Effective Crystalline Electric Field Potential in a j-j Coupling Scheme

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Abstract

We propose an effective model on the basis of a <I>j</I>–<I>j</I> coupling scheme to describe local <I>f</I>-electron states for realistic values of Coulomb interaction <I>U</I> and spin–orbit coupling λ, for future development of microscopic theory of magnetism and superconductivity in <I>f<SUP>n</SUP></I>-electron systems, where <I>n</I> is the number of local <I>f</I> electrons. The effective model is systematically constructed by including the effect of a crystalline electric field (CEF) potential in the perturbation expansion in terms of 1⁄λ. In this paper, we collect all the terms up to the first order of 1⁄λ. Solving the effective model, we show the results of the CEF states for each case of <I>n</I>=2–5 with <I>O<SUB>h</SUB></I> symmetry in comparison with those of the Stevens Hamiltonian for the weak CEF. In particular, we carefully discuss the CEF energy levels in an intermediate coupling region with λ⁄<I>U</I> in the order of 0.1 corresponding to actual <I>f</I>-electron materials between the <I>LS</I> and <I>j</I>–<I>j</I> coupling schemes. Note that the relevant energy scale of <I>U</I> is the Hund’s rule interaction. It is found that the CEF energy levels in the intermediate coupling region can be quantitatively reproduced by our modified <I>j</I>–<I>j</I> coupling scheme, when we correctly take into account the corrections in the order of 1⁄λ in addition to the CEF terms and Coulomb interactions which remain in the limit of λ=∞. As an application of the modified <I>j</I>–<I>j</I> coupling scheme, we discuss the CEF energy levels of filled skutterudites with <I>T<SUB>h</SUB></I> symmetry.

Journal

  • Journal of the Physical Society of Japan

    Journal of the Physical Society of Japan 75(12), "124711-1"-"124711-15", 2006-12-15

    The Physical Society of Japan (JPS)

References:  42

Codes

  • NII Article ID (NAID)
    110005716699
  • NII NACSIS-CAT ID (NCID)
    AA00704814
  • Text Lang
    ENG
  • Article Type
    ART
  • ISSN
    00319015
  • NDL Article ID
    8573540
  • NDL Source Classification
    ZM35(科学技術--物理学)
  • NDL Call No.
    Z53-A404
  • Data Source
    CJP  NDL  NII-ELS  J-STAGE 
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