Brian Maple (slide 1)

1. Brian Maple (slide 1) • 1. The non-Fermi liquid (NFL) characteristics in a wide range of pure and chemically substituted compounds are rather similar; e.g., • (T) ~ ± Tn (1 ≤ n ≤ 1.5) (n usually close to 1) • C(T)/T ~ -lnT, T-n (n ~ 0.2 - 0.4) • (T) ~ -lnT, T-n (n ~ 0.2 - 0.4), 1 - T~0.5 (more difficult to analyze) • ’’(q,) ~ f(/T) These NFL characteristics are found near various types of QCP’s (e.g., AFM QCP - YbRh2Si2, CeRhIn5 under pressure, CeRh1-xCoxIn5; SG QCP - U1-xYxPd3Al2, UCu5-xPdx; FM QCP - URu2-xRexSi2, CePd1-xRhx) or far away from any readily identifiable QCP (e.g., single ion QCP? - Y1-xUxPd3, Sc1-xUxPd3, U1-xThxPd3Al2). Is there a more general scenario that encompasses these situations and presently proposed mechanisms (e.g., Kondo disorder, quadrupolar Kondo, Griffith’s phase, 2nd order AFM, SG, or FM transition suppressed to 0 K, etc.)? 2. In certain materials such as Y1-xUxPd3 (first f-electron material in which NFL behavior observed), Sc1-xUxPd3, and URu2Si2, there is evidence that U is tetra-valent (contains two f-electrons), there is f-electron - conduction electron hybridization, and possibility of 3 nonmagnetic doublet ground state, setting the stage for a quadrupolar Kondo effect, which was proposed for Y1-xUxPd3. Perhaps this scenario, modified to account for interactions between U ions, can, after all, account for NFL behavior in these systems. We should reexamine this situation.

2. Brian Maple (slide 2) 3. There are several compounds in which superconductivity (SC) occurs within the ferromagnetic (FM) state (e.g., UGe2 under pressure, URhGe, UCoGe). Does the coexistence of the SC and FM occur homogeneously (e.g., triplet spin pairing) or inhomogeneously in phase-separated regions (e.g., singlet spin pairing)? Coexistence of SC and FM in UGe2 under pressure has been observed in both high purity single crystals in which the mean free path l is much longer than the SCing coherence length  and in polycrystals in which l is comparable to  with essentially the same result. The SC is optimal at a certain pressure close to the critical pressure where the FM is abruptly suppressed. 4. FM compounds under pressure generally undergo a 1st order quantum phase transition (QPT) under pressure and a 2nd order QPT under chemical substitution. Is this simply due to disorder? How much disorder is required to change the order of the QPT? How resistant to disorder is superconductivity in such systems? 5. In the URu2-xRexSi2 system, the Re substitution suppresses the “hidden order” (HO) and induces a FM phase. The onset of FM with Re concentration grows linearly with x from a QCP at x ≈ 0.15 with FM critical exponents determined from scaling of the magnetization using an Arrott-Noakes approach. NFL characteristicsare observed deep into the FM region of the phase diagram. Slide 3 shows the T-x phase diagram of the URu2-xRexSi2 system and the slope of the lnT depen-dence of C(T)/T and the exponent n of the power law dependence of (T).

3. ? Brian Maple (slide 3) URu2-xRexSi2: Evolution of critical exponents, TC and Mo with x • TC, Mo,  and (-1) extrapolate to 0 at xc = 0.15 ± 0.03 • Critical exponents deviate sub-stantially from mean field values  = 0.5, = 1,  = 3, and values describing classical FM transitions where  < 0.5 and  > 3 • NFL behavior extends into FM region • HO phase boundary can only bedetermined to x = 0.10, but extra-polates to 0 near 0.15 • AFM correlations and magnetic excitations associated with HOphase persist to x = 0.35, according to INS measurementsV. V. Krishnamurty et al., PRB (08)