media with a high characteristic impedance z$_{0}$ ≥ 50Ohm, the field is negligible at the rear film surface (see Eq.(44) and Fig. 7 in Ref.[14]). The derivation of this result is not trivial, and details can be found in Ref. [14]. (See also Eqs.(3-4) in the present paper.) It is important to note that the microwave shielding effect is not seen in the cavity FMR measurements, as the microwave magnetic field of the cavity is incident on both SSDF surfaces (see Eq.(4.1) in Ref.[24]). As a result the total microwave magnetic field inside an SSDF sample is close to homogeneous. If there is no magnetization pinning at the film surfaces, the fundamental mode only displays an FMR response. Intensities for higher- order SSWMs are observable in the cavity FMR only for samples with a very high level of asymmetry; e.g. with spins almost pinned at one of the film surfaces. The enhanced inhomogeneity originates from an extension of the classical skin depth effect to samples of finite thicknesses (see [25] and references therein). The phase of the back-reflection of the total microwave magnetic field from the boundary between two media with a large difference in values of electric conductivity is important for such samples. The total microwave magnetic field incident on the rear surface interferes destructively with the back reflected field. As a result, the usual skin-depth law | h$_{t}$ ( y ) | ∝ exp ( − √ ( iσω ) y ) which is valid for for the half-space is modified. For a single layer of thickness L the expression is h$_{tx}$ ( y ) ∝ sinh ( √ ( iσω )( y − L )), where y = 0 is the coordinate for the film surface facing the transducer and and y = L is for the rear film surface. For films which are much thinner than the classical microwave skin depth this expression reduces to a linear function h$_{tx}$ ( y ) ∝ ( y − L ) /L . From this formula one sees that the total microwave magnetic field inside the samples is indeed highly inhomogeneous and strongly asymmetric. Since magnetization precession is driven by the total field, conditions are thereby formed for efficient excitation of non-uniform eigenmodes of precession. If eigenmodes of the system lack inversion symmetry the SSDF broadband FMR response will depend on layer ordering with respect to the direction of the incident microwave flux. For single films absorption by the first SSWM with odd symmetry is most strongly affected. For insulating samples with unpinned surface spins this mode is not seen in FMR spectra. Our experiments demonstrate that the situation is quite different for conducting films, and this mode can even provide the largest response. We note also that efficient excitation of high order modes was previously seen in experiments on a thicker sample in Ref.[37] (see Fig.5 in that paper). 14