Persistent spin fluctuations

In summary, we showed that near a FQCP, spin fluctuation exchange gives rise to a strong first order transition into a triplet superconducting state. As a result, Tc saturates at a nonzero value at criticality. The first order transition persists up to a finite distance from the FQCP, where it becomes second order. 

Fig. 3.30. Phase diagram of the U(Pt1 Pd l)3 system. Tc ( ) and TN (o) as a function of Pd concentration up to 10 at.% of Pd. S indicates the superconducting phase, AF the antiferromagnetic phase, K the Kondo regime, and SF the spin-fluctuation region which persists into the AF region. The arrows indicate the sign of the increasing pressure effect on C> 7sF> and 7V Note the expanded scale for Pd concentrations below 0.5 at.% (Franse et al. 1987a).

In summary, the work of Yaouanc et al. (1999b) finds no magnetic phase transition, only comparatively slow paramagnetic spin fluctuations persisting down to 40 mK coupled to a strongly reduced Yb moment. 

Other samples enter into the quasistatic ordered AFM spin state. As in CeNiSn one might suspect that the persistence of spin fluctuations for T —> 0 which, on account of their independence from temperature are likely to be quantum fluctuations, are the underlying reason that AFM order does not set in. 

A preliminary report (Amato et al. 1998) presents ZF- and LF-pSR data down to 0.1K. The ZF spectra are characterized by nuclear-electronic double relaxation. The nuclear part can be suppressed in LF = 20 G. No magnetic transition was observed. Below 10 K, the electronic relaxation rate increases monotonically with decreasing temperature. Application of LF = 200 G also suppresses electronic relaxation, indicating rather slow dynamics of the spin system. From the field dependence of relaxation rate the spin fluctuation frequency was found to be V4f(r —> 0) 2.7 MHz. It appears that this is another case where spin correlations develop at low temperatures, but persistent slow spin dynamics prevent the formation of an ordered magnetic state (see CeNiSn in sect. 9.2 for comparison). 

Up to now, we have concentrated on the physics at zero kelvin. In this section, we extend the studies to finite temperatures and discuss finite temperature phase diagrams. The physics at finite temperatures is dominated by thermal fluctuations between low lying excited states of the system. These fluctuations can include spin fluctuations, fluctuations between different valence states, or fluctuations between different orbitally ordered states, if present. Such fluctuations can be addressed througih a so-called alloy analogy. If there is a timescale that is slow compared to the motion of the valence electrons, and on which the configurations persist between the system fluctuations, one can replace the temporal average over all fluctuations by an ensemble average over all possible (spatially... 

Coexistence of FM order and superconductivity under pressure The experimental phase diagram of FM collapse under pressure and simultaneous appearance of superconductivity is shown in fig. 43. The critical pressure for disappearance of FM order is pc2 = 16-17 kbar. The SC phase appears between pc = 10 kbar and pc2 = 16 kbar which is also the critical pressure for the FM-PM transition. The critical temperature Tx p) of the jc-phase hits the maximum of Tdp) at the optimum pressure pm = 12.5 kbar. As mentioned before the nature of the order parameter in the jc-phase remains elusive. The coincidence of maximum Tc with vanishing jc-phase order parameter suggests that the collective bosonic excitations of the X-phase which supposedly become soft at pm mediate superconductivity and not quantum critical FM spin fluctuations which are absent due to the persisting large FM... 

If, however, some correlation effect exists avoiding formation of excessive spin density in an atom (for instance making a state with aligned spins stable because of Hund s principle) this state of alignment in the atom may persist much longer than the band hopping time hAV of the electrons. The fluctuations, typical of the band, will tend to even out, and the electrons wiU stay in the atomic ground state of the core (localization). 

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