Mass Enhancement and Reentrant Ground State in Magnetic Field

Three different cases of magnetic field reentrant ground states in heavy fermion systems, URhGe, UGe2 and CeRhIn5 recently studied in Grenoble, are discussed. URhGe is a ferromagnetic superconductor with reentrace of superconductivity under magnetic field (H) which is associated to the spin reorientation field. UGe2 is a ferromagnetic superconductor with an enhancement of the upper critical field Hc2 of superconductivity at its metamagnetic transition between 2 ferromagnetic phases. CeRhIn5 is a superconductor with H reentrant antiferromagnetism. We analyze the links between the H enhancement of the different contributions to the effective mass and the field reentrant phase. The unconventional superconductivity (SC) of heavy fermion compounds often occurs close to quantum singularities driven by magnetic or valence instabilities. Here we will present three cases of field reentrant phenomena linked to the interplay between field changes of their magnetic and superconducting properties. URhGe is a very nice example of ferromagnetic (FM) superconductor; i.e. i) its critical superconducting transition temperature Tsc ∼0.27 K is far below its Curie temperature TCurie ∼ 9.5 K [1], ii) applying a pressure drives the system deeper in the FM domain as shown in Fig. 1(a) [2, 3]; thus, one escapes from a FM quantum singularity where Tsc ∼ TCurie; iii) at TCurie, the Fermi surface is well formed and thus the Fermi liquid regime as AT 2 resistivity law is also well established; iv) furthermore, the rather weak magnetic anisotropy leads to the remarked phenomena that the sublattice magnetization M0 changes its alignment from the initial c-axis to the b-axis at HR ∼12 T along one of the hard axis (the b-axis) without any drastic change of M0 ∼ 0.4 μB [4]. The surprising result is that when H increases along the b-axis, the reentrant superconductivity (RSC) is observed in a rather large H window sticked to HR [4]. By a careful study of the resistivity under pressure and magnetic field, we have recently demonstrated that the SC properties can be well understood via a McMillan type formula, Tsc = T0 exp(−m ∗/m∗∗), where the effective mass m∗ is the sum of a renormalized band mass mB and of a correlated mass m∗∗ source of the SC pairing [3]. Field enhancement of m∗∗(H) will occur in the vicinity of HR, while mB appears as field and pressure invariant. Under pressure, m ∗∗(0) decreases thus Tsc(m ∗∗(0)) and the upper critical field (Hc2(0,m ∗∗(0)) decrease slowly. The RSC is strongly affected by the concomitant decrease of Tsc(m ∗∗(H)) and of Hc2 ∼ (m ∗ H) T 2 sc(m ∗ H). As predicted by our simple model, the RSC collapses at a pressure PRSC ∼ 1.5 GPa far lower than the pressure Psc where the low field SC will disappear, i.e. m ∗∗(0) will collapse. The low field SC seems to disappear only near 4 GPa (Fig. 1(b)) [3]. 0 1 2 3 4 5 0 5 10 15 0 1 2 3 4 5 0 0.1 0.2 0.3 0.4 0.5