Heavy Fermion Superconductivity in PrOs4Sb12 UCu5-xPdx

1
Tuning Unconventional CeMIn5 and PuMGa5
Superconductors
Eric Bauer Los Alamos National Laboratory Collabo
rators J. Sarrao, J. Thompson, L. Morales, N.
Curro, T. Caldwell, T. Durakiewicz, J. Joyce, A.
Balatsky, M. Graf
2
Localized-Itinerant Crossover in Pu 5f electrons
3
Conventional vs Unconventional Superconductivity

• Conventional
• Electrons pair with opposite spin and momentum
• ? is finite over entire Fermi surface
• Finite ? ? exponential T- dependence of
  physical properties below Tc
• C T1-1 e -D/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 Tc
• C T2, T1-1 T3 (line nodes)
• Magnetic impurities essential for
  superconductivity
• Magnetic (spin) fluctuations are glue ?
  
  
  
  
  
  

s-wave isotropic gap
d-wave nodes in k-space where gap vanishes
J
J
I
e-
e-
f
f
4
PuCoGa5 Superconductivity
J. L. Sarrao et al., Nature 02

• Perfect diamagnetism (small Meissner effect) and
  zero resistivity below Tc18.5 K
• C/T ? bulk superconductivity
• Assuming BCS weak coupling, ?C/?Tc1.43 ? ? 77
  mJ/molK2

5
Normal State Properties of PuCoGa5
m0.68 mB, qCW-2 K m(Pu3)0.84 mB
?(T) T4/3
PuRhGa5 has similar normal state properties and
Tc 8.7 K
6
Unconventional Superconductivity in CeCoIn5 and
PuCoGa5
R. Movshovich et al. PRL 01 F. Wastin et al.
JPCM03 E. D. Bauer et al. PRL04

• Unconventional superconductivity (power laws in
  Csc(T), ?, and 1/T1)

7
PuMGa5 CeMIn5 Tc and c/a
Monthoux Lonzarich., PRB 02
Bauer et al. PRL 04

• CeMIn5 PuMGa5 isostructural but order of
  magnitude higher Tc in Pu-materials
• dlnTc/d(c/a) ?100 in both predicts PuIrGa5
  not superconducting and it is not
• Common underlying physics
• Origin of Tc ? c/a correlation in both 4f and 5f
  homologs?

8
PuMGa5 CeCoIn5 Similar T-P Phase Diagrams

• NFL normal state for CeCoIn5 and PuMGa5
• T-P phase diagrams difficult to reconcile with
  phonon mediated superconductivity
• Similar diagram to CeIn3
• Tuning of relevant spin fluctuations
• (Magnetically mediated superconductivity)

CeCoIn5 bandwidth tuning PuCoGa5, Tc 2.3 K
? 18.5 K
Sidorov et al. PRL 01, Griveau et al. ICM
(2003), Bauer et al. PRL (2004)
9
Energy Scale Tuning in CeCoIn5 AMGa5

• S-shape of r(T) curve suggests role of spin
  fluctuations important
• Increase in bandwidth may be responsible for
  large increase in Tc

10
NMR Spin Singlet Superconductor

• Cooper pairs have singlet pairing
  cspin ( ??gt - ??gt ) /?2
• Odd parity under particle exchange
• To satisfy Fermi statistics, y(r) must have even
  parity L 0, 2, (s-, d-, wave)
• Finite residual spin susceptibility from
  impurities (radioactive decay)

(N. Curro, Nature 05)
Cooper pair y(r) cspin
11
Spin Lattice Relaxation
Power law behavior T1-1 T3
Most likely a d-wave superconductor!

• Power law behavior of normal state T1-1 ?
  Proximity to AFM QCP (T. Moriya,85,96)

Sakai 05
12
Scaling of Normal and Superconducting States
(S. Nakamura,96)
Curro et al. Nature 05

• Single energy scale Tsf (or TK) largely
  responsible for pairing mechanism

T1T scales with T/Tc

• s-wave T1T constant (Fermi liquid)
• d-wave T1T (T T0)b (Antiferromagnetic
  fluctuations)

13
Conclusions

• Plausible relation among
• CeIn3 ? CeCoIn5 ? PuCoGa5
• CeIn3 layering CeCoIn5,
• Tc 0.2 K ? 2.3 K
• CeCoIn5 bandwidth tuning PuCoGa5,
• Tc 2.3 K ? 18.5 K
• d-wave (magnetically mediated) superconductivity
  in PuCoGa5
• Continuum of energy scales in AFM mediated
  mechanism of superconductivity

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15
mSR Results
G. Morris et al., (2005)

• No evidence for static (ordered) magnetic
  moment in superconducting state (ZF mSR)
• No evidence for time-reversal symmetry breaking
  SC state

• Penetration depth increases with decreasing T
  down to 3 K
• ? consistent with unconventional (d-wave)
  superconductivity

16
5f Configuration Photoemission and Models

• For high Z elements, especially 5fs, with less
  than half-filled f-shell, expect sextet to be
  filled as shown with increasing f-count

