On dimensional cyclotron resonance

Cyclotron resonance (CR) in a metal plate whose thickness d is less than the charge-carrier mean free path l and the maximum diameter 2r of the electron orbits in a magnetic field, but considerably greater than the depth δ of electromagnetic wave penetration into the metal is investigated. New resonance frequencies originate in such conductors, which are determined by the characteristics of electrons with an orbit diameter equal to the plate dimension. The influence of the slope of the magnetic field on this dimensional CR is studied for all angles at which it can occur. For quite small slopes φ<δ/l to which CR is not generally sensitive in bulk conductors, in thin specimens d≪δl in the range of angles (d/l)2≪δ/l CR is possible only in higher approximations in the small parameter (d/l)2φ−1. In the domain of larger angles δ/l≪φ≪δ/r Doppler frequency splitting of the dimensional CR occurs. Cyclotron resonance in an oblique magnetic field has the greatest intensity in sufficiently thick conductors when d>(δl)1/2. As φ increases in such conductors, doubling of the resonance frequencies occurs in the range of angles δ/r≪φ<d/l.

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