  We report on the optical characterization of non-magnetic metal/ferromagnetic
(Co$_{20}$Fe$_{60}$B$_{20}$)/MgO heterostructures and interfaces by using mid
infrared spectroscopic ellipsometry at room temperature. We extracted for the
mid-infrared range the dielectric function of Co$_{20}$Fe$_{60}$B$_{20}$, that
is lacking in literature, from a multisample analysis. From the optical
modelling of the heterostructures we detected and determined the dielectric
tensor properties of a two-dimensional gas (2DEG) forming at the non-magnetic
metal and the CoFeB interface. These properties comprise independent Drude
parameters for the in-plane and out-of plane tensor components, with the latter
having an epsilon-near-zero frequency within our working spectral range. A
feature assigned to spin-orbit coupling (SOC) is identified. Furthermore, it is
found that both, the interfacial properties, 2DEG Drude parameters and SOC
strength, and the apparent dielectric function of the MgO layer depend on the
type of the underlying nonmagnetic metal, namely, Pt, W, or Cu. The results
reported here should be useful in tailoring novel phenomena in such types of
heterostructures by assessing their optical response noninvasively,
complementing existing characterization tools such as angle-resolved
photoemission spectroscopy, and those related to electron/spin transport.
