Transcript Document

Observation of a possible Fulde-Ferrell-Larkin-Ovchinnikov
(FFLO) state in CeCoIn5
Roman Movshovich
Andrea Bianchi
Los Alamos National Laboratory, MST-10
Cigdem Capan
Filip Ronning
Pascoal Pagliuso
John Sarrao
• Fulde-Ferrell-Larkin-Ovchinnikov inhomogeneous superconductivity - competition
between superconductivity and Pauli paramagnetism.
CeCoIn5 meets all the requirements:
• Very clean heavy-fermion superconductor, most likely d-wave
• First order phase transition, phase diagram  strong Pauli limiting
• Low temperature anomaly in specific heat  second superconducting phase. FFLO?
A. Bianchi et al., Phys. Rev. Lett. 91, 257001 (2003), R. Movshovich et al., Nature 427, 802 (2004).
Superconductors,
Tc up to 2.3 K at
ambient pressure
Ce2CoIn8,
Ce2RhIn8
under pressure
Tc < 200 mK
P ~ 25 kbar
FFLO state (III) appears if certain conditions are satisfied.
(1) clean superconductor
(2) Pauli limited
(3) PL is strong enough compared
to orbital limiting: Maki
parameter  is large enough. GG:
 > 1.8
Good candidates:
• low dimensional sc (organics)
• heavy fermion sc: weak orbital
limiting.
CeCoIn5 combines both of these
properties
From Gruenberg and Gunther, Phys. Rev. Lett. 16, 996 (1966)
Pauli limiting
PL is due to the competition between Zeeman energy of electrons’s spins in the
normal state and the superconducting condensation energy. PL is mostly
pronounced for the singlet superconductivity, with S = 0, since superconducting
electrons in a pair with opposite spins can not take advantage of the Zeeman energy.
Pauli limiting will have effect of suppressing superconductivity and the
superconducting critical field.
PL field HP for s-wave BCS singlet superconductor is
HP 
0
g
2 B
2
For CeCoIn5 this formula gives HP = 4.2 T, if we use weak coupling BSC value
for 0 = 1.76 Tc and g = 2.
Problem: experimental values: Hc2 = 5 T for H || [001] and 12 T for H ||[110]!!! 
theoretical estimate of 4.2 T is unphysical since HP can not be less then
experimental value Hc2.
Solution: g  2, strong coupling.
Superconductivity is suppressed with respect to theoretical prediction
of Hc2 without PL  CeCoIn5 is Pauli limited.
CeCoIn5 – upper critical field for H II c
0.8
50
0.7
l = 0, clean limit
dHc2/dT = -66.7 (kG/K)
0.6
40
30
h
Hc2 (kG)
0.5
0.4
0.3
20
0.2
10
0.1
h = Hc2/(Tc·-(dHc2/dT IT ))
Tc = 2.27 K
0
0.0
0.5
1.0
1.5
T (K)
c
2.0
2.5
3.0
0.0
0.0
0.2
0.4
0.6
0.8
1.0
t = T/Tc
E. Helfand and N.R. Werthamer Phys.Rev. 147 313 (1967)
  T3 at low temperature  lines of nodes in the energy gap in
clean limit,
Impurity band width is less than 30 mK  very clean material.
Order of magnitude rise in /T  qp mean free path of few m.
10
CeCoIn5
2
2
/T (W/K m)
 (W/Km)
1
0.1
0.01
1
0
0.0 0.2 0.4 0.6 0.8 1.0
2
-2
2
T (10 K )
0.1
1
T (K)
10
R. Movshovich et al., PRL 86, 5152 (2001)
Symmetry of the order parameter of CeCoIn5
Pauli limiting


