Nuclear Magnetic Resonance (NMR) - ISU Sites · 2020. 5. 6. · Nuclear Magnetic Resonance (NMR) Yuji Furukawa A121 Zaffarano [email protected]. 2 Jan 26 Introduction of NMR Jan

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Nuclear Magnetic Resonance (NMR)

Yuji Furukawa

A121 Zaffarano

[email protected]

2

Jan 26 Introduction of NMRJan 28 Basics of NMR IJan 30 Basics of NMR IIFeb. 2 Example I (low-D spin system)Feb. 4 Example II (superconductors)Feb. 6 Introduction of ESR

Principle of NMR ・・・・・ a little bit complicatedNMR experiments ・・・・・ a little bit complicatedData analysis of NMR results ・・・・・・ a little bit complicated

But, NMR measurements give us very important information which can not be obtained by other experimental techniques

3

H i s t o r y

1936 Prof. Gorter, first attempt to detect nuclear magnetic spin(But he did not succeed,

1H in K[Al(SO4)2]12H2O and 19F in LiF)) 1938 Prof. Rabi, First detection of nuclear magnetic spin

(1944 Nobel prize)1942 Prof. Gorter, First use of terminology of “NMR”

(Gorter, 1967, Fritz London Prize) 1946 Prof. Purcell, Torrey, Pound, detected signals in Paraffin.

Prof Bloch, Hansen, Packard, detected signals in water (Purcell, Bloch, 1952 Nobel Prize)

1950 Prof. Haln, Discovery of spin echo.-> Spin echo NMR spectroscopy

Remarkable development of electronics, technology and so on-> Striking progress of NMR technique!!

4

Nuclear property

IIμn hng γμ == NNNuclear magnetic moment c.f. Proton (three quarks)

I=1/2 γN/2π=42.577 MHz/T

gN:g-factor (dimension less) γN:nuclear gyromagnetic ratio (rad/sec/gauss)

(erg/gauss)

c.f. electron spin momentμe=-gμBS

241005.52

−×==cm

e

pN

hμ201092.0

2−×==

cme

eB

hμ(erg/gauss)

|μＢ/μＮ|~1800

5

Nuclear magnetism

IIμn hng γμ == NNNuclear magnetic moment

zzN HIgHU μμ −=⋅−=

( )( )xBNgI

TkU

TkU

IgM NI

II B

I

II BzN

Z

z μμ

=

⎟⎟⎠

⎞⎜⎜⎝

⎛ −

⎟⎟⎠

⎞⎜⎜⎝

⎛ −−

=

∑

∑

−=

−=

exp

exp

( )TkIINg

HM

B

NN 3

122 +≈=

μχ

Much less than χe (electron spin)

Magnetism of material is mainly dominated by χe!!

Nuclear magnetism

Curie law

6

(ｈ：Planck’s constant、ν：frequency、γN：nuclear gyromagnetic ratio、H：magnetic field)

NMR （Nuclear Magnetic Resonance)

Nucleus has magnetic moment (nuclear spin)nucleus is very small magnet

HI・hNZeemanH γ−=Zeeman interaction

Hhh Nγω =

Magnetic resonance can be induced by application of radio wave whose energy is equal to the energy

between nuclear levels

7

Application of NMR

NMR is utilized widely not only Physics and/or chemistry but also medical diagnostics (MRI) and so on.

・ PhysicsCondensed matter physics、Magnet, Superconductor、and so on

・Chemical Analysis and/or identification of material

・BiophysicsAnalysis of Protein structure

・MedicalMRI (Magnetic Resonance Image)

Brain tomograph

For example;

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NMR in condensed matter physics

])))((3()(38[( 353 r

Ir

rSrIr

SIrgH BNnell

h････

･ +−−=− SIπδμγ

Fermi contact dipole interaction orbital interaction

NMR measurements investigation of static and dynamical properties of hyperfine field (electron spins)

One of the important experimental method for the study on magnetic and electronic properties of the materials from the microscopic point of view. (nucleus as a probe)

Hyperfine interaction between nuclear spin and electron spins

NMR spectrum

⇒ static properties of spinsNMR relaxation time (T1, T2)⇒dynamical properties

9

NMR spectrum

NMR spectrum measurements （static properties of hyperfine field）

① magnetic systemspin structure, spin moments and so on

② metal local density of state at Fermi level

HH0=ω/γ

⊿H

NMR shift：Ｋ＝ΔＨ／Ｈ

ΔＨ：contribution from electronＨ

H0

ΔＨ

Ｈ

Ｈ＝Ｈ０＋ΔＨ

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Nuclear spin-lattice relaxation time（Ｔ１）

