A New Spin on Photoemission Spectroscopy Page: 92 of 259
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structures of ferromagnets to have a spectral response to the removal of an electron depen-
dent on its spin. This is expressed as the spin-dependence of the spectral function term,
A(k, w, a) = Z (4'-1 ck ) 2 (L - EN-1 + EN). Spin-polarization can also arise in
non-ferromagnetic systems from the matrix element term in equation 3.1 through dipole
The matrix elements were investigated using a spinless Hamiltonian of Schrbdinger form
in section 2.6. Here we begin with a proper Dirac form which takes the electron spin into
1 e 2 eh ieh eh
H 2me ( c} +e 2m o axA + 4mec2 E p 4mec2(Exp) (3.2)
where a is the vector of Pauli matrices used to represent the electron spin (using the
notation from section 1.2 we have S = ia). The first two terms were used previously in
section 2.6, and the fourth term is a relativistic energy correction, which we can ignore here.
The first two terms can be again reduced to the electric dipole A - p perturbation term as
in section 2.6. Electric dipole transitions are spin-conserving; (O 'fA - p o>7i 0 only
when a = a2.
The third term, which can be written as - 2mn a- B, represents the direct coupling
between the spin and the magnetic field. Photoexcitation through this term (where B is
the magnetic field of the incident radiation) leads to spin-flip transitions where the electron
spin is switched. In fact, with circularly polarized light of positive helicity, only initial state
electrons with spin-down (along the light propagation direction) can be excited and get
flipped to spin-up final state photoelectrons, and vice versa for light of negative helicity.85
This seems to lead to 100% spin polarized photoemission even from non-magnetic samples.
The cross section for these magnetic transitions to occur, however, need to be compared with
the other terms of equation 3.2. An early calculation86 estimates that the ratio of spin-flip
ao-B transitions to spin-conserving A-p transitions go as ~ hv/(mec2). At by = 100 eV, this
means spin-flip transitions will be only 0.02% as likely as spin-conserving ones. This ratio
can increase in geometries where the A - p matrix elements vanish (section 2.6), however
the a - B matrix elements will still be quite small resulting in little total photoemission to
practically measure. A somewhat intuitive explanation for the relatively small probability
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Jozwiak, Chris. A New Spin on Photoemission Spectroscopy, thesis or dissertation, December 1, 2008; United States. (https://digital.library.unt.edu/ark:/67531/metadc1014237/m1/92/: accessed April 19, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.