Association

2.5. Magnetic circular dichroism in core-level photoemission 33
will occur in two groups with six and four final states, respectively. In between the limits of
dominant or negligible spin–orbit interaction (λ ≫ ζ, orλ → 0), the intermediate coupling
scheme is suited to describe the total angular momenta, as seen for the complex example of
Gd 4d. In the following, we express the final state momenta m J for the Eu core orbitals either
via jj or LS-coupling, dependent on their classification on λ in Fig. 2.20.
We begin with a simple orbital: the Eu np 6 shell. In Tab. 2.1, the six final final states are
derived under assumption of a pure spin–orbit coupling of the photoionized p 5 orbital. For
the Eu 3p, the spin–orbit splitting is clearly dominant (ΔE SO = 135 eV, E B = 1500 eV), and
exchange interaction is negligible.
Table 2.2.: Photoemission final states of Eu nd shells in jj-coupling (a) and LS-coupling (b) with the
8 S 7/2 open shell. In this work, we consider orbitals with principal quantum number n = {3; 4}.
(a) jj-coupling. j = + s, J = j i .
core hole
(
m J of
s ∗ m j nd 9 ) (
m j 4f 7 ) final state
+ 1 2
− 1 2
5/2 7/2 6
3/2 7/2 5
1/2 7/2 4
−1/2 7/2 3
−3/2 7/2 2
−5/2 7/2 1
3/2 7/2 5
1/2 7/2 4
−1/2 7/2 3
−3/2 7/2 2
(b) LS-coupling. L = i , S = s i , J = L + S.
core hole
m J of
s ∗ m L m S final state
+ 1 2 2 4 6
1 4 5
0 4 4
−1 4 3
−2 4 2
− 1 2 2 3 5
1 3 4
0 3 3
−1 3 2
−2 3 1
We proceed with the Eu nd 10 orbitals, which show a characteristic multiplet structure in
Eu 110,111 and Gd 112 compounds. In Tab. 2.2 (a), we discuss the final states for jj-coupling,
which is a good assumption for the deeply bound Eu 3d core-levels due to their large spin–
orbit interaction of ΔE SO = ∼30 eV and deep binding (E B = 1125 eV). In the 4d core-levels,
however, which are more weakly bound at ∼120 eV, the spin–orbit interaction is weaker.
Thus, a suitable model for the Eu 4d level is the LS-coupling (Tab. 2.2 (b)) showing two parts
of the multiplet, from m J =2...6 in the low binding energy part and m J =1...5 at higher
binding energy. The best description for the Eu 4d spectra, however, is the more complex
intermediate coupling. For a comprehensive discussion on the 4d final states, we may refer
to literature. 112–115
A significant spectral separation due to intra-atomic exchange splitting can be observed in
the Eu ns 1 orbital of the photoemission final state. Due to the effect of core polarization (as
described in Ch. 2.4.2), the core hole with spin s ∗ can be aligned either parallel or antiparallel
with respect to the spin-aligned 8 S J open 4f shell. 116 This yields two spectral features, which
can be practically observed for Eu 3s (weak), 4s and 5s photoemission, as listed in Tab. 2.3. In
this work, we show only the Eu 4s orbital due to its large cross-section and exchange splitting.
Finally, we consider the Eu 4f 7 level. Upon 4f photoemission, the finals states are created as
∣
〉
∣4f 7 ; 8 photoionization
S J −→
∣
∣4f 6 ; 7 F J ; εl 〉 . (2.35)