T. Hotta and K. Ueda PRB 03 T. Maehira et al.,
PRL 03
Ce3 4f1
U3 5f3
Pu3 5f5
Np3 5f4

• j-j coupling scheme ? Pu3 hole analog of Ce3,
  and, consequently, expect similar Fermi surfaces
  for isoelectronic Ce-based homologs of PuCoGa5

17
Fermi Surfaces of CeCoIn5 ACoGa5 (A U, Np, Pu)
R. Settai et al., JPCM 01
PuCoGa5
CeCoIn5
UCoGa5

• Quasi-2D Fermi surfaces in CeCoIn5 and PuCoGa5
• Fermi-surface topology different for UCoGa5 and
  NpCoGa5
• -- Larger volume (itinerant behavior)
• -- more 3D-like

NpCoGa5
T. Maehira et al., PRL 03 I. Opahle and P. M.
Oppeneer, PRL 03
18
Prospects for Applied Superconductivity

• Large magnetic irreversibility in aged PuCoGa5
  even at Tgt0.9Tc
• Estimate Jc from M(H) and Bean model
• Jcgt104 A/cm2

• Competitive performance for superconductor
  applications
• Due to radiation-induced self-damage,
• Tc decreases, Jc increases with time

19
Total Energy Calculations
J. M. Wills, unpublished

• ? 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

20
Magnetically Mediated Superconductivity
CeIn3

• Ambient pressure antiferromagnet, TN10 K
• Non-Fermi liquid normal state near QCP
• Tc 200 mK at 25 kbar
• Evidence for unconventional superconductivity in
  1/T1
• (Kawasaki et al.)

N.D. Mathur et al., Nature (1998)
21
Unconventional Superconductivity in CeCoIn5

• Unconventional superconductivity
• (power laws in Csc(T), ?, and 1/T1)
• 4-fold modulation of ? for H ab-plane
• Consistent with d-wave symmetry
• (Izawa et al. PRL 01)

CeMIn5
22
Generalized Doping-Temperature Phase Diagram
Pagliuso et al.
G.-q. Zheng et al.

• 1/T1 measured on same NQR line for all T ?
  coexistence of superconductivity and magnetism
• Single T1 below TN ? spatially homogeneous SC

CeCoIn5
CeRhIn5
CeIrIn5
CeCoIn5
23
CeMIn5 Tc and c/a
CeMIn5

• Structural tuning of relevant spin fluctuations
  responsible for superconductivity
• CeIn3 layering CeCoIn5
• ? Tc 0.2 K ? 2.3 K

Monthoux Lonzarich., PRB 02
24
Outline

• Introduction
• Superconducting and normal state properties of
  PuCoGa5
• Similarity to CeMIn5 (MCo, Rh, Ir)
  heavy-fermion superconductors
• Two ways to enhance superconducting properties
  in 115 materials
• Evidence for magnetically mediated
  superconductivity in PuCoGa5
• PuCoGa5 a bridge between heavy-fermion and
  high-Tc superconductors
• Conclusions

25
Quantum Criticality
Non Fermi Liquid (unusual metal)
T
(Anti-) Ferromagnet
SC?
Fermi Liquid (simple metal)
d (x, P, etc.)
dc

• Unusual T-dependences of properties at low-T
  (non-Fermi Liquid)

Localized f-electrons
Itinerant f-electrons
Quantum Critical Point
26
Quantum Criticality
J. Custers et al., Nature (2003)
n

M. Jaime et al., (2003)
Unusual low-T behavior
Emergence of exotic phases
rr0ATn
R. B. Laughlin et al., Adv. Phys. (2001)
27
Itinerant/Localized Behavior in ACoGa5
AmCoGa5 Localized Paramagnet
NpCoGa5 Itinerant AFM
UCoGa5 TIP
J. Joyce PRL, 03

• Agreement with calculated PES, assuming 4 of 5
  5fs localized in a magnetic singlet and
  itinerant 1 5f

PuCoGa5 Itinerant/Localized SC
28
Structural Tuning of CeMIn5 AMGa5 (A U, Np,
Pu)
Sarrao et al. Physica B 05

• Slope of linear relation between tetragonality t
  (2zc-a)/a and Tc order of magnitude higher in
  PuMGa5 compared to CeMIn5
• ? factor of 10 increase in Tc likely due to
  increased hybridization in Pu-materials
• Magnetic structure and TN of UMGa5 NpMGa5 of
  depend crucially on t (Kaneko PRB 03,
  Hotta PRB 03)

29
PuCoGa5 Superconductivity

• Estimates of g
• DC/Tc? g 100 mJ/molK2
• dHc2/dT ? g 160 ? g 100 mJ/molK2
• Sel(T) ? g 80
• Power law in SC specific heat
• Csc a T2 (5.3 K lt T lt 7.2 K)

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31
Heavy Fermions

• Ce, Pr, Yb, U-based intermetallic compounds
• Large electronic specific heat coefficient C/T
  g 1 J/mol K2
• g a N(EF) a m a 1/TK
• Kondo effect believed to be origin of
  heavy-fermion behavior

32
UCoGa5 Temperature Independent Paramagnet

• Weak T-dependence of c(T)
• T2 behavior of r(T)
• Small electronic specific heat g 20
  mJ/mol K2