Magnetic ratchets -- two-dimensional systems with superimposed non-centrosymmetric ferromagnetic gratings -- are considered theoretically. It is demonstrated that excitation by radiation results in a directed motion of two-dimensional carriers due to pure orbital effect of the periodic magnetic field. Magnetic ratchets based on various two-dimensional systems like topological insulators, graphene and semiconductor heterostructures are investigated. The mechanisms of the electric current generation caused by both radiation-induced heating of carriers and by acceleration in the radiation electric field in the presence of space-oscillating Lorentz force are studied in detail. The electric currents sensitive to the linear polarization plane orientation as well as to the radiation helicity are calculated. It is demonstrated that the frequency dependence of the magnetic ratchet currents is determined by the dominant elastic scattering mechanism of two-dimensional carriers and differs for the systems with linear and parabolic energy dispersions.
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