The electric field gradient in heavy rare earth metals

Estimates of the electric field gradient in heavy rare earth metals have been evaluated from experimental hyperfine interaction data. In addition, the magnetic hyperfine fields are analyzed. In the metals the effective radial integrals 〈r ^?3〉_4f of the magnetic and quadrupole hyperfine interaction are reduced at most by 10% compared with the free ion values. The electric field gradients due to the crystalline field have been found to be 200 times larger than those predicted from point charge calculations. This antishielding effect can be explained by an enhanced conduction electron density at the interstitial sites and an increase of the Sternheimer factor γ_∞ in the metallic environment.     

Electric field gradient in pure hexagonal transition metals

Using a general calculation of the nuclear quadrupole interaction in non-cubic metals which was presented in a previous paper, this article gives an interpretation of experimental data dealing with signs and temperature dependence of the electric field gradient in 3d(Sc, Ti), 4d(Y, Zr, Tc, Ru) and 5d (Hf, Re, Os) transition hexagonal close-packed metals.     

Temperature dependence studies of the electric field gradient at cadmium impurities in heavy rare earth metals

Several of the rare earth metals (Gd, Tb, Dy, Ho and Er) containing¹¹¹Cd impurities have been studied by the method of time differential perturbed angular correlations (TDPAC) to study electric field gradients. Experiments have been made over a temperature range in which no magnetic interactions are expected. We have observed general correlation patterns whose shapes are temperature dependent. We suggest this provides evidence of a reversible temperature dependent strain or distortion near the impurity atom.Supported in part by the US Energy and Research Development Administration under grant #E(11-1)-2184.     

Revised model for 5d electrons in the heavy rare earth metals

A revised version of a recently published model for 5d electrons in the ferromagnetic state of the heavy rare earth metals is described. The model involves the broadening of local 5d states into overlapping bands with individual widthsW. In the new approach it is assumed that the local 5d wave functions lie at some point between those for atomic 4f _n 5d 6s ² configurations and those calculated for such configurations subject to the restriction that the 4f shell is kept with its moment rigidly fixed in some given direction. The admixture of non-aligned 4f states as in the atom lowers the local energy, but it also lowers the 5d bandwidth due to misfit of the 4f states which occur with and without the presence of a 5d electron. This second effect raises the energy of the low lying states in the band. The best local states are determined by minimising the total electronic energy of the system, using approximations which are most suitable for 4f shells with large excitation energies. Bandwidths are found by fitting the observed saturation magnetic moments in Gd and Tm, and satisfyW?1 eV.     

Polarization of conduction electrons and hyperfine field on impurities in ferromagnetic metals

The temperature dependence of the polarization of conduction electrons and that of the magnetization are shown not to coincide in the presence of a sharp structure in the density of states in ferromagnetic metals. This effect can explain the experimentally observed temperature anomalies of the hyperfine field on impurities in ferromagnetic matrices.     

Additional crystalline electric field potentials for heavy rare earth metals

A derivation is given of additional crystalline potential energy terms due to the interaction of conduction electrons with the localised electrons of ions in pure heavy rare earth metals. Explicit expressions for theA ₄ ⁰ andA ₆ ⁰ coefficients are given to supplement those ofA ₂ ⁰ andA ₆ ⁶ given in a recent paper. Additional contributions which arise from the unfilledf shells of the neighbours of any particular ion under consideration, are derived but shown to be of such a magnitude that, for most purposes, they can be neglected. The use of Slater orbitals in calculating enhancement factors forA ₄ ⁰ andA ₆ ⁰ is discussed with particular reference to those contributions which involve resonance amplitudes and mainly involve thef orbitals.     

Models for the heavy rare earth metals and (rare earth) Fe2 compounds involving 5d and 6s electrons

A model involving 5d electrons is introduced to explain the differences between the observed saturation moments in the heavy rare earth metals and those of the corresponding tripositive ions. Atomic 5d states, whose energies are determined by 4f–5d and spin-orbit interactions, are assumed to be broadened into partly overlapping bands with individual widths of the order of 1 eV. The 5d electrons produce negative contributions to the hyperfine fields but positive or near zero contributions to the magnetic moments. It is postulated that the 5d electrons are transferred from the rare earth ions to those of the iron in the (Rare Earth) Fe₂ compounds. This leads to increases in the magnetic hyperfine fields because the negative 5d contributions are lost, but in detailed application of the model increases in the 6s contributions also play a large part. Published energy level and wave function analyses for atomic Gd, Tb, Dy, Er and Tm are used in order to apply the theory to these materials.     

