Spin effects on the cyclotron frequency for a Dirac electron

TL;DR

This paper investigates how the spin of a Dirac electron influences its cyclotron frequency in a magnetic field, revealing spin-dependent variations from the classical cyclotron frequency.

Contribution

It extends the Barut--Zanghi classical spinning electron model to include external magnetic fields, deriving a spin-dependent correction to the cyclotron frequency.

Findings

Electron's angular velocity depends on spin orientation.

Electrons with magnetic moment parallel to the magnetic field rotate faster.

Spin effects cause slight deviations from classical cyclotron frequency.

Abstract

The Barut--Zanghi (BZ) theory can be regarded as the most satisfactory picture of a classical spinning electron and constitutes a natural "classical limit" of the Dirac equation. The BZ model has been analytically studied in some previous papers of ours in the case of free particles. By contrast, in this letter we consider the case of external fields, and a previously found equation of the motion is generalized for a non-free spin-1/2 particle. In the important case of a spinning charge in a uniform magnetic field, we find that its angular velocity (along its circular orbit around the magnetic field direction) is slightly different from the classical "cyclotron frequency" eH/m which is expected to hold for spinless charges. As a matter of fact, the angular velocity results to depend on the spin orientation. As a consequence, the electrons with magnetic moment mu parallel to the magnetic field do rotate with a frequency greater than that of electrons endowed with mu antiparallel to H.