  We exploit magnetostriction in polydisperse ferrofluids in order to generate
nonlinear responses, and apply a thermodynamical method to derive the desired
nonlinear magnetic susceptibility. For an ideal gas, this method has been
demonstrated to be in excellent agreement with a statistical method. In the
presence of a sinusoidal ac magnetic field, the magnetization of the
polydisperse ferrofluid contains higher-order harmonics, which can be extracted
analytically by using a perturbation approach. We find that the harmonics are
sensitive to the particle distribution and the degree of field-induced
anisotropy of the system. In addition, we find that the magnetization is higher
in the polydisperse system than in the monodisperse one, as also found by a
recent Monte Carlo simulation. Thus, it seems possible to detect the size
distribution in a polydisperse ferrofluid by measuring the harmonics of the
magnetization under the influence of magnetostriction.
