Nematic order in ferrofluids

With the help of a Landau free energy we discuss the phase transition from an isotropic ferrofluid to a nematic one. The latter can be either superparamagnetic or ferromagnetic. The transitions are first order and the ferromagnetic state can be reached directly from the isotropic one or via the superparamagnetic nematic one. An external magnetic field induces magnetic as well as nematic order. The transition to the ferronematic state is then via an imperfect bifurcation switching from a state of low nematic and magnetic order to one with strong nematic order and either (still) low or high magnetic order. In the latter case the director is either parallel or perpendicular to the external field (and the magnetization parallel to it) or all three directions are different (but lie in a common plane). Some hydrodynamic features of these phases are listed