### 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 V_{c} which acts on the open 4f shell. Generally, one takes V_{c}=Σ _{n,m}A_{n}
^{m}r_{n}
^{n} Y _{n}
^{m}(θ, φ). In fitting observed spectra, matrix elements of V_{c} over the 4f electrons alone are considered and one is left with the quantities V_{n}
^{m}=A_{n}
^{m} 〈r^{n}〉 (where 〈r^{n}〉 is the integral of r^{n} 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 shown^{1} that, in addition to the occurrence of substantial linear shielding effects^{1,2} (which reduce the magnitude of the V_{n}
^{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 work^{1} 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, Ce^{3+}, Tb^{3+}, Er^{3+}, Tm^{3+}, Ho^{3+}, Dy ^{3+}, and Yb^{3+}. 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 V_{2} and V_{4} external fields were determined as a function of atomic number as were their effects on apparent V_{2}, V_{4}, and V_{6} 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 V_{4} and V_{6} shielding being very small. The most severe nonlinear effects arise when relatively strong V_{2} and V_{4} fields contribute to a relatively weak V_{6} field. A full report will be submitted to the Physical Review.

Original language | English |
---|---|

Pages (from-to) | 928 |

Number of pages | 1 |

Journal | Journal of Applied Physics |

Volume | 36 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1965 |

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### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

*Journal of Applied Physics*,

*36*(3), 928. https://doi.org/10.1063/1.1714265

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

Research output: Contribution to journal › Article

*Journal of Applied Physics*, vol. 36, no. 3, pp. 928. https://doi.org/10.1063/1.1714265

}

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.

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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 -