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.     

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.     

The electric fieldgradient at Cd-impurities in heavy rare earth metals

The static electric quadrupole interaction of¹¹¹Cd in the heavy rare metals Gd, Tb, Ho and Er has been studied at room temperature by time differential perturbed angular correlation techniques. From these measurements the effective electric field-gradient,V _zz ^eff , at the Cd-site was derived on a relative scale. The lattice contributions,V _zz ^lat , to the total electric fieldgradient have been determined by lattice-sum calculations. The ratioα=V _zz ^eff /V _zz ^lat , which to a certain extent represents the conduction electron contribution to the electric fieldgradient, decreases with increasing atomic number. Possible reasons for this behaviour are discussed.     

Electric field gradient produced by conduction electrons in rare earth metals

The electric field gradient produced by conduction electrons in the heavy rare earth metals has been calculated taking into account non-spherical effects due to the magnetic ordering in these metals. To our knowledge the values obtained are the first to agree with the sign of the experimental results.     

Saturation magnetic moments,magnetic hyperfine fields and electric field gradients at nuclei in the heavy rare earth metals

The contributions of 4f, 5d and 6s electrons to the saturation magnetic moments and magnetic hyperfine fields in the heavy rare earth metals are calculated using the model described in the previous paper. It is found that 4f shell moments are reduced from their free ion values by amounts varying from 0.05µ _B in Gd to several tenths of a Bohr magneton in Tb and Dy, in qualitative agreement with a recent published analysis of neutron diffraction results in Tb, but that the calculated total saturation moments in Tb and Dy are slightly larger than commonly accepted experimental values. After 6s contributions to magnetic hyperfine fields are determined by fitting observations in Gd, the predicted differences between the fields for metals and those for free ions are such that the estimated uncertainty ranges of the theoretical values overlap the experimental ranges. The 5d contribution in the model is negative, varying from about –40 kOe in Tb to –200 kOe in Er. Electric field gradients are also analysed. Observed results can be fitted if the average effective Sternheimer screening factorR _d ^* for 5d electrons in the metals satisfies (1 —R _d ^* )0.7.     

Pressure dependence of the electric field gradient at Cd-impurities in the heavy rare-earth metals

The pressure dependence of the electric field gradient at Cd impurities in Gd, Tb, Dy, Ho and Er have been measured at room temperature.The average isotropic volume dependence is dlneq/dlnV –4.4 and no systematic trend within the RE series is observed. The rather large volume dependence can be explained if the screening charge distribution of the host ions is considered.On leave from Panjab University, Chandigarh, India     

Semi-empirical models for the electric field gradient in metals

A survey over the present state of the empirical investigation of the electric field gradient at the nuclear site of impurity atoms and of matrix atoms in noncubic metal matrices is given. A qualitative explanation in terms of the electronic charge distribution typical for the host's group in the periodic system of elements is discussed. For group IIb hosts, two semi-empirical models which were developed in Bonn are described in more detail, i.e. the ‘naive model’ and the ‘Thomas-Fermi model’.     

Crystal potential model for the description of crystalline electric field effects in rare earth metals and intermetallics

A crystal potential model is suggested. It allows us to interpret crystalline electric field effects in optical, EPR, NMR, NGR and neutron spectroscopy measurements in rare earth metals and intermetallics. The crystal potential character and space distribution are discussed. The model is used for the theoretical interpretation of the effects of the crystalline field in the compound PrAl₃.     

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.     

On the electric field gradient in non-cubic metals: The isotopic mass effect

Using the phonon model of Nishiyama and Riegel for the electric field gradient we have investigated the possibility of an isotopic mass effect. We will show that there is an isotopic mass effect nearT=0 K. In this temperature region the electric field gradient depends on the probe atom mass only.     

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.     

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.     

The magnetic hyperfine fields of rare earth ions in metals

Data for the magnetic dipole hyperfine interaction of essentially single rare earth ions in metals, measured with different experimental methods, are collected and discussed. Depending on the host, the magnetic hyperfine field of these paramagnetic ions remains undisturbed by the environment, or it is enlarged, or weakened or can even become completely lost. If there are magnetic ions in the neighbourhood, the magnetic interaction can enlarge the hyperfine field of the single ion by a transferred hyperfine field. The reason of the demagnetization effect may be crystal field splitting and hybridization. The core polarization field of the free rare earth ions is redetermined from measurements of the hyperfine interaction in nonmagnetic metals at low magnetic ion concentration.     

The electric field gradient at tantalum in yttrium

A uniform, axially symmetric electric field gradient at ¹⁸¹Ta in hcp Y of |eq| = (5.9 ± 0.3) × 10¹⁷V/cm² at 300 K, increasing by 11% upon cooling to 4.2 K, was found using the time differential perturbed angular correlation technique.