Nonlinear shielding in rare-earth crystal field interactions

Arthur J Freeman, R. E. Watson

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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,mAn mrn n Y n m(θ, φ). In fitting observed spectra, matrix elements of Vc over the 4f electrons alone are considered and one is left with the quantities Vn m=An m 〈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 Vn m 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
Pages (from-to)928
Number of pages1
JournalJournal of Applied Physics
Volume36
Issue number3
DOIs
Publication statusPublished - 1965

Fingerprint

crystal field theory
shielding
rare earth elements
interactions
ions
estimates
parameterization
electronic spectra
configuration interaction
field strength
electrons
perturbation theory
breakdown
energy levels
spacing
occurrences
magnetic properties
matrices
electronics

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

Cite this

Nonlinear shielding in rare-earth crystal field interactions. / Freeman, Arthur J; Watson, R. E.

In: Journal of Applied Physics, Vol. 36, No. 3, 1965, p. 928.

Research output: Contribution to journalArticle

@article{a5219ec7ab5f4af49a282c4e8c441fe4,
title = "Nonlinear shielding in rare-earth crystal field interactions",
abstract = "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 Vc=Σ n,mAn mrn n Y n m(θ, φ). In fitting observed spectra, matrix elements of Vc over the 4f electrons alone are considered and one is left with the quantities Vn m=An m 〈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 Vn m 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.",
author = "Freeman, {Arthur J} and Watson, {R. E.}",
year = "1965",
doi = "10.1063/1.1714265",
language = "English",
volume = "36",
pages = "928",
journal = "Journal of Applied Physics",
issn = "0021-8979",
publisher = "American Institute of Physics Publising LLC",
number = "3",

}

TY - JOUR

T1 - Nonlinear shielding in rare-earth crystal field interactions

AU - Freeman, Arthur J

AU - Watson, R. E.

PY - 1965

Y1 - 1965

N2 - 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 Vc=Σ n,mAn mrn n Y n m(θ, φ). In fitting observed spectra, matrix elements of Vc over the 4f electrons alone are considered and one is left with the quantities Vn m=An m 〈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 Vn m 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.

AB - 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 Vc=Σ n,mAn mrn n Y n m(θ, φ). In fitting observed spectra, matrix elements of Vc over the 4f electrons alone are considered and one is left with the quantities Vn m=An m 〈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 Vn m 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.

UR - http://www.scopus.com/inward/record.url?scp=36849142307&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36849142307&partnerID=8YFLogxK

U2 - 10.1063/1.1714265

DO - 10.1063/1.1714265

M3 - Article

VL - 36

SP - 928

JO - Journal of Applied Physics

JF - Journal of Applied Physics

SN - 0021-8979

IS - 3

ER -