Dai Aoki (CEA, Grenoble): Re-entrant superconductivity and the field-induced magnetic instability in uranium compounds

 Dai's talk was a great introduction and summary of the issues around the heavy fermion ferromagnetic superconductors. 

In his introduction, Dai showed a great diagram, attributed to Miyake, which shows the convergence of research into magnetism and superconductivity - these two areas were once viewed as mutually exclusive, but today we know that magnetism is a major driver in unconventional superconductivity.

  

The three actors on the stage are: UGe2, URhGe and UCoGe. Experimentally the fact that these materials are able to exceed the Pauli pair breaking limit for superconductivity is very suggestive that they are triplet superconductors. Dai reminded us of the old Fay and Appel paper which considered how ferromagnetic fluctuations can produce a triplet superconductor whose maximum in Tc is near the FM quantum critical point. Crucially ferromagnetic fluctuations can pair break as well as pair and according to the theory of Fay and Appel, Tc goes to zero at the critical point itself.

Aoki discussed first UGe2, and here, he showed from their experiments, that the sc is occuring in the vicinityof a tri-critical point, where the FM phase boundary switches from 2nd, to 1st order.  The vicinity to a metamagnetic QCP is important for this system, and the daughter compounds URhGe and UCoGe.

UGe2 is the "mother compound" for the other UTGe materials.  As one changes T, one finds a correlation between the linear specific heat and the U-U distance.  Thus for G=Ru, gamma~ 40mJ/mol/K^2 and dUU=3.4A, but for Rh, dUU~ 3.5A shows gamma~ 150mJ/mol/K^2. dUU~3.5A is the "Hill Limit", and beyond this value, U systems become ferromagnetic, thus for T= Ir, Ni and Pd, where dU-U rises above 3.5A, the ground-state is ferromagnetic.   Based on the Hill criterion, URhGe is teetering on the edge of ferromagnetism. This is a bit confusing, because actually, both URhGe and UCoGe are actually ferromagnets, even though dUU < 3.5A. Dai discussed the remarkable example of URhGe, which displays re-entrant superconductivity. This system has Tc~ 0.2K with an anisotropic upper critical field with Hc2 much larger than the value expected for a Pauli-limited superconductor. He argued it must therefore be a spin-triplet sc. Remarkably, if you tune up the field, URhGe becomes sc again above H=8T, and continues to be so all the way up to 12T! Dai explained that this remarkable effect arises because as one tunes the field, the system passes close to a quantum-critical end point somewhere around 10T.  The mass of the quasiparticles rises rapidly around 10T.  Using a model where m*=(1+lambda)mb, the coherence length and hence the upper-critical field of the superconductor is tuned by the field-dependent m^*, as follows:

In the regions where Hc2(H)>H, re-entrant superconductivity develops!

Aoki ended with a mystery. He showed the phase diagram of UCoGe as a function of pressure. In this system, Fm and SC co-exist, and if you tune TCurie to zero with pressure, one finds that contrary to Fay and Appel, the SC Tc is smooth around the FM QCP.  Why is this - what is different about the FM/SC interplay in this fascinating U system?