Order parameter symmetry in the superconducting ferromagnets UGe ₂ and URhGe

In UGe ₂, ZrZn ₂ and URhGe the co-existence of superconductivity and ferromagnetism appears to arise as a co-operative phenomena rather than as the overlap of two mutually competing orders. In all three compounds the magnetism is in intimate contact with the electronic degrees of freedom while the Curie temperatures are more than an order of magnitude higher than their critical temperatures for superconductivity. The most direct indication that the two orders are conjugate however is that the superconductivity and ferromagnetism are suppressed at the same critical pressure in both UGe ₂ and ZrZn ₂. This has motivated the recent theoretical classification of the permitted superconducting order parameter symmetries for such states. In the following we will review the experimental evidence relevant to the identification of the actual symmetries. This is followed by a discussion of the possible states allowed theoretically. Finally we discuss briefly whether the magnetic order can indeed lead to an enhancement of the superconductivity.