A New Spin on Photoemission Spectroscopy Page: 93 of 259
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of a - B transitions can be found by multipole expansion: in the absence of strong spin-orbit
splitting, the magnetic dipole (M1) excitations are forbidden (due to parity), and so the
strongest contribution will be from only quadrapole (M2) or higher order terms.85 Due to
the domination of the A - p over the a - B term, we can treat the photoexcitation step as a
The last term in equation 3.2 represents spin-orbit coupling, introduced in section 1.2.3,
and can have considerable effects in determining the initial and final states. These can
lead to measurable and even large spin-polarization effects in photoelectrons through the
dominant electric dipole transition term. The mechanism which can make this occur is
better explained in section 3.2.
We have found, then, that the matrix element in equation 3.1 can be be well approxi-
(4f' HradokY'i) aO (48f'"A . pi5k 'i) (3.3)
which can be reduced to the same electric dipole matrix element as arrived at in section 2.6,
except with explicit spin dependence included in the initial and final states. As discussed
above, these transitions are spin-conserving; non-zero matrix elements can only occur for
a = an, so we can drop the i notation and remove the sum over ar in equation 3.1. So after
all our work, we find that the spin-dependence of the photoexcitation intensity is just
I(k, w, a) x 1( fl A- p. P~j')12f (w)A(k, w, a)6 (w + EK - hy). (3.4)
3.1.2 Steps two & three
Photoexcited electrons from step one must still travel through the solid and transmit
through the surface before we are able to measure them. A natural concern is the degree to
which spin polarization of the photoelectrons is maintained through steps two and three.
For non-magnetic materials, the mean free paths of electrons tend not to be spin depen-
dent, and so if photoelectrons from step one are not spin-polarized they will not gain spin
polarization through scattering in the bulk. In certain non-magnetic semiconductors, like
GaAs, the conduction band can be populated with spin-polarized carriers from excitation
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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/m1/93/: accessed April 24, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.