Cyclotron Frequency

the orbital frequency Ω of an electron in a constant magnetic field H in the plane perpendicular to H. For a free electron, the cyclotron frequency, or gyrofrequency, is given by the equation for the Lorentz force and the centrifugal force

Ω = eH/m₀c

where e is the charge of the free electron, m₀ is its mass, and c is the speed of light in vacuum. For a relativistic electron, Ω = ecH/ℰ, where ℰ is the energy of the electron.

In solids, the motion of an electron is complicated by interaction with the crystal lattice. When a current carrier, such as a conduction electron, moves in a constant magnetic field, the carrier’s energy ℰ and the projection of its quasimomentum p in the direction H(p_c) are conserved, so that in momentum space (p space) the carrier moves along a curve where the plane p_c = const, intersects the isoenergetic surface ℰ(p), If the curve is closed, the motion is periodic and occurs at the cyclotron frequency

Ω = eH/m*c

where m* is the effective mass of the conduction electron.