Abstract
From the theory of many-electron states in atoms, we know that there exists a strong Coulomb repulsion, which results in the electronic term structure of atoms and is responsible for Hund’s rules. By expanding the Coulomb on-site repulsion into a multipolar series, we derive this interaction and show that it is also present in solids as a correlation effect, which means that the interaction requires a multideterminant version of the Hartree-Fock method. Of particular interest is the case where this interaction couples states of localized (f) and delocalized (s) electrons. We show that the interaction is bilinear in the creation/annihilation operators for localized electrons and bilinear in the operators for conduction electrons. To study the coupling, we consider a simple model in the framework of an effective limited configuration interaction method with one localized f-electron and one itinerant s-electron per crystal site. The on-site multipole interaction between the f- and s-electrons is explicitly taken into account. It is shown that depending on the low-lying excitation spectrum imposed by the crystal electric field, the model can lead not only to ferromagnetism but also to a nonmagnetic state. The model is relevant for solids with localized and itinerant electron states.
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References
P. Fulde, Electron Correlations in Molecules and Solids (Springer, Heidelberg, 1995).
A. V. Nikolaev and K. H. Michel, Phys. Rev. B: Condens. Matter 66, 054 103 (2002).
A. V. Nikolaev, Phys. Rev. B: Condens. Matter 71, 165102 (2005).
A. V. Nikolaev and K. H. Michel, J. Chem. Phys. 117, 4761 (2002).
E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra (Cambridge University Press, Cambridge, 1967).
C. Zener, Phys. Rev. 81, 440 (1951); Phys. Rev. 82, 403 (1951).
Yu. Ralchenko, A. E. Kramida, J. Reader, et al. (NIST ASD Team), NIST Atomic Spectra Database (Version 3.1.5); http://physics.nist.gov/asd3 [October 6, 2008] (National Institute of Standards and Technology, Gaithersburg, MD, United States, 2008).
S. Lebègue, A. Svane, M. I. Katsnelson, A. I. Lichtenstein, and O. Eriksson, Phys. Rev. B: Condens. Matter 74, 045 114 (2006).
S. Lebègue, G. Santi, A. Svane, O. Bengone, M. I. Katsnelson, A. I. Lichtenstein, and O. Eriksson, Phys. Rev. B: Condens. Matter 72, 245 102 (2005).
A. I. Lichtenstein and M. I. Katsnelson, Phys. Rev. B: Condens. Matter 57, 6884 (1998).
D. J. Singh, Planewaves, Pseudopotentials, and the LAPW Method (Kluwer, Boston, MA, United States, 1994).
L. L. Hirst, Adv. Phys. 27, 231 (1978).
C. J. Bradley and A. P. Cracknell, The Mathematical Theory of Symmetry in Solids (Clarendon, Oxford, 1972).
A. V. Nikolaev and P. N. Dyachkov, Int. J. Quantum Chem. 89, 57 (2002).
J. C. Slater and G. F. Koster, Phys. Rev. 94, 1498 (1954).
M. T. Hutchings, in Solid State Physics: Advances in Research and Applications, Ed. by F. Seitz and D. Turnbull (Academic, New York, 1964), Vol. 16, p. 227.
J. Mulak and Z. Gajek, The Effective Crystal Field Potential (Elsevier, Amsterdam, 2000).
D. J. Newman, Adv. Phys. 20, 197 (1971); D. J. Newman, J. Phys. F: Met. Phys. 13, 1511 (1983).
K. W. H. Stevens, Proc. Phys. Soc., London, Sect. A 65, 209 (1952).
P. Fulde and M. Loewenhaupt, Adv. Phys. 34, 589 (1986).
G. A. Gehring and K. A. Gehring, Rep. Prog. Phys. 38, 1 (1975).
R. M. Lynden-Bell and K. H. Michel, Rev. Mod. Phys. 66, 721 (1994).
P. Wachter, in Handbook on the Physics and Chemistry of Rare Earths, Ed. by K. A. Gschneidner, Jr., L. Eyring, G. H. Lander, and G. R. Choppin (Elsevier, Amsterdam, 1994), Vol. 19, p. 177.
D. C. Koskenmaki and K. A. Gschneidner, Jr., in Handbook on the Physics and Chemistry of Rare Earths, Ed. by K. A. Gschneidner, Jr. and L. Eyring (North-Holland, Amsterdam, 1978), p. 337.
J. L. Sarrao, Physica B (Amsterdam) 259–261, 128 (1999).
J. A. Paixão, C. Detlefs, M. J. Longfield, R. Caciuffo, P. Santini, N. Bernhoeft, J. Rabizant, and G. H. Lander, Phys. Rev. Lett. 89, 187 202 (2002).
L. Forró and L. Mihály, Rep. Prog. Phys. 64, 649 (2001).
P. W. Anderson, Phys. Rev. 124, 41 (1961).
M. A. Ruderman and C. Kittel, Phys. Rev. 96, 99 (1954); T. Kasuya, Prog. Theor. Phys. 16, 45 (1956); K. Yosida, Phys. Rev. 106, 893 (1957); J. H. Van Vleck, Rev. Mod. Phys. 34, 681 (1962).
O. Eriksson, M. S. S. Brooks, and B. Johansson, Phys. Rev. B: Condens. Matter 41, 7311 (1990).
S. V. Beiden, W. M. Temmerman, Z. Szotek, and G. A. Gehring, Phys. Rev. Lett. 79, 3970 (1997).
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Nikolaev, A.V., Michel, K.H. Elusive s-f intrasite interactions and double exchange in solids: Ferromagnetic versus nonmagnetic ground state. J. Exp. Theor. Phys. 109, 286–292 (2009). https://doi.org/10.1134/S1063776109080147
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DOI: https://doi.org/10.1134/S1063776109080147