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2.4. Hard X-ray photoemission spectroscopy 25
etc. shells). The branching ratio of the two final state peaks is calculated as
I l−s ∗
I l+s ∗
= 2( )
l − 1 2 +1
2 ( l + 1 2
)
+1
= l
l +1 . (2.23)
This reveals intensity ratios of 1:2 for p shells, 2:3 for d shells, and 3:4 for f shells. The spin–
orbit splitting is realized prefereably for heavy elements and deep core-levels. In this thesis,
the deeply bound Eu 3d peak structure is well described by a spin–orbit doublet, but Eu 4d
and lower core-levels require other coupling schemes, as will be discussed in section 2.5.2.
Core-hole polarization. Core-level photoemission always produces a final state with spin
and angular momentum. If the system has a valence state configuration l n with corresponding
spin and orbital momenta, the coupling with the core-hole orbital and angular momenta
leads to different final states. For an s 1 final state, the photohole has a spin of s ∗ = 1/2. This
spin can be either parallel or antiparallel to the net spin S of the valence shell. The exchange
splitting is then
Δ exch (s, l, S)=
( ) 2S +1
G l (s, l), (2.24)
2l +1
where G l (s, l) is the exchange integral. 93 Thereby, the Eu 4s and 5s core-levels exhibit a
double-peak structure which is well-described by this model. 80 Remarkably, this exchange
splitting is largest in the 4s levels of Eu, Gd, and Tb, thus rendering that effect of fundamental
interest. 95
2.4.3. Implications of hard X-ray excitation
Conventional X-ray photoemission spectroscopy (XPS) is limited to a probing depth of a
few surface atomic layers. Modern solid state and material science research, however, often
requires the selective probe of buried layers or interfaces in a depth of several hundred
Ångström from the surface. A solution for these experimental needs is the use of hard X-ray
excitation, exceeding the limited probing depth of common XPS experiments.
The first hard X-ray photoemission experiment at hν = 17.4 keV using a Mo anode was carried
out by Nordling, Sokolowski, and Siegbahn 96 in 1957. However, the energy resolution
and brilliance were not sufficient to resolve small chemical shifts or multiplet fine structures.
Subsequently, low energy anodes with Al Kα and Mg Kα radiation were subsequently established,
and synchrotron light up to 1.5 keV enabled a success story of XPS. Nowadays, highly
brilliant synchrotron hard X-ray sources 85,97,98 offer a wealth of experimental opportunities
with an energy resolution down to 0.2 eV. 98,99
An excitation of photoelectrons with hard X-rays implies major differences in view of conventional
XPS. We discuss (i) changed photoemission cross-sections and (ii) Debye-Waller
factors for photoemission, both of which directly affect the photoexcitation process. Finally
(iii), hard X-ray-excited photoelectrons offer a largely increased inelastic mean free path in
the solid, which is a major experimental benefit of HAXPES.
Gd 4s and 5s core-hole polarization was recently discussed in Tober et al. (2013). 94