Nuclear spin-lattice relaxation time

Dynamical properties of hyperfine field ( )tHI hfNrr

h ⋅=′ γ-H

( )yx

yx iHHHiIII

tHItHI

hfhfhf

hfhfN

,

)()(2

-

±=±=

+

±±

+−−+hγ

Iz=1/2

-1/2

( ){ } ( )

( ){ } ( ) ( )iii SAHdttitSSAdttitHH

Trr

==

=

∫

∫∞

∞−

+−

∞

∞−

+−

hfN

2N

2

Nhfhf

2N

1

exp,2

exp,2

1

ωγ

ωγ

Ex. Metal ⇒ T1T＝const. （Korringa relation）Superconductor ⇒ T-dependence of T1 provides information of

symmetry of SC gapfull gap ⇒ 1/T1~exp(-Δ/kbT)anisotropic gap ⇒ 1/T1~Tα

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Characteristics of NMR

1) Local properties information at each nuclear site

(e.g., local density of states, spin state for each site…)

microscopic measurements (NMR, μＳＲ，ESR, Mossbauer ND, )macroscopic measurements (Magnetization, specific heat,

resistively…)

2) Low energy excitationinformation of low energy (electron) spin excitation(energy scale in different experiments

NMR, μSR : MHz, Mossbauer：γ-ray, ND: ～meV）

3) Laboratory size NMR spectrometer can be set up in lab space.(you can modify the spectrometer as you like!)

μＳＲ measurements －＞ need to go facility(in principle, you can NOT modify the equipment)

For exampleｆ＝100ＭＨｚ

⇒5ｍＫ

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NMR spectroscopy in condensed matter physics

NMR spectroscopyContinuous wave (CW) NMRPulse NMR (FT (Fourier transform) –NMR) ←mainstream

・Spectrometer frequency range 1～500MHz

・Magnetic field up to 2Ｔ ; electron magnetup to 9T ; superconducting magnet (Nb3Ti) up to 23T ; superconducting magnet (Nb3Sn)up to 35T ; Hybrid magnet more than 40 T ; pulse magnet

Temperature down to 77K ; liquid N2 (less than $1/liter)down to 1.5K ; liquid He (boiling T ～4.3K) (more than $10/liter)down to 0.3K ; 3He cryostat ($100K)down to 0.01K ; 3He-4He dilution refrigerator ($300K)

NMR lab at ISU (at present, just a couple of months after I moved in)

f=1-500MHz, H=9T, T=1.5KPlan to purchase DR refrigerator

One 3He cryostat: not available now

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NMR laboratory in the world

There are many NMR labs in the world !

Tallahassee (USA), Grenoble (France), Tohoku,(Japan), Tsukuba (Japan )…

NMR spectroscopy with Hybrid magnet (~35T)

NMR spectrometer with DR refrigerator

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NMR laboratory in the world

Pulse NMR spectroscopy with pulse magnet

Japan project of “100T spin science”Germany Dresden

Exciting new challenge!

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Magnetic resonance

H0 = 0 H0 ≠ 0

m = -1/2

m = +1/2

HI・hNZeemanH γ−= In the case of I=1/2 and H=(0, 0, H0),Eigen energies for two quantum levels are given

02/1 21 HE Nhγ−= 02/1 2

1 HE Nhγ=−

0HE nhγ=ΔHΝΝ = γω

To make a resonance, one needs time dependent perturbation and non-zero matrix element

)cos()(' 1 tIHtH NxN ωγ h= 2−+ +=

III x

0)('1 >≠±< mtHmMagnetic transition

H0

alternating current ⇒ alternating field

Using a coil perpendicular to H0, you can apply an alternating field which induces magnetic transition. But how can you detect the signal (magnetic transition)Need to think about motion of nuclear magnetic moment

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Motion of magnetic moment

Classical treatment

HNdt

Id×== μh H

dtd

Nγμμ

×=μ

H

Larmor precessionω＝γNH

(Time variation of angular momentum is equal to torque)

Rotating coordinate system (Ω）

Ω

)( Ω+×= Ht

γμδδμ

effHγμ ×=

(With a simple assumption H=H0k)

If Ω＝ｰγH0 then Heff=0 -＞δμ/δｔ＝ 0

No change in time ! (since we are looking at spin moment on rotating frame with same frequency of γH0）

If H=(0,0,H0), then μｘ=Asin(ωt+a), μy=Acos(ωt+a), μz=const.

