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Crystalline electric fields in metals

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  • Dixon, J.M.
  • Wardlaw, R.S.

Abstract

A method is described for calculating crystal fields for rare-earth ions in non-magnetic hosts. Screening is included by performing a Bohm-Pines-like unitary transformation on the starting Hamiltonian which contains kinetic-energy and Coulombic energies of electrons in the presence of fixed nuclei. Contributions from core orbitals are included as well as components from a 5d virtual bound state assumed to contain no more than one electron. The coupling between the 4f impurity and the majority s-like conduction band is assumed to be weak. Degenerate perturbation theory has been used and in zeroth order it has been assumed that the impurity potential is sufficiently strong to remove one state from the s-band. The many-body nature of the problem has been incorporated using a second quantised representation. Further unitary transformations are performed to weaken the 4f-conduction band coupling before averaging over the conduction states to obtain an effective 4f Hamiltonian.

Suggested Citation

  • Dixon, J.M. & Wardlaw, R.S., 1986. "Crystalline electric fields in metals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 135(1), pages 105-138.
    • Handle: RePEc:eee:phsmap:v:135:y:1986:i:1:p:105-138
    DOI: 10.1016/0378-4371(86)90108-1
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    1. Dupree, A. Hunter, 1971. "Engineering in American Society, 1850–1875. By Raymond H. Merritt. Lexington, Kentucky: The University of Kentucky Press, 1969. Pp. xii, 199. $7.95," The Journal of Economic History, Cambridge University Press, vol. 31(2), pages 511-512, June.
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