  A model for 3:2 high-frequency quasi-periodic oscillations (HFQPOs) with 3:2
pairs observed in four black hole X-ray binaries (BHXBs) is proposed by
invoking the epicyclic resonances with the magnetic connection (MC) between a
spinning black hole (BH) with a relativistic accretion disc. It turns out that
the MC can be worked out due to Poynting-Robertson cosmic battery (PRCB), and
the 3:2 HFQPO pairs associated with the steep power-law states can be fitted in
this model. Furthermore, the severe damping problem in the epicyclic resonance
model can be overcome by transferring energy from the BH to the inner disc via
the MC process for emitting X-rays with sufficient amplitude and coherence to
produce the HFQPOs. In addition, we discuss the important role of the magnetic
field in state transition of BHXBs.
