Eric Bauer Los Alamos National Laboratory Collaborators: J. Sarrao, J. Thompson, L. Morales, N. Curro, T. Caldwell, T. Durakiewicz, J. Joyce, A. Balatsky, M. Graf Tuning Unconventional CeMIn 5 and PuMGa 5 Superconductors

Localized-Itinerant Crossover in Pu 5f electrons

Conventional Electrons pair with opposite spin and momentum  is finite over entire Fermi surface Finite   exponential T- dependence of physical properties below T c C ~ T 1 -1 ~ e -  /kT Superconductivity destroyed by magnetic impurities BCS theory  electron- lattice interaction is “glue” Unconventional Electrons pair with more complicated spin/momentum relationships  is zero over certain parts of Fermi surface Gap zeros  power law dependence of physical properties below T c C ~ T 2, T 1 -1 ~ T 3 (line nodes) Magnetic “impurities” essential for superconductivity Magnetic (spin) fluctuations are “glue” ? Conventional vs Unconventional Superconductivity s-wave: isotropic gap kxkx kyky Fermi surface  kxkx kyky d-wave: nodes in k-space where gap vanishes J I J e-e- f e-e- f

PuCoGa 5 Superconductivity Perfect diamagnetism (small Meissner effect) and zero resistivity below T c =18.5 K C/T  bulk superconductivity Assuming BCS weak coupling,  C/  T c =1.43   =77 mJ/molK 2 J. L. Sarrao et al., Nature ‘02

Normal State Properties of PuCoGa 5  =0.68  B,  CW =-2 K  (Pu 3+ )=0.84  B PuRhGa 5 has similar normal state properties and T c = 8.7 K  (T) ~ T 4/3

Unconventional Superconductivity in CeCoIn 5 and PuCoGa 5 Unconventional superconductivity (power laws in C sc (T), к, and 1/T 1 ) R. Movshovich et al. PRL ‘01 F. Wastin et al. JPCM’ 03 E. D. Bauer et al. PRL’04

PuMGa 5 & CeMIn 5 : T c and c/a CeMIn 5 & PuMGa 5 isostructural but order of magnitude higher T c in Pu-materials dlnT c /d(c/a)  100 in both; ‘predicts’ PuIrGa 5 not superconducting and it is not Common underlying physics Origin of T c  c/a correlation in both 4f and 5f homologs? Bauer et al. PRL ‘04 2D 3D 2D 3D Monthoux & Lonzarich., PRB ‘02

PuMGa 5 & CeCoIn 5 : Similar T-P Phase Diagrams NFL normal state for CeCoIn 5 and PuMGa 5 T-P phase diagrams difficult to reconcile with phonon mediated superconductivity Similar diagram to CeIn 3 Tuning of relevant spin fluctuations (Magnetically mediated superconductivity) Sidorov et al. PRL ‘01, Griveau et al. ICM (2003), Bauer et al. PRL (2004) CeCoIn 5 + bandwidth tuning = PuCoGa 5, T c : 2.3 K  18.5 K

Energy Scale Tuning in CeCoIn 5 & AMGa 5 “S”-shape of  (T) curve suggests role of spin fluctuations important Increase in bandwidth may be responsible for large increase in T c T max (K) CeCoIn 5 50 PuCoGa UCoGa  (mJ/mol K 2 )

NMR: Spin Singlet Superconductor Cooper pairs have singlet pairing:  spin = ( |  > - |  > ) /  2 Odd parity under particle exchange To satisfy Fermi statistics,  (r) must have even parity: L = 0, 2, … (s-, d-, …wave) Finite residual spin susceptibility from impurities (radioactive decay) Cooper pair  (r)  spin (N. Curro, Nature ‘05)

Spin Lattice Relaxation Power law behavior: T 1 -1 ~ T 3 Most likely a d-wave superconductor! Power law behavior of normal state T 1 -1  Proximity to AFM QCP (T. Moriya,‘85,‘96) Sakai ‘05

Scaling of Normal and Superconducting States Single energy scale T sf (or T K ) largely responsible for pairing mechanism T 1 T scales with T/T c : s-wave: T 1 T ~ constant (Fermi liquid) d-wave: T 1 T ~ ( T – T 0 )  (Antiferromagnetic fluctuations) (S. Nakamura,‘96) Curro et al. Nature ‘05

Conclusions Plausible relation among CeIn 3  CeCoIn 5  PuCoGa 5 CeIn 3 + layering = CeCoIn 5, T c : 0.2 K  2.3 K CeCoIn 5 + bandwidth tuning = PuCoGa 5, T c : 2.3 K  18.5 K d-wave (magnetically mediated) superconductivity in PuCoGa 5 Continuum of energy scales in AFM mediated mechanism of superconductivity

(0) =2500 A BCS No evidence for static (ordered) magnetic moment in superconducting state (ZF  SR) No evidence for time-reversal symmetry breaking SC state G. Morris et al., (2005)  SR Results Penetration depth increases with decreasing T down to 3 K  consistent with unconventional (d-wave) superconductivity

5f Configuration: Photoemission and Models Ce 3+ 4f 1 U 3+ 5f 3 Pu 3+ 5f 5 Np 3+ 5f 4 T. Hotta and K. Ueda PRB ‘03 T. Maehira et al., PRL ‘03 J. Joyce PRL, ‘03 Agreement with calculated PES, assuming 4 of 5 5f’s localized in a magnetic singlet and itinerant 1 5f For high Z elements, especially 5f’s, with less than half-filled f-shell, expect sextet to be filled as shown with increasing f-count j-j coupling scheme  Pu 3+ hole analog of Ce 3+, and, consequently, expect similar Fermi surfaces for isoelectronic Ce-based homologs of PuCoGa 5