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Effects of alternating field

Hx=Hx0 cosωt i

x

y

Hx

Hx=HR+HLHR=H1(i cosωt ＋ j sinωｔ）HL=H1(i cosωt - j sinωｔ）

H1=H0/2

)( 10 HHdtd

+×= γμμ ⎥⎦

⎤⎢⎣

⎡++×= iHkH

t 10)(

γωγμ

δδμ

Laboratory frame Coordinate system rotating about z-axis

When ω＝-γH0, you have resonance and have only H1 magnetic field along to x-axis

This means spin rotates about x-axis with frequency γH1

x

y

z

spin

H0

without H1x

y

z

with H1 (rotating frame)

H1

You can control the direction of spins!

Manipulation of spin

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19


Larmor precession

20


21


22


23


24


25

Effects of alternating field

x

y

z

H1

x

y

zSpin rotes in xy-plane in laboratory frame (spin rotates in the coil)

⇒ this induces voltage

You can detect the voltage -> observation of signal from nuclear spin!

Typically the induced voltage is ~10-6 V We need to amplify the voltage to observe easily (with amplifier)

x

y

z

H1

x

y

z

H1

t=0 t=π/2γH1 (π/2 pulse) t=π/γH1 (π pulse)

If you stop to give H1 just after t (π/2 pulse)

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FID signal

27

Spin echo method

τ τa b c

ed

π/2 pulse πpulse Spin echo signal

Two pulse sequence

ω+⊿ω

ω-⊿ω

ｔ

28

Quantum treatment of Spin echo

29

Quantum treatment of Spin echo

30

Absorption energy and spin lattice relaxation T1

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Nuclear spin lattice relaxation T1

32

H0 = 0 H0 ≠ 0

Iz= -1/2

Iz = 1/2


Boltzmanndistribution

thermal equilibrium state

Resonance(absorption)

nonequilibriumstate

HΝΝ = γω

Relaxation(energy emission to lattice

(electron system)

-> thermal equilibrium state

T1 is a time constant (from nonequilibrium to equilibrium states)

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Relaxation is induced by fluctuations of hyperfine field with NMR frequency

34

How to measure nuclear spin lattice relaxation T1

xy

z

H1

0.0

0.2

0.4

0.6

0.8

1.0

Spin

ech

o in

tens

aity

time

t-dependence of signal intensity I(t)=I0(1-exp(-t/T1))

T1 can be estimated

x

y

z

H1

Saturation

2/π

π

No mag. in xy-planeＩ(0)＝0

When ｔ~0t= ∞

x

y

z

2/π

πI(t)=I0

Signal intensity is proportional to xy-component of nuclear magnetization

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block diagram (NMR spectrometer)

Receiver AmpPSD LPF

[ ]

[ ]βαωω

βαωω

βωαω

++++

−+−=

++

t

t

tt

)(cos21

)(cos21

)sin()sin(

21

21

21

PSDMultiplication of Input frequencies-> out put

frequency difference and sum

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NMR spectrum

QH

⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

∂∂−∂∂≡

∂∂

≡

⎥⎦⎤

⎢⎣⎡ ++−

−= −+

22

2222

2

2

22222

)(21)3(

)12(4

zVyVxV

zVq

IIIIIIqQe

z

η

η

　　　　　　　

Zeeman interaction(interaction between magnetic moment and magnetic field)

Electric quadrupole interaction (I>1/2)( interaction between electric field gradient and nuclear quadrupole moment)

+ + ++

Nuclear is NOT spherical but ellipsoidal body (I>1/2)

[ ]

)12(4

)1(32

2

−≡

+−=

IIqQeA

IImAEm 　

ZnZeeman IHHH 0- hγμ −=⋅=

For η＝0

η: assymmetry parameter

37

NMR spectrum

0ω

hA120 +ω

hA60 +ω

0ω

hA60 −ωhA120 −ω

m=±5/2

m=±1/2

m=±3/2

12A

6Aeq=0

eq≠0

[ ])I(I

qQeA)I(ImAEm 12413

22

−≡+−= 　　

1. Hquadrupole≠0，Ｈ＝0 2. Hzeeman >> Hquadrupole

ω6Ａ 12Ａ

Hq＝0I=5/2

NQR (nuclear quadrupole resonance)ω

5/2

3/2

1/2

-1/2

-3/2

-5/2

38

NMR spectrum in powder sample

-3/2

3/2

-1/2

1/2

ℏω3/2→1/2

ℏω-1/2→-3/2

ℏω1/2→-1/2

( )( ) ( )h12831312

22

n1 −−θ−+ω=ω −→ II

qQecosmmm

powder pattern (I=3/2)

