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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

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Localized-Itinerant Crossover in Pu 5f electrons

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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

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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

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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

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Unconventional Superconductivity in CeCoIn 5 and PuCoGa 5 Unconventional superconductivity (power laws in C sc (T), , and 1/T 1 ) R. Movshovich et al. PRL 01 F. Wastin et al. JPCM 03 E. D. Bauer et al. PRL04

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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

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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

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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 5 375 UCoGa 5 675 (mJ/mol K 2 ) 1000 100 10

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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)

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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

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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

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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

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(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

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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 5fs localized in a magnetic singlet and itinerant 1 5f For high Z elements, especially 5fs, 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

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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

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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

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as with -Pu, minimum total energy with correct cell volume when 4 of Pus 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

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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

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

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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

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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

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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

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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