Microwave modes of a two dimensional electron systems in the presence of a perpendicular magnetic anisotropy provided by a macroscopic ferromagnet

We report on a resonance in the microwave absorption spectrum of a high mobility two dimensional electron system (2DES) in a spatially varying magnetic field from a ferromagnet placed near the sample. The ferromagnet, made of Dy, cylinder or plates, with a hole through it. Microwave transmission between contacts capacitively coupled to the 2DES near the hole or cylinder shows a resonant absorption peak f$_{pk}$ for holes and cylinders with varying radii, r$_{m}$, from 0.5 mm to .125 mm. The resonance absorption is present for a uniform external field B$_{o }$less than 1 T and only for specific magnetization of the ferromagnet with respect to B$_{0}$ with f$_{pk}$ decreasing as either B$_{o}$ or r$_{m}$ increase. We will interpret the data in terms of plasma excitations similar to edge magnetoplasmons [1] confined along the magnetic field inhomogeneity by the large magnetic field gradients there. [1] See, for example, V. A. Volkov and S. A. Mikhailov, Sov. Phys.-JETP \textbf{67}, 1639(1988).