The gamma-to-alpha transition in cerium (continued)

In 1977, Börje Johansson, then at Uppsala University, suggested that the transition was an example of a Mott transition, which is due to the competition between the coulomb interaction energy between pairs of electrons on an atom. A Mott transition can be written in terms of the number of electrons with spin up η↑ and spin down η↓ as Hint = Uη↑η↓ .

When U is greater than the bandwidth Δ (which represents the kinetic energy of 4f electrons that move between the atoms), electrons are prevented from hopping onto a 4f orbital that is already occupied by an electron. The Fermi energy μ is defi ned as the energy of the highest occupied state. In this localized state, the spin-up and spin-down density of states are split so that the peak in the spin-up density of states lies below the Fermi energy and is occupied, while the peak in the spin-down density of states is located above the Fermi energy and is mostly unoccupied. Hence, there is a net localized magnetic moment.

On the other side of the transition where U is less than Δ, the electrons travel between all the 4f shells of all the atoms. This state is nonmagnetic because both peaks in the 4f density of states at Εf are pinned at the Fermi energy. Consequently, there should be a concomitant change in the electron excitation spectra at the Mott transition. The excitation spectrum of cerium from photof emission experiments was found to be inconsistent with Johansson’s picture. However, recent calculations indicate that besides the peaks in the spectra above and below the Fermi energy, the spectra may contain a narrow peak near the Fermi energy similar to the spectrum of the model developed by the Nobel Prize winner Philip W. Anderson to describe the Kondo effect.

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