Nonlinear shielding in rare-earth crystal field interactions

A. J. Freeman*, R. E. Watson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


A number of the magnetic properties of rare-earth ions, which depend strongly on their interaction with the crystalline environment, are inferred by studying their electronic spectra. Basic to current methods for analyzing these spectra is the assumption of a static crystalline field Vc which acts on the open 4f shell. Generally, one takes Vcn,mAnmrnn Y nm(θ, φ). In fitting observed spectra, matrix elements of Vc over the 4f electrons alone are considered and one is left with the quantities Vnm=Anm 〈rn〉 (where 〈rn〉 is the integral of rn over the 4f radial density) which are taken to be empirical parameters which somehow absorb all environmental effects not included in V c. These empirical parameters have been used "successfully" to interpret other rare-earth properties. However, if one considers multi-electron Coulomb and exchange contributions arising from the closed shells, it may be shown1 that, in addition to the occurrence of substantial linear shielding effects1,2 (which reduce the magnitude of the Vnm parameters), there may be significant nonlinear shielding contributions which change the ordering and spacing of the electronic energy levels. When these latter terms are significant, the standard parameterization scheme breaks down. Previous work1 on Ce 3+, using perturbation theory techniques, was seen to be inadequate for accurate estimates of nonlinear shielding. We have extended these investigations using configuration interaction methods to estimate the leading nonlinear (and linear) shielding terms in a number of ions, Ce3+, Tb3+, Er3+, Tm3+, Ho3+, Dy 3+, and Yb3+. Calculations have been carried out as a function of crystalline field strength since the nonlinear shielding is dependent, of course, on the strength of the applied external field. Nonlinear shielding of V2 and V4 external fields were determined as a function of atomic number as were their effects on apparent V2, V4, and V6 crystal field parameters. From these certain conclusions may be drawn. Antishielding rather than shielding of the V 4 field occurs, but only by a few percent at most, whereas the V 2 field is always shielded. For the heavy rare-earth ions, the shielding effects are much smaller than for the lighter ions, with the apparent V4 and V6 shielding being very small. The most severe nonlinear effects arise when relatively strong V2 and V4 fields contribute to a relatively weak V6 field. A full report will be submitted to the Physical Review.

Original languageEnglish (US)
Pages (from-to)928
Number of pages1
JournalJournal of Applied Physics
Issue number3
StatePublished - 1965
Externally publishedYes

ASJC Scopus subject areas

  • General Physics and Astronomy


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