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2.5. Magnetic circular dichroism in core-level photoemission 29
2.5. Magnetic circular dichroism in core-level photoemission
Dichroism is derived from Greek and means the “effect of two colors”, originally used for
natural materials showing two colors due to surface effects. The magnetic circular dichroism
(MCD) uses circularly polarized light for excitation and is caused by a directional symmetry
breaking. This can be a magnetic order in the solid. In contrast to itinerant ferromagnets
(e. g. Fe), the “magnetic” open shell in EuO is localized and treated as a core-level in terms
of photoemission spectroscopy. The well-understood core-level photoemission and the completely
available MCD theory render the MCD effect in Eu core-level photoemission an ideal
tool for investigations of tunable effects on the magnetic interaction in EuO thin films: biaxial
strain, stoichiometry, etc. By using hard X-ray photoemission, the MCD effect can be
analyzed at a selected information depth down to 20 nm, thus providing insight into buried
magnetic layers and interfaces.
In this section, we first introduce the basic theory of MCD in photoemission. We proceed
with a simple example: MCD in 2p core-level photoemission. Finally, coupling schemes of
the angular momenta of the Eu photoemission final states are discussed, as a first step for a
future determination of the line strengths in MCD of Eu core-level photoemission spectra.
2.5.1. Atomic multiplet theory including MCD
In order to understand the MCD effect in photoemission, we need to analyze the photoemission
process excited by circularly polarized light, thus including the magnetic quantum
number M. During the photoemission process, an electron from a core-level with w electrons
of orbital momentum l is excited into a free electron state |ɛl ′ 〉 with an orbital momentum l ′
and energy ɛ. Finally, w − 1 electrons are left in the final state configuration |l w−1 〉:
∣
∣l w〉
}{{}
|J,M〉
∆J,∆M
−→ ∣ ∣l w−1 ; ɛl ′〉 . (2.27)
}{{}
|J ′ ,M ′ 〉
The final states |J ′ , M ′ 〉 emerge via the dipole selection rules, according to:
∆J = 0, ±1 ∆M = 0, ±1. (2.28)
The photoemission spectrum is composed of the core final states |l w−1 〉 and transferred to
the detector by the photoelectron |ɛl ′ 〉. In order to quantify the MCD effect, a theoretical
prediction of photoemission line strengths is desirable. A formal description of the MCD in
core-level photoemission considers two interactions, 104 (i) intra-atomic exchange coupling,
which connects core-level spins with the magnetically aligned spins of an open shell, and (ii)
the spin–orbit interaction, which couples the orbital “magnetic” momentum of the circularly
polarized photon to the system of magnetically aligned spins of the sample. We discuss
the analytical derivation, as published in Starke (2000), 105,106 in a shortened form in the
following.
First, the total photoemission intensity is described by Fermi’s golden rule, similar to corelevel
photoemission with unpolarized light (Ch. 2.4). However, for an MCD experiment, we
Herein, ∆J = 0 is only possible if J 0, due to the enforced momentum change of the photohole l w−1 .