ωnωn-2A1 ωn-A1 ωn+A1 ωn+2A1

A1=1/4e2qQ/ℏ

ωn－16A2/9ℏ ωn+A2/ℏωn

2nd oeder splitting of central transition for powder pattern spectruim

( )( )

( )( )

0

22

22

222

01/21/2

12432

649

cos-19cos-1

ω

θθωω

h

h

qQeII

IA

A

−+

=

+=−→

θ=0

θ=90

Hz>>HQ (I=3/2)

Center line is affected in 2nd order perturbation

39

NMR spectrum in powder sample

60 65 70 75 80

Spi

n ec

ho in

tens

ity

H ( T )

93Nb-NMR in NbO

93Nb-NMR in NbO (field sweep spectrum)

Textbook like typical powder pattern spectrum

I=9/2

ωn－16A2/9ℏ ωn+A2/ℏωn

Central transition lineOpposite?!

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NMR spectrum

ω

signal (A)

H

signal (B)

(1) ω－sweep ( H=constant;H0)

ＮＭＲspectrumMagnetic field sweep and frequency sweep

H0

ωωＢ ωＡ

(２) Ｈ－ｓｗｅｅｐ (ω＝constant; ω0）ω

signal (A)

H

signal (B)

ωＡ

ωＢ

ω0

ＨＡＨＢ

ＨＨＡＨＢ

Opposite!!Need to pay attentions !!

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Hyperfine field at nuclear site

These give additional field (Hhf) at nuclear site-> shift in spectrum (NMR shift）

ωω0 ω0+⊿ω

Fermi contact

Dipole interaction

orbital interaction

S-electron2)0(3

8 ψγπ sheFH −=

( )ψψγ 53

* 3rr

H ediprrss ⋅

−= h

ψψγ 3* 1

rH eorb lh=−

Core-poratizationinteraction ( )∑ ↓↑ −−=

iii

ecpH

22 )0()0(3

8 ψψγπ sh

⊿ω=γＨhf

In the material, nuclear experiences additional field due to hyperfine interaction

3d system~-100kOe/μB

μS

Hint

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Ｒｅｌａｔｉｏｎ between NMR shift and magnetic susceptibility

H=Hz+Hhf

Hamiltonian

Hz=Hzeeman (H=H0)

Hhf=Hdipole+HFermi+Hcore-polarization+…..=AI・S A: hyperfine coupling constant

)( hf0 HHIH n +−= hγ ASH =hfNMR shift originates from thermal average value of Hhf

=ASince is expressed by (thermal average value of electron magnetization),

=A～A (=AχH0)

Knight shift is given by K = Hhf/H = AχH/H ～Aχ

K is proportional to χ ！！

increases with increasing H -> high accuracy

(hyperfine field)

43

Example

0 50 100 150 200 250 3000.0

0.1

0.2

0.3

0.4

0.5

0.6

K (

%)

T (K)

Spin dimer system VO(HPO4)0.5H2O

V4+ (3d1: s=1/2)

0 50 100 150 200 250 3000.0

2.0x10-6

4.0x10-6

6.0x10-6

8.0x10-6

1.0x10-5

1.2x10-5

1.4x10-5

1.6x10-5

1.8x10-5

mag

netic

sus

cept

ibili

ty (

emu/

g)

T ( K )

AF interaction Magnetic susceptibility NMR shift (31P-NMR)

χtotal(T)=χspin(T)+χorb+・・・+χimpurity Ktotal(T)=Kspin(T)+Korb

What is ground state ? Spin singlet ? or magnetic?

From the NMR measurements, increase of χ at low temperature is concluded to be due to magnetic impurities

NMR can see only intrinsic behavior (exclude the impurity effects!!)

