HAL Id: jpa-00218918
https://hal.archives-ouvertes.fr/jpa-00218918
Submitted on 1 Jan 1979
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Influence of fd mixing on electronic impurity levels in rare earth semiconducting compounds
R. Camley, J. Parlebas, K. Subbaswamy, D. Mills
To cite this version:
R. Camley, J. Parlebas, K. Subbaswamy, D. Mills. Influence of fd mixing on electronic impurity levels in rare earth semiconducting compounds. Journal de Physique Colloques, 1979, 40 (C5), pp.C5-372- C5-373. �10.1051/jphyscol:19795132�. �jpa-00218918�
JOURNAL DE PHYSIQUE Collogue C5, supplement au n° 5, Tome 40, Mai 1979, page C5-372
Influence of fd mixing on electronic impurity levels in rare earth semi- conducting compounds (*)
R. Camley, J. C. Parlebas, K. R. Subbaswamy and D. L. Mills Department of Physics, University of California, Irvine, California 92717, U.S.A.
Résumé. — Nous étudions les énergies des niveaux électroniques des premiers voisins d'une impureté anionique de substitution dans un composé de type SmS. Dans le cas d'une hybridation entre les états localisés et la bande de conduction, nous trouvons qu'une transition de valence localisée peut apparaître entre les niveaux f et les orbitales de la bande de conduction.
Abstract. — We consider the electronic energy levels on the nearest neighbors to a substitutional anion impurity in a SmS type compound. In the presence of mixing between the localized f levels and the conduction band, we find a local valence transition may occur between the f levels and conduction band orbitals on the nearest neighbors.
Many rare earth monochalcogenides exhibit inter- mediate valence characteristics [1]. Among them is SmS, a semiconductor at low pressure and a metal at high pressure. Under pressure, the Sm2 + releases an electron to the conduction band, with a consequent sharp reduction in lattice constant. Recently Holtz- berg et al. [2] reported data on SmS doped with small concentrations ( < 5 %) of A s ; evidently a dramatic change in electronic structure occurs on the six Sm ions nearest neighbors to the As. The precise electronic configuration of the nearest neighbors is unclear to us,
but drastic changes clearly occur.
This data has led us to inquire into the general question of the electronic states on the nearest neigh- bors to an anion impurity for such a system, where the Fermi energy EF lies in the very small gap between a narrow f band (presumed here of zero width) and a broad conduction band. We mimic the host by tight binding orbitals (nondegenerate) on each lattice site to form the f band, and a conduction band formed from tight binding (again nondegenerate) but over- lapping d-like orbitals. Thus, the Hamiltonian for the pure material, in the Bloch representation, is
J£0 = X (Ef ak+ au + Ed(k) b£ bk + Fk[at+ Z>k + h.c.]).
k
(1) The impurity is presumed to (i) shift the energy of the nearest neighbor Wannier orbitals by V0, presumed negative, and (ii) alter the overlap integral between these orbitals by the amount At > 0. Presumably, part of the d-d overlap comes from hybridization of the d states with the anion outer p orbitals.
The above model may be solved in closed form.
The following intriguing phenomenon may occur.
(*) Supported in part by AFOSR Grant No. F49620-78-C-0019.
Suppose first Vk = 0. For V0 or At sufficiently large, bound states are driven from the bottom of the con- duction band. Each bound state wave function is (to good approximation) a linear combination of the
Fig. 1. — (a) The density of states of the host, (b) A bound state pushed out of the conduction band below the f levels, with no fd mixing, (c) When fd hybridization is turned on, a local level of f character may be pushed above the Fermi level.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19795132
INFLUENCE OF fd MIXING ON ELECTRONIC IMPURITY LEVELS C5-373
six nearest neighbor conduction orbitals. If a bound state lies below E,, and Vk is turned on, an f level splits off from the f band, and is pushed upward in energy, repelled through Vk from the bound conduc- tion level. If the f level is pushed above the Fermi level E, (it only need move a small fraction of a volt to do this), we have a local valence transition, where an electron shifts from the f shells of the nearest neigh- bors (the wave function is a linear combination of f orbitals with the same point group symmetry as the conduction band bound state) into the bound state formed from the conduction orbitals. The one elec- tron energy gain increases with At which has an exponential variation with local lattice constant.
Thus, we have a local collapse of the lattice.
With V, = 0 and Vo = 0, the energy E, of the bound conduction level is found from a condition of the form 1 = AtG(Eo), where we give the detailed
form of G(E) elsewhere. When V, is turned on, the f level described above is shifted upward by the energy
where A 2 z 12 Atyll
r 1
and we assume E, - E, > A . Herer
= At(aG/aE),o, and y x ( V:)/w2,
with W the width of the conduction band, ( V: ) is V:averaged over the Brillouin zone. As k -P 0, V, vanishes for df mixing [3], but in ( V: ) large k are important. Hence the df mixing may play an appre- ciable role in impurity problems such as the present.
In figure 1, we summarize the picture described above.
.
Local valence instabilities such as that described here may influence systems like dilute
SmS
: As significantly, though our model is too crude for explicit contact with available data.References
[I] JAYARAMAN, A,, Comments on Solid State Phys. 7 (1977) 135.
[2] HOLTZBERG, F. et al., in Valence Instabilities and Related Narrow- Band Phenomena, edited by R. D. Parks (Plenum Press, New York) 1977, p. 507.
[3] VARMA, C. M. and HEINE, V., Phys. Rev. B 11 (1975) 4763.
