  We apply a Langevin model to investigate the nonlinear ac responses of
electro-magnetorheological (ERMR) fluids under the application of two crossed
dc magnetic (z axis) and electric (x axis) fields and a probing ac sinusoidal
magnetic field. We focus on the influence of the magnetic fields which can
yield nonlinear behaviors inside the system due to the particles with a
permanent magnetic dipole moment.
  Based on a perturbation approach, we extract the harmonics of the magnetic
field and orientational magnetization analytically. To this end, we find that
the harmonics are sensitive to the degree of anisotropy of the structure as
well as the field frequency. Thus, it is possible to real-time monitor the
structure transformation of ERMR fluids by detecting the nonlinear ac
responses.
