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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 31<br />

Figure 2.19.: Right: MCD components m J for 2p level<br />

photoemission with dominant spin–orbit interaction.<br />

In (a), the lines correspond to p 5 final states in the<br />

limit of dominant SO interaction. (b) MCD simulation<br />

including lifetime broadening. The energy separation<br />

between the pure spin components m J = ±3/2 is always<br />

equal to the exchange coupling strength ζ.<br />

Bottom: MCD of p-level photoemission components<br />

for dominant spin–orbit interaction λ. They depend<br />

on radial matrix elements Δ = 1/3(2R 2 2 − R2 0 + ˜R 0 ˜R 2 ). 107<br />

Adapted from Starke (2000). 105<br />

j m j I MCD (j, m j )<br />

3/2 3/2 3<br />

3/2 1/2 <br />

3/2 −1/2 −<br />

3/2 −3/2 −3<br />

1/2 −1/2 −2<br />

1/2 1/2 2<br />

<br />

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<br />

<br />

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<br />

<br />

<br />

<br />

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<br />

<br />

<br />

elements from literature 107 allow one to express the resulting MCD intensities I MCD (j, m j )<br />

for every final state |j, m j 〉, as shown in Fig. 2.19.<br />

In this example, the spin–orbit-only MCD final states of the Fe 2p photoemission can be<br />

analytically quantified. A prediction of MCD line strengths is also desirable for Eu corelevels,<br />

which would allow for a direct comparison of the magnetic coupling in epitaxial EuO<br />

under different biaxial strain. For EuO core-levels, however, the intra-atomic coupling is<br />

more complex, being a composition of spin–orbit and exchange interaction. As a first step,<br />

we discuss the possible intra-atomic couplings schemes of Eu core-levels in the following<br />

section.<br />

2.5.2. Coupling schemes of atomic angular momenta in Eu 2+ core-level photoemission<br />

final states<br />

Now, we consider the single photoemission final states of the Eu core-levels, which are the<br />

basis for a further analysis yielding MCD line strengths. In order to obtain information on the<br />

core hole final state | l w−1 〉, one has to decouple the photoelectron from the total photoemission<br />

final state | l w−1 ; ɛl ′ 〉. In case of the electronically similar system Gd 4f , the decoupling<br />

of the photoelectron final state has been conducted analytically by Starke (1999). 106 However,<br />

for the MCD in Eu core-level photoemission, this decoupling and an evaluation of σq<br />

JJ′<br />

of eq. (2.30) has not been published to date. Therefore, as a first step we discuss possible<br />

coupling schemes of the angular momenta in order to obtain J and m J in the following.<br />

The Eu deep core-levels couple via exchange interaction with the 4f 7 open shell, which we<br />

denote as 8 S J using the term symbol. With the initial state orbital nl ν , the final states are<br />

created via<br />

∣<br />

∣nl ν〉<br />

photoionization<br />

−→<br />

∣<br />

∣nl ν−1 ; 8 S J ; εl 〉 . (2.33)

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