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Nuclear Magnetic Resonance (NMR)
Yuji Furukawa
A121 Zaffarano
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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
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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!!
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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
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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
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(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
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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
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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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Motion of magnetic moment
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Motion of magnetic moment
Larmor precession
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Motion of magnetic moment
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Motion of magnetic moment
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Motion of magnetic moment
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Motion of magnetic moment
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Motion of magnetic moment
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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
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Spin echo method
τ τa b c
ed
π/2 pulse πpulse Spin echo signal
Two pulse sequence
ω+⊿ω
ω-⊿ω
t
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Quantum treatment of Spin echo
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Quantum treatment of Spin echo
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Absorption energy and spin lattice relaxation T1
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Nuclear spin lattice relaxation T1
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H0 = 0 H0 ≠ 0
Iz= -1/2
Iz = 1/2
Nuclear spin lattice relaxation T1
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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Nuclear spin lattice relaxation T1
Relaxation is induced by fluctuations of hyperfine field with NMR frequency
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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
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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
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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
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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
HA HB
HHA HB
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)
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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”
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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
=
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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
=
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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
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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
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(1) NMR study of low dimensional spin systemnanoscale molecular magnet
(2) NMR studies of itinerant system
(3) NMR study of superconductor
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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 !
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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)
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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!
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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
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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
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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)
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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
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NMR example (itinerant AF magnet)
Itinerant antiferromagnet V3S4
Y. Kitaoka et al. JSPJ 48 (1980)1460
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NMR example
Spin fluctuation localized at q=Q
SCR theoryV3S4
VS1.1
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Superconductivity
T (K)
R (Ω
) Tc
Zero resistivity
SC
manget
Meissner effects(perfect diamagnetism)
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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
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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
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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
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NMR example (Superconductor)
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)
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NMR example (Superconductor)
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
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65
NMR studies in High Tc Cuprates)
AF
SC
La1-xSrxCuO4
CuO2 plane
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NMR example
(1) Antiferromagnet (for example, AF insulator La2CuO4 :TN~300K)
Very precise measurement of sub-lattice magnetization!
Evidence of AF magnetic ordering !!
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NMR studies in High Tc Cuprates)
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
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NMR studies in High Tc Cuprates)
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
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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
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NMR example (Superconductor)
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
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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?
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NMR example (Superconductor)
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
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NMR example (Superconductor)
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
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Novel superconductors
・ newly discovered LaOFeAsCo(K)-doped BaFe2As2 system
Prof. Canfield’s grouphas succeeded to make very good quality samples
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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
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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
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Introduction of Electron Spin Resonance (ESR)
Yuji FurukawaA121 Zaffarano
Principle is same as NMR, but now electron spin!
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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)
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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
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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
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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
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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)
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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
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84
ESR
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4
ESR
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ESR
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ESR
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88
ESR
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ESR
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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
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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
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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
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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
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ESR
W. Lu et et al., PRB 67 (1991) 3716
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95
ESR
A direct observation of Haldane gap
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Summary
Magnetic resonance is one of the powerful tools to study magnetic and electronic properties of Materials