Magnetic effects on the phase transitions in unconventional superconductors

The effect of magnetic fluctuations on the critical behaviour of unconventional ferromagnetic superconductors (UGe2, URhGe, etc.) and superfluids is investigated by the renormalization-group method. For the case of isotropic ferromagnetic order a new unusual critical behaviour is predicted. It is also shown that the uniaxial and bi-axial magnetic symmetries produce fluctuation driven phase transitions of first order. The results can be used in interpretations of experimental data and for a further development of the theory of critical phenomena in complex systems. Experiments [1, 2] at low temperatures (T ∼ 1 K) and high pressure (P ∼ 1 GPa) demonstrated the existence of spin triplet superconducting states in the metallic compound UGe2. The superconductivity is triggered by the spontaneous magnetization of the ferromagnetic phase that occurs at much higher temperatures [3, 4, 5]. The ferromagnetic order coexists with the superconducting phase in the whole domain of its existence below T ∼ 1.2. The same phenomenon of existence of superconductivity at low temperatures and high pressure in the domain of the (T, P ) phase diagram where the ferromagnetic order is present was observed in URhGe [6]). These remarkable phenomena occur through phase transitions of first and second order and multi-critical points which present a considerable experimental and theoretical interest. A fragment of (P, T ) phase diagrams of itinerant ferromagnetic compounds [1] is sketched in fig. 1, where the lines TF (P ) and Tc(P ) of the paramagnetic(P)-to-ferromagnetic(F) and ferromagnetic-tocoexistence phase(C) transitions are very close to each other and intersect at very low temperature or terminate at the absolute zero (P0, 0). At low temperature, where the phase transition lines are close enough to each other, the interaction between the real magnetization vector M(r) = {Mj(r); j = 1, ..., m} and the complex order parameter vector of the spin-triplet Cooper pairing [10], ψ(r) = {ψα(r) = (ψ α+ iψ α);α = 1, ....n/2} (n = 6) cannot be neglected [7] and, as shown here, this interaction produces new fluctuation phenomena. In this letter a new critical behavior for this type of systems is established and described. The new critical behaviour occurs in real systems with isotropic magnetic order but does not belong to any known universality class [7]. Thus it could be of considerable experimental and theoretical interest. Due to crystal and magnetic anisotropy a new type of