Y. Furukawa et al., J. Phys. Soc. Japan 65 (1996) 2393

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Example of K-χ plot

K-χplot K ＝ Aχ/NμB,

0.0 5.0x10-6 1.0x10-5 1.5x10-50.0

0.1

0.2

0.3

0.4

0.5

0.6

K (

%)

χ (emu/g)

Good linear relationK is proportional to χ

Hyperfine coupling constant can be estimated from the slope

BNA

ddK

μχ=

Ahf =3.3 ｋＯｅ/μB

This is a value at P site per one Bohr magneton of V4+ spin(Vanadium spin produces the hyperfine field at P-site)

The origin of this hyperfine field is“transferred hyperfine field”

45

NMR in simple metal

1) NMR shift (Knight shift)K=(A/μB)χpaulisince χpauli is expressed by (1/2)g2μB2NEf2

2)Nuclear spin lattice relaxation time T1Relaxation mechanism

scattering of free electron from ┃k,↑> to ┃k’,↓> nuclear spin can flop from ↓ ⇒ ↑ state

Pauli paramagnetism χpauliNo electron correlation

Simple metal (like Cu and Al and so on)

( ) ( ) ( ){ } ( )↓′↑′

−+ −↓′−↑↑↓↓↑= ∑ kkkk

N EEkfkfsIATδγπ 11

,

222

1

hh

( ) ( ){ } ( )Fk EETkfTkkfkf −=∂∂

=↓′−↑ δε BB

1

( ){ } TkNgAT FN B

2222

1

)(1 εγπ hh

=

1/T1 is proportional to T

T1T= constant

K is independent of T( ){ }FB Ng

AK εμ 22

=

46

Korringa relation

Skg

kTKT

≡⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛=

2

B

NB

2

B

NB2

1

441γγπ

μγπ

h

h

h

( ){ } TkNgAT FN B

2222

1

)(1 εγπ hh

=

This does not depend on material !Korringa Relation

However deviation from the Korringa relation is observed in many material.

Model was simple importance of Interaction between electrons (electron correlation)

( ){ }FB NgAK εμ 22

=

47

Modified Korringa relation

Skg

kTKT

≡⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛=

2

B

NB

2

B

NB2

1

441γγπ

μγπ

h

h

h

Korringa Relation

Modified Korringa Relation

Kα>1：AF spin correlationKα

48

NMR in magnetic material

Do we always need to apply magnetic field to observe NMR signal?In some case, the answer is No!

In magnetically ordered state, you have spontaneous magnetization (M) without applying external magnetic field.

=A～A≠0

hfIHH nhγ−=Therefore, Hamiltonian for nuclear is not zero without external field

(1) For example, AF insulator spinel Co3O4 :TN=33K)

┃Hint ┃ = 5.5Tesla

59Co-NMR under H=0

If you know Ahf, You can estimate orderedmagnetic moment =Hint/Ahf

Internal field

T. Fukai, Y.F., et al., JPSJ 65 (1996) 4067.

f=γNHint

49

(1) NMR study of low dimensional spin systemnanoscale molecular magnet

(2) NMR studies of itinerant system

(3) NMR study of superconductor

50

Distance between the clusters is over 10Å

M12 cluster a

b

c

β

αγ

molecular formula

structure of molecule

Crystal structure

Mn3+ (S=2)

Mn4+ (S=3/2)O 2-

Mn3+ (S=2)

Mn12 ([Mn12O12(CH3COO)16(H2O)4])

How can one see spin structure in the each Molecule?

Use NMR !

51

55Mn-NMR spectrum in Mn12

240 280 320 360 400

H=0

Mn4+

Mn3+ Mn3+P3P2

P1

T=1.5K

Spi

n ec

ho in

tens

ity

frequency (MHz)

μS

Hint

Core- polarization

Mn4+(3μB) : Hint ~ 22.0T

Mn3+(4μB) : Hint ~ 26.4T

Mn3+(4μB) : Hint ~ 34.7T

The direction of Hint is opposite to the that of spin moments

Observation of 55Mn-NMR signalUnder zero magnetic field

(super-paramagnetic state)(Spin freezing at low temperature)

52

Internal spin structure of Mn12 (parallel field)

0 2 4 6 8 10 12 14 16100

150

200

250

300

350

400

γN=10.5MHz/T

P1 (Mn4+)

P2 (Mn3+)

P3 (Mn3+)

peak

freq

uenc

ies

(MH

z)

parallel field (T)

Hext

Y. Furukawa et al., PRB 64 (2001) 104401

｜Heff ｜ = ｜ Hint+Hext ｜

For Mn4+ (S=3/2) ionsHint is parallel to Hext

(spin direction is antiparallel)

For Mn3+ (S=2) ionsHint is antiparallel to Hext

(spin direction is parallel)

ωres= γN Heff

To determine the spin direction, one can apply external field

NMR can determinespin structure!

