  The pseudo-PT symmetric Dirac equation is proposed and analyzed by using a
non-unitary Foldy-Wouthuysen transformations. A new spin operator PT symmetric
expectation value (called the mean spin operator) for an electron interacting
with a time-dependent electromagnetic field is obtained. We show that spin
magnetization - which is the quantity usually measured experimentally - is not
described by the standard spin operator but by this new mean spin operator to
properly describe magnetization dynamics in ferromagnetic materials and the
corresponding equation of motion is compatible with the phenomenological model
of the Landau-Lifshitz-Gilbert equation (LLG).
