Josephson-type oscillations in a moving charge-density wave interacting with magnetic impurities

The theory of Josephson-type oscillations in a moving charge-density wave proposed by Barnes and Zawadowski is extended to include the interaction with spin-$\frac{1}{2}$ magnetic impurities in the presence of a constant magnetic field. The current oscillations of the Josephson type are found to exhibit a magnetic field dependence providing that the conduction electron and impurity $g$ factors are different. This effect could be used experimentally to distinguish between classical and Josephson-type contributions to the narrow-band noise in materials such as Nb${\mathrm{Se}}_3$ and Ta${\mathrm{S}}_3$ doped with magnetic impurities.