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Fine electronic structure

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In solid state physics and physical chemistry, the fine electronic structure of a solid are the features of the electronic bands induced by intrinsic interactions between electron magnetic moments (LS coupling and jj coupling) and their interactions with the electric potential of the surrounding crystal lattice.[1] The name comes from the fine structure of atoms, where energy levels split slightly from the non-relativistic calculation due to effects like spin–orbit interaction, zitterbewegung or corrections to the kinetic energy. The fine electronic structure in a solid material is fundamental for the understanding of single ionic properties of materials with localized magnetic moments.[2]

The electric interaction of the many-electron system of an atom/ion is usually described using crystal field theory. The term "fine electronic structure" means the existence of a structure close lying many-electron energy states, derived from the abolition of degenerate electronic configurations of a paramagnetic atom or ion. The fine electronic structure is formed from the atomic term structure and multiplet structure under the influence of multipolar electrostatic interactions which further energy levels splitting – Stark effect.

Depending on the accounting methodology of calculating, the fine electronic structure is carried out on the basis of many-electron wave functions written as components of the quantum numbers of the total angular momentum operator of the electron subshell '"`UNIQ--postMath-00000001-QINU`"' or the spin and orbital angular momentum ('"`UNIQ--postMath-00000002-QINU`"' and '"`UNIQ--postMath-00000003-QINU`"').

Interactions of electrons from unclosed electronic subshell (in spectroscopic notation: p, d or f) with the resultant electric field of the crystal, can be described by the Hamiltonian in the basis '"`UNIQ--postMath-00000004-QINU`"'[3] or '"`UNIQ--postMath-00000005-QINU`"'.[4]

In a non-zero temperature, the fine electronic structure determines the magnetic (single-ionic magnetic anisotropy, magnetic susceptibility) and thermodynamic properties (Schottky-type specific heat, entropy etc.). Fine electronic structure calculations has been developed for a vast group of solid compounds containing transition metals[5] and rare earth elements[4] (groups 3d, 4d, 4f and 5f).

The fine electron structure is shaped by the crystalline field whose effect is described using the multipolar operators defined by Wybourne [6] or Stevens conventions.[3] Both conventions are consistent, providing the crystal field parameters Bmn, Bkq and Amn. The fine electronic structure a the material containing paramagnetic ions determines the single ionic anisotropy of material and provides a basic knowledge about the behaviour of atoms or ions in a solid material from low to medium temperatures.

See also[edit | edit source]


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References[edit | edit source]

  1. Electronic structure and magnetism of inorganic compounds. Vol 7, A review of the recent literature. Day, P. (Peter), 1938-. London: Chemical Society. 1982. ISBN 9781847555977. OCLC 232639420.
  2. Radwanski, R.; Michalski, R.; Ropka, Z. (2000). "Magnetism and Electronic Structure of PrNi5, ErNi5, LaCoO3 and UPd2Al3". Acta Physica Polonica B. 31 (12): 3079.
  3. 3.0 3.1 Stevens, K.W.H (1952). "Matrix Elements and Operator Equivalents Connected with the Magnetic Properties of Rare Earth Ions". Proceedings of the Physical Society, Section A. doi:10.1088/0370-1298/65/3/308.
  4. 4.0 4.1 A., Abragam,; Bleaney, Brebis (2012). Electron paramagnetic resonance of transition ions. Oxford: Oxford University Press. ISBN 0191023000. OCLC 903261681.
  5. Mulak, K.; Żołnierek, Z. (1977). Fizyka i chemia ciała stałego (in polish). Ossolineum.CS1 maint: Unrecognized language (link)
  6. Wybourne, Brian G. (1970). Symmetry principles and atomic spectroscopy. Wiley-Interscience,.


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