The influence off-d interactions on effective crystal fields seen by 4f electrons in the heavy rare earth metals

A method is given for determination of the influence off-d interactions on the effective crystal field seen by 4f shells in a previously published model for 5d electrons in the heavy rare earth metals. With the ratios of effectivei-th order fields felt by 4f shells to those acting on 5d electrons denoted by multiplication factorsM _i , it is shown thatM ₂ lies between ?2 and ?6 for the five metals Tb, Dy, Ho, Er and Tm. The factorM ₄ is also negative for all the heavy rare earths except Tm. It is larger in magnitude thanM ₂ , and varies quite sharply from one metal to another.     

The effect of orthogonalization on the conduction electron electric field gradient in noncubic metals

By orthogonalizing the conduction electron states of model potential theory to the core electron states, the local conduction electron electric field gradient (EFG) is expressed by a model wave function EFG enhanced by a factor correlated with the Sternheimer antishielding factor.     

Spin properties of conduction electrons in the noble metals

The g-factors of the conduction electrons have been determined for various orientations of magnetic field in Cu, Ag and Au crystals from de Haas-van Alphen oscillation amplitudes at temperatures high enough to avoid magnetic interaction.     

Exchange in rare earth metals and intermetallic compounds

Analytical expressions of the isotropic and the anisotropic exchange integrals in rare earth (RE) metals and intermetallic compounds are derived using the augmented-plane-wave (APW) formalism. Numerical results for DyZn indicate that the d electrons contribute predominantly to both isotropic and anisotropic exchange at most points on the Fermi surface.     

The entropies of liquid rare earth metals

The entropies of the liquid rare earths are explained using hypotheses about the electronic structure which closely parallel some believed to be correct for the corresponding solids.     

Electric field gradient on Fe,Sc and Os impurities in hexagonal transition metals

The localized electronic contribution to the electronic field gradient in transition dilute systems is calculated for Fe, Sc and Os impurities in hexagonal metals of the 3d (Sc, Ti) 4d (Y, Zr, Ru) and 5d (Hf, Re, Os) series. Both sign and temperature dependence of experimental values of quadrupole interactions are correctly interpreted within the model hypotheses.     

Electric field gradient studies in SnSe

The EFG in IV–VI compound semiconductor SnSe was studied using two hyperfine interaction techniques, namely, TDPAC and Mössbauer spectroscopy. The EFG in this material increases sharply up to 300 K and thereafter at higher temperatures it gets saturated. However, the conductivity increases steadily at all the temperatures. The conductivity curve has two slopes. The first portion is due to the population of shallow Cd acceptor levels. Thus, in SnSe also the variation of the EFG with temperature is complex, as in other medium-gap semiconductors.

     

Hyperfine interaction of rare earth impurities in ferromagnetic metals

The present knowledge concerning rare earth impurities implanted in iron and nickel is reviewed. New Mössbauer spectra on the isotopes¹⁶¹Dy,¹⁶⁶Er and¹⁶⁹Tm are presented. In the case of¹⁶¹DyFe and¹⁶¹DyNi both the annealing behaviour and the temperature dependence have been studied. It is shown that in almost all cases about half of the rare earth impurities end up in substitutional sites, whereas the other part probably is associated with vacancies. The temperature dependence for these systems is in accordance with the generally accepted local moment picture, with fast relaxation behaviour on the electronic moment at the substitutional sites. For the iron host the exchange interaction dominates the cubic crystalline electric field, but for nickel both interactions are of comparable magnitude, leading to a considerable decrease of the hyperfine interaction.     

Electric field gradients in amorphous metals

The⁵⁷Fe-Mössbauer spectroscopy has been used in order to study the quadrupole splitting E_Q at the Fe-site and its dependence on temperature in Fe_85–XCr_XB₁₅ and Fe_80–XMo_XB₂₀ amorphous alloys. In all investigated compositions the local symmetry was lower than cubic with room temperature values of E_Q in the range of 0.4–0.5 mm/s. In all cases relatively broad distributions of E_Q and therefore of the EFG have been obtained. The EFG of the investigated compounds changes reversibly with temperature up to about 650 K according to the relation E_Q (T)=E_Q (O)·(1-BTV^3/2) as in the case of crystalline noncubic metals. Assuming that the same dependence of B on the Debye temperature as in crystalline non-cubic metals holds for amorphous alloys, values of have been obtained in good agreement with those determined from the temperature dependence of the Mössbauer f-factor.