Anisotropic Spin Fluctuations and Superconductivity in ‘115’ Heavy Fermion Compounds : 59Co NMR Study in PuCoGa5
Kazuhiro NishimotoKitaoka lab.
S.-H. Baek et. al.PRL 105,217002(2010)
1
Contents• Introduction - History of superconductivity - Heavy fermion system - Transuranic HF compounds - Motivation
•Measurement - NMR (Nuclear Magnetic Resonance)
• Experimental Results (PuCoGa5)
• Summary 2
under high pressure
0
50
100
150
200
SmO0.9F0.11FeAs
LaO0.89F0.11FeAs
LaOFeP
Hg-Ba-Ca-Cu-O( )Hg-Ba-Ca-Cu-O
Tl-Ba-Ca-Cu-O
Bi-Sr-Ca-Cu-O
Y-Ba-Cu-O
MgB2
NbGeNbNNbC
NbPb
high-Tc cuprate
metal
iron-based system
Tran
sitio
n te
mpe
ratu
re (K
)
1900 1920 1940 1960 1980 2000 2020
Year
Hg
La-Ba-Cu-O
Discovery of superconducting phenomenon
1911
1986
High-Tc cuprate superconductor
2006
Iron-based high-Tc superconductor
77
163
1979
Heavy fermion superconductor
CeCu2Si2
heavy fermion system
PuCoGa5
History of Superconductivityintroduction
3
Normal metal Heavy Fermion system
f
f f
ff
f
+ + +
+ + +c-f hybridization( c-f 混成)
+ + +
+ + +
What does “Heavy” mean?
“Heavy” large effective mass ⇒
Heavy Fermion Systemintroduction
Strong electron correlation makes effective mass large.
4
Heavy Fermion Systemintroduction
Example of heavy fermion superconductor compounds
UPt3 UPd2Al3
CeCu2Si2 CePd2Si2 CeRh2Si2 CeIn3 CeRhIn5 PrOs4Sb12
PuCoGa5
All of HF compounds have f-electrons.
lanthanide compounds⇒some 4f electrons
actinide compounds⇒some 5f electrons
5
transuranium elements ( 超ウラン元素 )
• don’t exist in nature• Handling is difficult because of strong radioactivity
Transuranic HF Compounds
example : PuCoGa5 , PuRhGa5 , NpPd5Al2
introduction
6
Motivation
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
introduction
iso-structural superconductor
7
m=+1/2
m=-1/2
g ℏ H0
Zeeman splitting
NM
R In
tens
ity
ω0
Introduction
I =1/2
NMR spectra measurement
8
NM
R In
tens
ity
H0HresH
HΔ
𝐼
electron
Δ𝑯
𝑯 0
Knight shiftℋ 𝑍𝑒𝑒𝑚𝑎𝑛=−𝛾ℏ 𝑰 ∙ (𝑯 0+Δ𝑯 )
Knight shift measurement
9
T1~spin-lattice relation time measurement
electronic spin
I=+1/2
I=-1/2
Excitation energy Release the energy
nuclear spinspin-lattice interaction Energy-
transfer
1/T1 is quite sensitive to spin fluctuations
10
59Co NMR Spectra at 19 K result
Co : I =7/2 g = 10.103MHz/T
νQ
• Quadrupole Interaction : I >1 (電気四重極相互作用)• νQ = 1.02 MHZ
Spectra
11
Knight shifts and 1/T1result
• Knight shifts show strongly anisotropic behavior.
• At Tc both sifts drop sharply , indicating spin-singlet pairing.
• 1/T1 d-wave superconductor ⇒ S=0
Spin singlet
anisotropic : 異方性
~ T3
12
1/T1T in 115 compounds result
• LuCoGa5
1/T1T = constconduction electrons ⇒ metallic
• PuCoGa5 conduction electrons + 5f-electrons⇒heavy fermion state
Anisotropy (T1T)∥-1 / (T1T)⊥
-1 reaches a maximum just above Tc .
PuCoGa5
PuCoGa5 LuCoGa5
5f-electrons 5 個 0 個
LuCoGa5
Spin fluctuations develop as temperature decrease.
13
Korringa ratio result
Korringa ratio
RK > 1 ⇒ antiferromagneticRK ~ 1 Fermi gas⇒RK < 1 ⇒ ferromagnetic
From K(T) and 1/T1T ,Rk ranges from 5 to 16
Strong AFM fluctuations in PuCoGa5
14
Anisotropic nature result
PuCoGa5 : tetragonal structure (a=b≠c)
new spin-lattice relaxation rate
• in-plane component : Ra
• out-of-plane component : Rc
(1/T1T )H c ∥ = 2Ra (1/T1T )H c ⊥ = Ra+Rc
AFM spin fluctuation is strong In XY-plane.
15
Ratio of spin fluctuation energy : ρ result
115 HF compoundsρ > 1 ⇒ XY-like anisotropy
Cuprates : YBa2Cu3O7 ρ 1⋍ ⇒ isotropic
gR
An2
)0(Spin fluctuation energy :
c
a
c
a
a
c
c
a
a
c
RR
TKTK
RR
)()(
AA
a
c
ratio :
χ″(q=Q,ω)
ω
Γ
16
Magnetic order
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
• 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 .
PuCoGa5 : 59CoNMR study in the normal state
18
a : 71Ga NMR spectra in 8Tb : 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.
59Co
71Ga
(T 1T )-1/(T 1T )-10 versus T/Tc
(T 1T )-10 is given by the value of (T 1T )-1
at 1.25Tc
10 100 1000 100000.1
1
10
100
1000
HgBa2Ca
2Cu
3O
8+
Tl2Ba
2Ca
2Cu
3O
10
YBa2Cu
3O
6+x
La1.85Sr0.15CuO4
PuCoGa5
U6Fe
URu2Si
2
UPd2Al
3
UNi2Al
3
CeCoIn5
CeCu2Si
2
UBe13
UPt3
CeRhIn5
CeIrIn5
T c
(K)
T0 (K)
Tc versus the characteristic spin fluctuation energy T0
T0 = ΓqB2/2π
c/a ratio of tetragonal structure parameter versus Tc
Temperature - pressure phase diagram
C 軸となす角度H c θ=0°∥H c θ=90°⊥
電気四重極相互作用
Crystal structure in 115 compounds
遍歴的 局在的
Cooper pairing state
ψ(r1-r2;s1,s2) = Φ(r1-r2) σ (s1,s2)
orbital spin
What can we know from Knight shift ? ~Symmetry of Cooper pair~
s-wave d-wave
p-wave
orbital part spin part
even function (s, d wave)Φ (-(r1-r2)) =Φ (r1-r2)
spin-singlets (s2,s1) = -s (s1,s2)
odd function (p wave)Φ (-(r1-r2)) = - Φ (r1-r2)
spin-triplets (s2,s1) = s(s1,s2)
S=0
S=1
cTkBeT
1
1N0
NS(E)
EF EF +Δ0
1/T1 in various superconductorsConventional type (BCS)
s-wave
d-wave p-wave
unconventional superconductors (non BCS)
3
1
1 TT N0
NS(E)
EF EF +Δ0
Line nodes
EF
5
1
1 TT
EF +Δ0
Point nodes
1 10 100
10- 2
10- 1
100
101
2/kBT
c=2.85
2/kBTc=5
Tc(H)
Tc=5K
NbB2
~exp(-/kBT)
1/ T
1 ( s
ec-1
)
Temperature ( K )
MgB2
~T