Anisotropic Spin Fluctuations
and Superconductivity in ‘115’
Heavy Fermion Compounds :
59Co NMR Study in PuCoGa
5
S.-H. Baek et. al.
PRL 105,217002(2010)
Kazuhiro Nishimoto
Kitaoka lab.
1
Contents
• Introduction
- History of superconductivity
- Heavy fermion system
- Transuranic HF compounds
- Motivation
•Measurement
- NMR (Nuclear Magnetic Resonance)
• Experimental Results (PuCoGa5)
• Summary
2
introduction
History of Superconductivity
Transition temperature (K)
200
metal
heavy fermion system
high-Tc cuprate
163
iron-based system
150
1911
Hg-Ba-Ca-Cu-O
（under high pressure）
Discovery of
superconducting
phenomenon
Hg-Ba-Ca-Cu-O
Tl-Ba-Ca-Cu-O
Bi-Sr-Ca-Cu-O
100
Y-Ba-Cu-O
77
1979
Heavy fermion
superconductor
1986
50
MgB2
Pb
Hg
Nb
NbC
La-Ba-Cu-O
PuCoGa5
NbGe
NbN CeCu2Si2
SmO0.9F0.11FeAs
LaO0.89F0.11FeAs
LaOFeP
0
1900 1920 1940 1960 1980 2000 2020
Year
High-Tc cuprate
superconductor
2006
Iron-based high-Tc
superconductor
3
introduction
Heavy Fermion System
What does “Heavy” mean?
Heavy Fermion system
Normal metal
＋
＋
＋
f ＋
f ＋
f ＋
＋
＋
＋
f ＋
f
f
＋
＋
c-f hybridization
( c-f 混成）
Strong electron correlation makes effective mass large.
“Heavy”
⇒ large effective mass
4
introduction
Heavy Fermion System
Example of heavy fermion superconductor compounds
CeCu2Si2 CePd2Si2
CeRh2Si2 CeIn3
CeRhIn5
PrOs4Sb12
lanthanide compounds
⇒some 4f electrons
UPt3 UPd2Al3
PuCoGa5
actinide compounds
⇒some 5f electrons
All of HF compounds have f-electrons.
5
Transuranic HF Compounds
introduction
transuranium elements (超ウラン元素)
• don’t exist in nature
• Handling is difficult because of
strong radioactivity
example : PuCoGa5 , PuRhGa5 , NpPd5Al2
6
introduction
Motivation
iso-structural superconductor
PuCoGa5 : Pu-115 compounds
5f-electron : 5個
Tc = 18.5 K
CeCoIn5 : Ce-115 compounds
4f-electron : 1個
Tc = 2.3 K
Amazingly high Tc
in HF 115 compounds
NMR study (PuCoGa5 in normal state)
• Spectra
• K (Knight shift)
• 1/T1T
7
Introduction
measurement
NMR spectra
I =1/2
m=-1/2
gℏ H0
m=+1/2
NMR Intensity
Zeeman splitting
0
ω
8
measurement
Δ𝑯
𝑯0
NMR Intensity
Knight shift
ΔH
𝐼
H
electron
H res
H0
ℋ𝑍𝑒𝑒𝑚𝑎𝑛 = −𝛾ℏ𝑰 ∙ 𝑯0 + Δ𝑯
𝜔 = 𝛾𝑯0
= 𝛾 𝑯𝑟𝑒𝑠 + Δ𝑯
= 𝛾 ∙ 𝑯𝑟𝑒𝑠(1 + 𝐾)
Knight shift
Δ𝐻
𝐾≡
𝐻𝑟𝑒𝑠
9
measurement
T1~spin-lattice relation time
Release the energy
Excitation energy
I=-1/2
I=+1/2
spin-lattice
interaction
nuclear spin
electronic spin
Energytransfer
1/T1 is quite sensitive to spin fluctuations
10
59Co
result
NMR Spectra at 19 K
Co : I =7/2
g = 10.103MHz/T
Spectra
• Quadrupole Interaction : I >1
（電気四重極相互作用）
• νQ = 1.02 MHZ
νQ
11
result
Knight shifts and 1/T1
～T3
• Knight shifts show strongly anisotropic behavior.
• At Tc both sifts drop sharply , indicating spin-singlet pairing.
Spin singlet
S=0
• 1/T1⇒d-wave superconductor
anisotropic : 異方性
12
result
1/T1T in 115 compounds
5f-electrons
PuCoGa5
LuCoGa5
PuCoGa5
LuCoGa5
5個
0個
• LuCoGa5
1/T1T = const
conduction electrons ⇒ metallic
• PuCoGa5
conduction electrons + 5f-electrons
⇒heavy fermion state
Spin fluctuations develop as temperature decrease.
Anisotropy (T1T)∥-1 / (T1T)⊥-1 reaches a maximum just above Tc .
13
result
Korringa ratio
Korringa ratio
RK > 1 ⇒ antiferromagnetic
RK ～ 1 ⇒Fermi gas
RK < 1 ⇒ ferromagnetic
From K(T) and 1/T1T ,
Rk ranges from 5 to 16
Strong AFM fluctuations
in PuCoGa5
14
result
Anisotropic nature
PuCoGa5 : tetragonal structure (a=b≠c)
new spin-lattice
relaxation rate
(1/T1T )H∥c = 2Ra
• in-plane component : Ra
• out-of-plane component : Rc
(1/T1T )H⊥c = Ra+Rc
AFM spin fluctuation is strong
In XY-plane.
15
result
Ratio of spin fluctuation energy : ρ
g n A (0)