Fermi Surfaces of CeCoIn 5 & ACoGa 5 (A = U, Np, Pu) Quasi-2D Fermi surfaces in CeCoIn 5 and PuCoGa 5 Fermi-surface topology different for UCoGa 5 and NpCoGa 5 -- Larger volume (itinerant behavior) -- more 3D-like R. Settai et al., JPCM ‘01 T. Maehira et al., PRL ‘03 I. Opahle and P. M. Oppeneer, PRL ‘03 CeCoIn 5 UCoGa 5 NpCoGa 5 PuCoGa 5

Large magnetic irreversibility in aged PuCoGa 5 even at T>0.9T c Estimate J c from M(H) and Bean model J c >10 4 A/cm 2 Competitive performance for superconductor applications Due to radiation-induced self-damage, T c decreases, J c increases with time Prospects for Applied Superconductivity

 as with  -Pu, minimum total energy with correct cell volume when 4 of Pu’s 5f electrons are localized -- consistent with photoemission results  also, total energy lowest for AFM/FM states (I. Opahle and P. M Oppeneer)  neglects potential role of Kondo or similar many-body effects J. M. Wills, unpublished Total Energy Calculations

N.D. Mathur et al., Nature (1998) CeIn 3 Ambient pressure: antiferromagnet, T N ~10 K Non-Fermi liquid normal state near QCP T c ~ 200 mK at 25 kbar Evidence for unconventional superconductivity in 1/T 1 (Kawasaki et al.) Magnetically Mediated Superconductivity

Unconventional Superconductivity in CeCoIn 5 Unconventional superconductivity (power laws in C sc (T), к, and 1/T 1 ) 4-fold modulation of к for H|| ab-plane Consistent with d-wave symmetry (Izawa et al. PRL ‘01) CeMIn 5 kxkx kyky Fermi surface

CeCoIn 5 CeRhIn 5 CeIrIn 5 CeCoIn 5 Generalized Doping-Temperature Phase Diagram Pagliuso et al. G.-q. Zheng et al. 1 /T 1 measured on same NQR line for all T  coexistence of superconductivity and magnetism Single T 1 below T N  spatially homogeneous SC

CeMIn 5 : T c and c/a Structural tuning of relevant spin fluctuations responsible for superconductivity CeIn 3 + layering = CeCoIn 5  T c : 0.2 K  2.3 K CeIn 3 CeMIn 5 2D 3D 2D 3D Monthoux & Lonzarich., PRB ‘02

Outline Introduction Superconducting and normal state properties of PuCoGa 5 Similarity to CeMIn 5 (M=Co, Rh, Ir) heavy-fermion superconductors Two ways to enhance superconducting properties in 115 materials Evidence for magnetically mediated superconductivity in PuCoGa 5 PuCoGa 5 a bridge between heavy-fermion and high-T c superconductors Conclusions

Quantum Criticality Unusual T-dependences of properties at low-T (non-Fermi Liquid): NFL  (T) -ln(T), T n C(T)/T -ln(T), T n  (T) T n (n<2) Fermi Liquid (FL)    0  0 + AT 2 Quantum Critical Point  (x, P, etc.) cc Localized f-electrons Itinerant f-electrons Fermi Liquid (simple metal) Non Fermi Liquid (unusual metal) T SC?

Quantum Criticality Emergence of exotic phases Pseudogap FL SC YBa 2 Cu 3 O 7-  AFI Sr 3 Ru 2 O 7 B//c T (K) n    R. B. Laughlin et al., Adv. Phys. (2001)  =  0 +AT n Unusual low-T behavior n M. Jaime et al., (2003) J. Custers et al., Nature (2003)

Itinerant/Localized Behavior in ACoGa 5 UCoGa 5 : TIP NpCoGa 5 : Itinerant AFM PuCoGa 5 : Itinerant/Localized SC AmCoGa 5 : Localized Paramagnet Itinerant Localized J. Joyce PRL, ‘03 Agreement with calculated PES, assuming 4 of 5 5f’s localized in a magnetic singlet and itinerant 1 5f

Structural Tuning of CeMIn 5 & AMGa 5 (A = U, Np, Pu) Slope of linear relation between tetragonality t = (2zc-a)/a and T c order of magnitude higher in PuMGa 5 compared to CeMIn 5  factor of 10 increase in T c likely due to increased hybridization in Pu-materials Magnetic structure and T N of UMGa 5 & NpMGa 5 of depend crucially on t (Kaneko PRB ‘03, Hotta PRB ‘03) Sarrao et al. Physica B ‘05

PuCoGa 5 : Superconductivity Estimates of  :  C/T c  mJ/molK 2 dH c2 /dT    mJ/molK 2 S el (T)  Power law in SC specific heat: C sc  T 2 (5.3 K < T < 7.2 K)

Heavy Fermions Ce, Pr, Yb, U-based intermetallic compounds Large electronic specific heat coefficient C/T =  1 J/mol K 2  N(E F )  m*  T K Kondo effect believed to be origin of heavy-fermion behavior Compound  mJ/mol K 2 ) CeCu 2 Si CeRhIn PrInAg YbBiPt8000 UBe URu 2 Si Na 1

UCoGa 5 : Temperature Independent Paramagnet Weak T-dependence of  (T) T 2 behavior of  (T) Small electronic specific heat:  ~ 20 mJ/mol K 2