Microwave mode of a two dimensional electron system in a spatially varying magnetic field

We find a resonance in the microwave absorption spectrum of a high mobility two dimensional electron system (2DES) in a spatially varying magnetic field produced by a long ferromagnetic cylinder of Dy placed, with its axis perpendicular to the 2DES, on the surface of the sample. An external field B$_{0}$ perpendicular to the 2DES is also applied. The resonance is present for B$_{0}$ less than about 0.5 T, and depends hysteretically on B$_{0}$, apparently due to the Dy magnetization. The resonance peak frequency, f$_{pk}$, decreases with B$_{0}$, and is about 1.4 GHz for a 1 mm diameter cylinder and B$_{0}$=0.2 T. For sufficiently large B$_{0}$, f$_{pk}\sim $1/ B$_{0}$, reminiscent of an edge magnetoplasmon [1]. This work is supported by MARTECH. [1] See for example, V. A. Volkov and S. A. Mikhailov, Sov. Phys.-JETP \textbf{67}, 1639(1988).