Specific heat
Thermal conductivity 
NQR

+
=
d-wave
CeCoIn5 – second order – first order
1.5
H || c
4.8
4.75
4.7
CP (J/mol K)
1.2
4.5
4.6
0.9
4.9
0.6
0.3
0.0
0.0
0.2
0.4
0.6
T (K)
0.8
1.0
1.2
A. Bianchi et al., PRL 89, 137002 (2002)
Magnetocaloric effect
for first order phase transition
H
dT/dHS = T/CH (-dM/dT)H
High entropy phase
Low entropy phase
Phase
Boundary
T
A. Bianchi et al., PRL 89, 137002 (2002)
A. Bianchi et al., PRL 89, 137002 (2002)
A. Bianchi et al., PRL 89, 137002 (2002)
H||[100]
H||[100]
C. Capan et al., submitted to PRB.
First order nature of the superconducting phase transition is reflected in a step in thermal
conductivity at Tc.
Conditions for formation of
the FFLO state:
(1) clean superconductor
(2) Pauli limited
(3) PL is strong wrt orbital
limiting: Maki parameter  is
large enough. GG:  > 1.8
H
  2 c 20
Hp
H c 20
dH c 2
 0.7
Tc
dT
Hp 
0
2
g
B
2
for CeCoIn5:
L. W. Gruenberg
and L. Gunther, PRL
Experimentally, for H || [001]: Hc2 = 5 T and
Hc20=13.2
T
& GG gives HP = 5.8 T, α = 3.6, T0=.35Tc
996
16,
C/T (J/mol K2)
CeCoIn5, H || [110]
(C-CSch)/T (J/mol K2)
4
12 T
11.4 T
11.2 T
11 T
10.6 T
10 T
8T
6T
1.2
T2
1.0
3
0.2
0.3
0.4
T (K)
2
1
0
0.0
(a)
0.4
0.8
1.2
1.6
2.0
2.4
A. Bianchi et al., Phys. Rev. Lett. 91, 257001 (2003)
CeCoIn5, H || [110]
4.5
10.77 T
11 T
10.51 T
Tc
4.0
2
(C-CSch)/T (J/mol K )
3.5
3.0
2.5
2.0
T2
1.5
1.0
0.5
0.0
0.2
0.4
0.6
0.8
T (K)
1.0
1.2
1.4
A. Bianchi et al., Phys. Rev. Lett. 91, 257001 (2003
CeCoIn5, C/T (J/mol K2)
11.4
0
0.5000
0.7500
11.2
1.000
1.250
11.0
1.500
2.000
10.8
2.500
H (T)
3.050
3.800
Tc
T2
10.6
5.000
10.4
10.2
10.0
9.8
0.0
0.2
0.4
0.6
0.8
1.0
1.2
T (K)
A. Bianchi et al., Phys. Rev. Lett. 91, 257001 (2003)
H. Adachi and R. Ikeda,
Phys. Rev. B 68, 186510 (2003)
Conclusions:
CeCoIn5 is a clean Type II strongly Pauli limited superconductor, as
seen from (1) the phase diagram and (2) the change of the
superconducting transition to first order at high magnetic fields close
to the superconducting critical field Hc2, as predicted by K. Maki in
1960’s.
The second phase transition within the superconducting state in the
high field-low temperature part of the phase diagram is consistent
with the formation of the inhomogeneous Fulde-Ferrell-LarkinOvchinnikov (FFLO) superconducting state predicted in 1960’s.
Needs:
• Theoretical support on the detailed predictions of various properties
of the FFLO state to compare with experiments.
• Experiments that probe directly the microscopic structure of the
FFLO state.
Specific heat C and thermal conductivity  can help to determine the
symmetry of the superconducting order parameter.
C  exp (-/T)
FS
  exp (-/T)
C  T2

FS
 
T in impurity
dominated region,
universal limit.
T3, clean limit
Cel  aT + bT2 at low temperature  lines of nodes in the energy gap
2
(C-CSch)/T (J/mol K )
0.3
In NQ Schottky
2
2
0.4
C/T (J/mol K )
0.5
1
0
0.2
0
1
2
3
T (K)
0.1
0.0
0.0
CeCoIn5
0.2
0.4
0.6
0.8
1.0
T (K)
R. Movshovich et al., PRL 86, 5152 (2001)