53

NMR example

31P-NMR Study of Low-Energy Spin Excitations in Spin Ladder (VO)2P2O7 and Spin Dimer VO(HPO4)0.5H2O Systems

Spin ladder spin dimer

H = -JS・SNeel state ┃↑ ↓＞

E=-J/4

Singleｔ state （┃↑ ↓＞ｰ┃↓↑＞）√２E=3J/4

J

54

NMR example

Both systems have a energy gap in spin excitation

T-dependence of K (NMR shift)

K~χ~(1/T)exp(-⊿/ｋＴ） for spin dimerK~χ~(1/T0.5)exp(-⊿/ｋＴ） for spin ladder

⊿ can be estimated

55

NMR example

1/T1~exp(-⊿/Ｔ）

⊿ can be estimated fromT-dependence of T1

ΔT1＝75 K (for dimer)ΔT1 =60 K (for ladder)

ΔK＝74 K (for dimer)ΔK =30 K (for ladder)

56

NMR example

K ~χ（ｑ＝0、ω＝0）

Comparison of K and T1 gives information about q-dependence of ⊿(q)

χ（ｑ）

Δ（ｑ）

1/T1TK = exp(-⊿T1/kT）/exp(-⊿K/kT） for dimerif ⊿K＝⊿T1, 1/T1TK should be constant

1/T1TK = exp(-⊿T1/kT）/exp(-⊿K/kT）/T0.5 for ladderif ⊿K＝⊿T1, 1/T1TK should increase at low T

Observation of decrease -> this is due to ΔT1>ΔK

ｑ

57

NMR example (itinerant AF magnet)

Itinerant antiferromagnet V3S4

Y. Kitaoka et al. JSPJ 48 (1980)1460

58

NMR example

Spin fluctuation localized at q=Q

SCR theoryV3S4

VS1.1

59

Superconductivity

T (K)

R (Ω

) Tc

Zero resistivity

SC

manget

Meissner effects(perfect diamagnetism)

60

NMR study of superconductor

Symmetry of cooper pair

s-wave (l=0, s=0)

p-wave (l=1, s=1)

d-wave (l=2, s=0)

Isotropic gap

Anisotropic gap

Anisotropic gap

S-wave

d-wave

61

NMR study of superconductor

Symmetry of cooper pair

s-wave (l=0, s=0)

p-wave (l=1, s=1)

d-wave (l=2, s=0)

Isotropic gap

Anisotropic gap

Anisotropic gap

)/exp(/1 1 kTT Δ−∝

Knight shift 1/T1

αTT ∝1/1

αTT ∝1/1

Just below TcHebel-Slichter peak

62

NMR example (Superconductor)

Al metalKnight shift

Enhancement of transition probabilityDivergence behavior of DOS

Hebel-Slichter peak

Above Tc1/T1~T

Below Tc1/T1 ~exp(-⊿/ｋＴ）

S-wave SC !

Decrease of spin susceptibilityT-dependence of 1/T1

63


Ru(Cu)

Sr

O

RuO2面

c

ab

Ru4+(4d4)

Crystal structure Sr2RuO4

Sr2RuO4 Tc~1.5K

No change! 1/T1~T3

suggesting P-wave SC!!

K. Ishida et al, Nature 396 (1998)658Ru4+ (4d4)

64


Kanoda, Miyagawa, Kawamoto et al., d-wave SC

Pairing symmetry of Cooper pair can be determined by NMR measurement

Important information oforigin for the SC appearance

65

NMR studies in High Tc Cuprates)

AF

SC

La1-xSrxCuO4

CuO2 plane

66

NMR example

(1) Antiferromagnet (for example, AF insulator La2CuO4 :TN~300K)

Very precise measurement of sub-lattice magnetization!

Evidence of AF magnetic ordering !!

67


1/T1T shows CW behavior

1/T1T~1/(T+a)1/T1 ~T3

q

χq

Q

Evidence of AF spin correlationsK is almost T-independent

68


SC: d-wave symmetry

Spin gap (SG) behavior at L-regionStrong AF spin fluctuations in metallic region

At the begging stage, NMR data indicates d-wave SC Other experiments suggests S-wave

Now most of people believes d-wave-SC!!

