Association

2.2. Electronic structure of EuO 9
Figure 2.3.: The rare earth electronic
structure as a shell scheme for Eu
metal.
The open shell 4f 7 and conduction
electrons of Eu are highlighted. The
conduction band is composed of
the 5d and 6s levels. The Eu 4f 7
levels are highly localized inside
the [Xe] core. In ferromagnetic
Eu 2+ O, the seven f electrons carry
the spin-only magnetic moment M.
After Dionne (2009). 37
2.2.1. The open shell 4f 7
The half-filled Eu 4f 7 orbitals constitute valence-like levels near the Fermi edge in EuO which
are often represented as bands, as depicted in Fig. 2.4. However, the 4f levels do not take
part in the ionic bondings. The narrow radial distribution of n = 4 shells is responsible for
the highly localized character of the 4f shell. 38 These properties justify a treatment of the
Eu 4f orbital as core-level rather than a valence band, in particular with regard to core-level
photoemission (see Ch. 2.4). In Eu 4f , the spin–orbit interaction is weak and the electron
exchange strong. This justifies the Russel-Saunders-coupling (LS) for which the Hund’s Rules
predict the filling of the 4f 7 level as follows:
1. The spin multiplicity S =2S + 1 is maximal.
S 4f 7 = ∑ s i = 7/2 (S = 8), in the FM state due to spin alignment.
2. With given spin multiplicity, the total angular momentum L is largest.
Due to Pauli’s exclusion principle, there is only one way to distribute seven electrons
with parallel spins in an f shell: l i = −3 ...+3, L 4f 7 = ∑ l i =0.
3. For a half-filled shell, the total angular momentum is J = L + S.
ForEu4f 7 : J 4f 7 =0+7/2 = 7/2.
Thus, the Eu 4f orbital is in the initial state with ferromagnetic order in a 8 S7/2 configuration.
The ferromagnetic moments in EuO originate from the 8 S7/2 spin-only states of the 4f orbital.
Correlations between the localized magnetic states 4f 7 and the itinerant electrons † are the
cause of the ferromagnetic exchange, as discussed in Ch. 2.3. The correlations in the 4f shell
are further discussed in literature. 18,39–42
This is the term symbol notation, S L J . The spin multiplicity S =2S + 1 quantifies the amount of unpaired
electron spins.
† Of course, in EuO there are no itinerant electrons. However, interactions between Eu 2+ sites work via 4f
spins and virtual excitations to 5d conduction bands, often referred to as d–f interaction, or as s–f model in
which s denotes the virtual itinerant electron in the conduction band.