on arguments of symmetry, to (μ/μ0)=1, (T=0 K) gives K1 ∼ 1010 erg/cm3, some 20 times more than found in TbFe2 at 0 K. The method we have used is with polarized neutrons. Because the neutron interaction with the magnetic moment is vectorial in nature we can determine individually the magnitude and direction of the moment in an applied field. In many cases this method has advantages over conventional methods, especially when the anisotropy is large.

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.

Relativistic effects in heavy elements

Abstract Relativistic effects upon the virial theorem and equation of state derived from variational calculations are described. In particular, it is shown that what is required in the calculation of the equation of state is the change in the sum of the one electron energies with Wigner-Seitz radius. Methods of obtaining the one electron energies are described and the differences between them explained. Various examples of the importance of relativistic effects are given: (1) the changes in the volumes of the elemental metals; (2) the difference between the volumes of the α and δ phases of Pu metal; (3) orbital magnetism in energy bands; (4) magnetic anisotropy in narrow band materials; (5) possible new semi-conductors.

Calculated cohesive properties of lanthanide and lanthanide-like actinide elements

Abstract Cohesive energies of divalent and trivalent lanthanide and lanthanide-like actinide metals are calculated. The stable valence state of the lanthanide metals is determined and found to agree with experiment. The heavier actinides are examined in the same manner and several elements at the end of the series are found to be divalent in their metallic state. Suggestions that lawrencium is a simple sp metal are refuted. Instead it is found that this element is the first member of the 6d transition series, in analogy with the position of lutetium relative to the 5d series. This conclusion is confirmed by calculations of the cohesive energy for kurchatovium. The crystal structure stability is investigated for the elements from americium to californium and rather good agreement with high pressure experiments is obtained.

Orbital magnetism in energy bands

Abstract Recent work on orbital magnetism in itinerant magnets is reviewed. It is shown that such an orbital contribution to the magnetic moment is especially important for magnets involving actinide systems and that it is of a size comparable to the spin contribution. In particular, the results for the AnFe 2 (An = U, Np and Pu) compounds are discussed and their anomalous properties, as compared to corresponding standard rare-earth systems, are explained in terms of 3d–5f hybridization and orbital polarization within the 5f band manifold. As an introduction to the AnFe 2 systems we discuss CeFe 2 for which we predict 4f band magnetism in addition to the normal iron magnetism. It is most significant that, in agreement with experiment, the size of the iron moment is found to be reduced in comparison to its value in rare-earth magnets like YFe 2 . The α-γ transition in Ce metal is also treated and the calculated volume collapse agrees with experiment. Related calculations for Pr and Nd are also briefly discussed. Finally, the orbital contribution to the magnetism in Fe, Co and Ni is considered, and its maximum for Co is explained as the result of the HCP crystal structure.

Magnetism of RFe2 compounds

The combination of itinerant transition metal (M=Fe) and localized rare earth (R=Gd‐Yb) magnetism in RFe2 compounds has been investigated in self‐consistent energy band calculations. The computed and measured total moments are in good agreement. We find, however, that there is a significant contribution to the moment from the R‐5d partial moments coupled antiparallel to the Fe‐3d moment which results from 3d‐5d hybridization. The R‐4f moments interact with the conduction band system solely by local exchange interactions which are calculated ab initio from density functional theory. A sum rule for the total 3d+5d moment is shown to be obeyed and an expression for the effective ferrimagnetic exchange interaction between 3d and 4f electrons is derived.