Doppler-Shifted Cyclotron Resonance with Helicon Waves

Abstract

Cyclotron resonance, with the static magnetic field normal to the surface of the metal, has been performed at frequencies several thousand times smaller than the electron cyclotron frequency, ω _c = eB/m. The low frequency at which resonance occurs (9 Mcps with a field of 23 kG for sodium) arises from the Doppler effect and the large difference between the Fermi velocity (~ 108 cm/sec) and the helicon wave velocity (~ 103 cm/sec). The condition for resonance is related to the Gaussian curvature at the point on the Fermi surface with the maximum component of velocity along the static magnetic field. The experiment measures the surface impedance of the metal as a function of magnetic field. The sample in the form of a plate (10 × 10 × 1 mm) is placed in a coil at liquid-helium temperatures; the inductance and the Q of the coil are measured using a Twin-T radio-frequency bridge. Measurements were made on polycrystalline sodium, potassium, and indium over the frequency range 1-50 Mcps. It is found that the magnetic field at which resonance occurs is proportional to the cube root of the frequency. The values obtained for the radius of the Fermi surface for sodium and potassium are in very good agreement with the theoretical values computed, assuming a spherical surface. The fractional width of the resonance was found to be inversely proportional to the electron mean free path.

Work supported by the U.S. Atomic Energy Commission and the Advanced Research Projects Agency.