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