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