SG

Anomalous Metallic state

69

NMR in vortex state

NMR can investigate electronic state at different spatial region of Vortex core lattice

Local field distribution associated with the vortex lattice

Hlocξ

λ( )H H e e

Gi

G

rG

G r=

+∑− ⋅

−

0

2

2 2

2 2

1

ξ

λ0 .999 1.000 1.001 1 .002

C

B

A

( ) ( )( )f h h H rS

= −∫ δ r d2

H /H 0

ABC

CoreSaddleCenter

Redfield patternλ：penetration depthξ: coherence length ξ＜λ type II SC

70


1 10 100

1

10

100

00

500

1000

1500

T C

T*

((a)

1 / (

T 1T)

( K

-1s-1

)

T ( K )

1 / T

1 (s

-1)

1/T1 is enhanced near the vortex core1/T1 shows a peak

Magnetic order in vortex core!!

K. Kakuyanagi, K. Kumagai, et al PRL90(2003)197003

205Tl NMR in Tl2Ba2CuO6+d

71

NMR example (magnetic superconductor)

CuO2 plane　⇒

CuO2 plane　⇒

RuO2 plane　⇒

RuO2 plane　⇒

Ru

O

Cu

c

RE

a

b

RuSr2YCu2O8 (layered Perovskite structure)

0 50 100 150 200 250 3000

200

400

600

800

1000

1200

TM~148K

H=5000(Oe)

RuSr2YCu2O8

M (

emu/

mol

)

T ( K )

35K

0 100 2000

0.1

0.2

0.3

T ( K )

ρ（Ω

・cm

) TC(onset)=65K

TC(R=0)=17KMagnetic order at T~148KSC transition at T~35K

・Coexistence of SC and magnetic order?・which ions are responsible to magnetic order?

72


40 60 80 100 120 140 160

99Ru

101Ru

T=4.2K

Spi

n ec

ho in

tens

ity (

arb

. uni

t )

Frequency ( MHz )

Observation of 101/99Ru NMR signal under zero magnetic field

101Ru (I=5/2) γ/2π=2.193MHz/T

Q=0.44×10-24 (cm2)

99Ru (I=5/2) γ/2π =1.954MHz/T

Q=0.07×10-24 (cm2)

Observation of Ru-NMR signal (below TC)→ magnetic ordering of Ru spins

Hzeeman>>HQuad

Hint=584kOe , νQ=15MHz

K. Kumagai, Y. Furukawa et al., PRB 63 (2001)180509

73


1 10 100

10

100

1000

10000

TC(onset)

1/T 1

( s

ec-1 )

T ( K )12 13 14 15 16

65Cu

63Cu

f=158.66MHz

63/65Cu-NMR

250K

220K

180K

130K

85K

50K

25K

T=4.2K

Spin

ech

o in

tens

ity (

arb

. uni

ts )

H ( T )

0 100 200 3000

2

4

6

63Cu-NMR in RuSr2YCu2O8

Magnetic broadening below TM

1/T1 decrease below Tc

Powder pattern (distribution of angle between H and principal axis of EFG)

Coexistence of SC and Mag. SC -> CuO2 plane

(because of small internal field)Mag. -> RuO2 plaen

Y. Furukawa et al., J. Phys. Chem. Solid 63 (2002) 2315

74

Novel superconductors

・ newly discovered LaOFeAsCo(K)-doped BaFe2As2 system

Prof. Canfield’s grouphas succeeded to make very good quality samples

75

NMR study of FeAs-system

139La-NMR in LaFeAs(O,F)

Y. Nakai et al., JPSJ 77(2008) 073701

X=0 ->AF order at T=142

139La: I=7/2

76

NMR study of FeAs-system

75As-NMR in LaFeAs(O,F)

Suggesting d-wave SC

Other experimental data indicates not d-wave but S-wave SCY. Nakai et al., JPSJ 77(2008) 073701

1/T1T increases with decreasing T⇒ evidence for AF spin fluctuations

75As:I=3/2

77

Introduction of Electron Spin Resonance (ESR)

Yuji FurukawaA121 Zaffarano

[email protected]

Principle is same as NMR, but now electron spin!