Spin fluctuation energy : 
2R
ratio :

c
A
 c
a A a
χ″(q=Q,ω)
Ra K c (T ) Ra  a

Rc K a (T ) Rc  c
Γ
Magnetic order
ω
115 HF compounds
ρ > 1 ⇒ XY-like anisotropy
Cuprates : YBa2Cu3O7
ρ ⋍ 1 ⇒ isotropic
16
Tc versus Γa/Γc for 115 HF superconductors
result
• Reduced dimensionality could enhance Tc .
• Anisotropy Γc/Γa is a good parameter for determining Tc .
17
Summary
PuCoGa5 : 59CoNMR study in the normal state
• Spin fluctuations promote d-wave superconductivity in the
iso-structural 115 HF compounds.
• Both the Knight shift K and the spin-lattice relaxation rate 1/T1
are strongly anisotropic.
• The ratio Γc/Γa (spin fluctuation energy) is a characteristic
quantity in 115 HF compounds. This suggest the possibility
that anisotropic spin-fluctuations enhance Tc .
18
a:
71Ga
NMR spectra in 8T
b : The normal-state magnetic shift K tot of the
59Co and 71Ga(1) versus bulk susceptibility x.
c : The total magnetic shift K tot of the 59Co
and 71Ga(1) versus temperature.
1/T1 温度依存性
～T0.35
～T3
Normalized spin susceptibility in the superconducting state.
71Ga
59Co
(T 1T )-1/(T 1T )-10 versus T/Tc
(T 1T )-10 is given by the value of (T 1T )-1 at 1.25Tc
Tc versus the characteristic spin fluctuation energy T0
T0 = ΓqB2/2π
1000
Tl2Ba2Ca2Cu3O10
YBa2Cu3O6+x
100
HgBa2Ca2Cu3O8+
Tc (K)
PuCoGa5
10
CeRhIn5
1
La1.85Sr0.15CuO4
CeCoIn5
U6Fe
UBe13
UPt3
CeIrIn5
CeCu2Si2
0.1
10
UPd2Al3
URu2Si2
UNi2Al3
100
T0 (K)
1000
10000
c/a ratio of tetragonal structure parameter versus Tc
Temperature - pressure phase diagram
電気四重極相互作用
C軸となす角度
H∥c θ=0°
H⊥c θ=90°
Crystal structure in 115 compounds
遍歴的
局在的
What can we know from Knight shift ?
~Symmetry of Cooper pair~
Cooper pairing state
ψ(r1-r2;s1,s2) = Φ(r1-r2) σ (s1,s2)
orbital
orbital part
spin
spin part
even function (s, d wave) spin-singlet
Φ (-(r1-r2)) =Φ (r1-r2)
s (s2,s1) = -s (s1,s2)
S=0
s-wave
odd function (p wave)
Φ (-(r1-r2)) = －Φ (r1-r2)
spin-triplet
s (s2,s1) = s(s1,s2)
S=1
d-wave
p-wave
1/T1 in various superconductors
Conventional type (BCS)
NS(E)
NS(E)
N0
1 e
T1
s-wave
EF
EF +Δ0


k BTc
Line nodes
N0
1 T3
T1
EF
EF +Δ0
NbB2
101
d-wave
Tc=5K
1/ T1 ( sec-1 )
unconventional superconductors (non BCS)
p-wave
MgB2
100
Tc(H)
Point nodes
~T
2/kBTc=2.85
10-1
1 T5
T1
~exp(-/kBT)
2/kBTc=5
10-2
1
10
Temperature ( K )
100
EF
EF +Δ0