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Tenfold d‐electron degeneracy in the Hubbard model and transition‐metal magnetism I. The paramagnetic‐ferromagnetic transition
Author(s) -
Siegel E. J.,
Kemeny G.
Publication year - 1972
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220500221
Subject(s) - condensed matter physics , paramagnetism , ferromagnetism , hubbard model , exchange interaction , degenerate energy levels , physics , magnetism , electron , degeneracy (biology) , quantum mechanics , superconductivity , bioinformatics , biology
Abstract Replacing the simplified s‐electron picture of Penn [a] [4], intrasite d–d interactions are included in the Hubbard model. Choosing k ‐space correlation functions to represent the paramagnetic and ferromagnetic states, the tenfold degenerate eigenvalue problem is solved and free energies are calculated self‐consistently for various combinations of the three parameters: bandfilling, direct interaction constant divided by the bandwidth, exchange interaction constant divided by the bandwidth. The paramagnetic‐ferromagnetic phase boundary surface is plotted at near zero and finite temperatures with the third dimension being exchange interaction constant divided by the bandwidth. The near‐zero‐temperature trend shows that the inclusion of exchange, as expected, enhances the ferromagnetic region at the expense of the paramagnetic region. This is exactly opposite to the nondegenerate, t‐matrix result of Caron and Kemeny [6]. Finite temperature calculations show the same trend with increasing exchange, but shift the phase boundary surface so as to decrease the ferromagnetic region.