In this work, we investigate the control of quantum vacuum friction (QVF) experienced by a rotating nanosphere near a graphene sheet. Our study reveals that the friction torque of QVF acting on nanospheres can be tuned by one to two orders of magnitude through an applied magnetic field. This modulation arises from the tunable coupling between the magnetoplasmon polaritons (MPPs) of graphene and the localized surface phonon polaritons (LSPhPs) of nanospheres. Moreover, a dissipationless friction known as the axial Casimir force (ACF), is also investigated. At a low temperature, the ACF of nanospheres exhibits a quantized staircase behavior as a function the chemical potentials and magnetic fields. At room temperature, the quantization disappears, while the ACF increases by approximately five orders of magnitude. Our study of magnetic control of QVF may find applications in particle manipulations.

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• Casimir effect & related phenomena
• Surface plasmon polariton
• Graphene
• Classical electromagnetism