Magnetic instabilities in unconventional superconductors

We discuss how an unconventional superconductor, in zero applied magnetic field, can be subject to a magnetic instability if the parameters in the Ginzburg-Landau functional are in the appropriate range. In the instability, the order parameter distorts and generates a supercurrent; this supercurrent generates a magnetic field, which then lowers the free energy through its interaction with the order parameter. We discuss the compatibility of this instability with the fundamental constraints on the parameters in the free-energy functional.