Lifshitz-point behaviour of ferromagnetic superconductors

The critical behaviour of the electromagnetically coupled superconductor magnet system is investigated by means of a generalized mean field theory and a renormalization group analysis. We show that in the presence of a genuine anisotropy in systems with an additional pressure-like parameter (like concentration in pseudo-ternary ferromagnetic superconductors (FMS), e.g. Er_1?x Ho _x Rh₄B₄) the indirect coupling between superconducting and magnetic order parameters (i.e. gauge coupling) can lead to a peculiar kind of critical behaviour characterized by Lifshitz points (LP). These points (quite generally) occur as merging points of three phases: a (magnetically) disordered phase, a homogeneously ordered phase and a modulated phase. In FMS the latter phase may result from exchange screening by supercurrents. This unusual critical behaviour is found in two varieties:

1. a regular LP which may occur on the lower transition line of a reentrant FMS
2. a similar but slightly different critical point which we term modified Lifshitz point (MLP), and which is to be expected at the merging point of the upper and lower superconducting transition lines with the magnetic order disorder transition lines in the (x, T) phase diagrams of FMS's.