78

E S R

1944 Prof. E.K. Zavoyskydiscovery of EPRat Kazan State University in Russia (Soviet union)

ESR: electron spin resonance EPR : electron paramagnetic resonance

AFMR : Antiferromagnetic resonanceFMR : Ferromagnetic resonance

100th anniversary of E.K. Zavoysky(2007: Kazan University)

79

E S R

S-S hee g γμ =−= Bμmagnetic moment of electron

gN:g-factor (2.0023)

201092.02

−×==cm

e

eB

hμ

H0 = 0 H0 ≠ 0

Sz= 1/2

Sz = -1/2

(erg/G)

In the magnetic field of H

HSgE zBe μμ =⋅−= H

Bohr magneton

Hgh Bμ=ω

γe/2π=28.02 ＧＨｚ/Ｔc.f., Proton γN/2π=42.577ＭＨｚ/Ｔ

ν（ＧＨｚ） ~ 28 Ｈ（Tesla）

S band ~3.2GHz ~9 cmX-band ~9.5 ~3 K-band ~24 ~1.2J (Q)-band ~34 ~ 0.9Ｗ-ban ~90 ~0.3

80

ESR

Advantage of high frequency (magnetic filed) ・increase of resolution・increase of sensitivity・simplification of the spectra and of their assignment

・Magnetic field up to 2Ｔ ; electron magnetup to 9T ; superconducting magnet (Nb3Ti) up to 23T ; superconducting magnet (Nb3Sn)up to 35T ; Hybrid magnet more than 40 T ; pulse magnetic field

ESR measurements using a pulsed magnet is much popular in comparison with NMR case.

(due to short T1 of electron spins)

On the other hand, pulse ESR is NOT popular

(due to short T1 (T2) of electron spins)

(CW method) |μＢ/μＮ|~1800

81

ESR

ESR with a pulsed magnet

H0 = 0 H0 ≠ 0

Sz= 1/2

Sz = -1/2

H0 ≠ 0

Sz= 1/2

Sz = -1/2

t>T1

Signal can be observed

Short T1 is important !!

~50T

t

c.f., in the case of NMR, usually T1 is not short enough

82

ESR

pulsed ESR

nano-second controlled system is required!

Short T1 -> short T2 (spin echo T2)

π/2 pulse πpulse Spin echo signal

ｔ

τ

If T2 is less than 1μＳτ should be less than 1 μＳ

JEOL (Japan)

83

ESR

What can one get information from ESR・investigation of electronic state ・energy level scheme of system

and so on・・・・

Since electrons are always in material,Can we observe ESR signal anytime?

⇒ NO!

To observe the signal, unpaired electron is needed!!・ 3d / 4f electrons of transition metal ions ・conduction electrons in metal ・radicals (molecule with odd-numbered electron)・trapped electron at defects (for example, F-center) and so on

84

ESR

85

4

ESR

86

ESR

87

ESR

88

ESR

89

ESR

90

[(C6H15N3)6Fe8O2(OH)12]Br8･9H2O

Eight Fe3+ (S=5/2) ions are almost coplanar

Strong AF interaction between Fe3+ spins→a total spin S=10 ground state

(S=5/2×6-5/2×2=10)

HS ⋅+−+=Η Byxz SSEDS μg)(222

Spin Hamiltonian for the S=10 ground state

medium

hard axis

91

E

H = 0

Δ E

m = 0

m = 1 0m = - 1 0

Energy levels for 21 sublevels in S=10 ground state

~27K

mHDmE Bm μg~2 +

Superparamagnetic stateQuantum tunneling of magnetization

(QTM)

W. Wernsdorfer et al. J. Appl. Phys. 87,5481 (2000)

⊿H~0.22T

92

0 2 4 6 8 10

-150

-100

-50

0

50

100

m=+9m=+10

m=-9m=-10

c//H

E m (K

)

H (T)

Magnetic MoleculeFe8 -> ground state is S=10

Need to know the parameters (D, B) to Determine the structure of energy levels

S. Hill et al., Phys. Rev. B 65, 224410 (2002)

One can determine the parameters

ESR

HS ⋅+−+=Η Byxz SSEDS μg)(222

D= ~ ‐0.27K E= 0.046K

93

ESR

ESR study of 1dimensional quantum spin system

1 dimensional AF spin system -> gapless ground state

However, if S=integer-> gapped ground state

(Haldane conjecture ‘83)

NENP(Ni(C2H8N2)2NO2(ClO4)(NTENP))

Ni2+ (3d8;S=1) S=1 spin chain

94

ESR

W. Lu et et al., PRB 67 (1991) 3716

95

ESR

A direct observation of Haldane gap

96

Summary

Magnetic resonance is one of the powerful tools to study magnetic and electronic properties of Materials

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Nuclear Magnetic Resonance (NMR) - ISU Sites · 2020. 5. 6. · Nuclear Magnetic Resonance (NMR) Yuji Furukawa A121 Zaffarano [email protected]. 2 Jan 26 Introduction of NMR Jan