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We model the magnetic ratchet effect in bilayer graphene in which a dcelectric current is produced by an ac electric field of frequency $\omega$ inthe presence of a steady in-plane magnetic field and inversion-symmetrybreaking. In bilayer graphene, the ratchet effect is tunable by an externalmetallic gate which breaks inversion symmetry. For zero in-plane magneticfield, we show that trigonal warping and inversion-symmetry breaking are ableto produce a large dc valley current, but not a non-zero total dc chargecurrent. For the magnetic ratchet in a tilted magnetic field, the perpendicularfield component induces cyclotron motion with frequency $\omega_c$ and we findthat the dc current displays cyclotron resonance at $\omega_c = \omega$,although this peak in the current is actually smaller than its value at$\omega_c = 0$. Second harmonic generation, however, is greatly enhanced byresonances at $\omega_c = \omega$ and $\omega_c = 2\omega$ for which thecurrent is generally much larger than at $\omega_c = 0$.

Cyclotron resonance of the magnetic ratchet effect and second harmonic generation in bilayer graphene