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1
Nuclear Magnetic Resonance (NMR)
Yuji Furukawa
A121 Zaffarano
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
IIn hng == NNNuclear magnetic moment c.f. Proton (three quarks)
I=1/2 N/2=42.577 MHz/T
gN:g-factor (dimension less) N:nuclear gyromagnetic ratio (rad/sec/gauss)
(erg/gauss)
c.f. electron spin momente=-gBS
241005.52
==cm
e
pN
h201092.0
2==
cme
eB
h(erg/gauss)
|/|~1800
5
Nuclear magnetism
IIn hng == NNNuclear magnetic moment
zzN HIgHU ==
( )( )xBNgI
TkU
TkU
IgM NI
II B
I
II BzN
Z
z
=
=
=
=
exp
exp
( )TkIINg
HM
B
NN 3
122 +=
Much less than e (electron spin)
Magnetism of material is mainly dominated by e!!
Nuclear magnetism
Curie law
6
(Plancks constantfrequencyNnuclear gyromagnetic ratioHmagnetic field)
NMR Nuclear Magnetic Resonance)
Nucleus has magnetic moment (nuclear spin)nucleus is very small magnet
HIhNZeemanH =Zeeman interaction
Hhh N =
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 physicsMagnet, Superconductorand so on
Chemical Analysis and/or identification of material
BiophysicsAnalysis of Protein structure
MedicalMRI (Magnetic Resonance Image)
Brain tomograph
For example;
8
NMR in condensed matter physics
])))((3()(38[( 353 r
Ir
rSrIr
SIrgH BNnell
h
+= SI
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
magnetic systemspin structure, spin moments and so on
metal local density of state at Fermi level
HH0=/
H
NMR shift
contribution from electron
H0
10
Nuclear spin-lattice relaxation time
Nuclear spin-lattice relaxation time
Dynamical properties of hyperfine field ( )tHI hfNrr
h = -H
( )yx
yx iHHHiIII
tHItHI
hfhfhf
hfhfN
,
)()(2
-
==
+
++h
Iz=1/2
-1/2
( ){ } ( )
( ){ } ( ) ( )iii SAHdttitSSAdttitHH
Trr
==
=
+
+
hfN
2N
2
Nhfhf
2N
1
exp,2
exp,2
1
Ex. Metal T1Tconst. Korringa relationSuperconductor T-dependence of T1 provides information of
symmetry of SC gapfull gap 1/T1~exp(-/kbT)anisotropic gap 1/T1~T
11
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, 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, SR : MHz, Mossbauer-ray, ND: meV
3) Laboratory size NMR spectrometer can be set up in lab space.(you can modify the spectrometer as you like!)
measurements need to go facility(in principle, you can NOT modify the equipment)
For example100
5
12
NMR spectroscopy in condensed matter physics
NMR spectroscopyContinuous wave (CW) NMRPulse NMR (FT (Fourier transform) NMR) mainstream
Spectrometer frequency range 1500MHz
Magnetic field up to 2 ; 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
13
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
14
NMR laboratory in the world
Pulse NMR spectroscopy with pulse magnet
Japan project of 100T spin scienceGermany Dresden
Exciting new challenge!
15
Magnetic resonance
H0 = 0 H0 0
m = -1/2
m = +1/2
HIhNZeemanH = In the case of I=1/2 and H=(0, 0, H0),Eigen energies for two quantum levels are given
02/1 21 HE Nh= 02/1 2
1 HE Nh=
0HE nh=H =
To make a resonance, one needs time dependent perturbation and non-zero matrix element
)cos()(' 1 tIHtH NxN 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
16
Motion of magnetic moment
Classical treatment
HNdt
Id== h H
dtd
N
=
H
Larmor precessionNH
(Time variation of angular momentum is equal to torque)
Rotating coordinate system (
)( += Ht
effH =
(With a simple assumption H=H0k)
If H0 then Heff=0 -/ 0
No change in time ! (since we are looking at spin moment on rotating frame with same frequency of H0
If H=(0,0,H0), then =Asin(t+a), y=Acos(t+a), z=const.
17
Effects of alternating field
Hx=Hx0 cost i
x
y
Hx
Hx=HR+HLHR=H1(i cost j sin HL=H1(i cost - j sin
H1=H0/2
)( 10 HHdtd
+=
++= iHkH
t 10)(
Laboratory frame Coordinate system rotating about z-axis
When -H0, you have resonance and have only H1 magnetic field along to x-axis
This means spin rotates about x-axis with frequency H1
x
y
z
spin
H0
without H1x
y
z
with H1 (rotating frame)
H1
You can control the direction of spins!
Manipulation of spin
18
Motion of magnetic moment
19
Motion of magnetic moment
Larmor precession
20
Motion of magnetic moment
21
Motion of magnetic moment
22
Motion of magnetic moment
23
Motion of magnetic moment
24
Motion of magnetic moment
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=/2H1 (/2 pulse) t=/H1 ( pulse)
If you stop to give H1 just after t (/2 pulse)
26
FID signal
27
Spin echo method
a b c
ed
/2 pulse pulse Spin echo signal
Two pulse sequence
+
-
28
Quantum treatment of Spin echo
29
Quantum treatment of Spin echo
30
Absorption energy and spin lattice relaxation T1
31
Nuclear spin lattice relaxation T1
32
H0 = 0 H0 0
Iz= -1/2
Iz = 1/2
Nuclear spin lattice relaxation T1
Boltzmanndistribution
thermal equilibrium state
Resonance(absorption)
nonequilibriumstate
H =
Relaxation(energy emission to lattice
(electron system)
-> thermal equilibrium state
T1 is a time constant (from nonequilibrium to equilibrium states)
33
Nuclear spin lattice relaxation T1
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/
No mag. in xy-plane(0)0
When ~0t=
x
y
z
2/
I(t)=I0
Signal intensity is proportional to xy-component of nuclear magnetization
35
block diagram (NMR spectrometer)
Receiver AmpPSD LPF
[ ]
[ ]
++++
+=
++
t
t
tt
)(cos21
)(cos21
)sin()sin(
21
21
21
PSDMultiplication of Input frequencies-> out put
frequency difference and sum
36
NMR spectrum
QH
++
= +
22
2222
2
2
22222
)(21)3(
)12(4
zVyVxV
zVq
IIIIIIqQe
z
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- h ==
For 0
: assymmetry parameter
37
NMR spectrum
0
hA120 +
hA60 +
0
hA60 hA120
m=5/2
m=1/2
m=3/2
12A
6Aeq=0
eq0
[ ])I(I
qQeA)I(ImAEm 12413
22
+=
1. Hquadrupole0 0 2. Hzeeman >> Hquadrupole
6 12
Hq0I=5/2
NQR (nuclear quadrupole resonance)
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
3/21/2
-1/2-3/2
1/2-1/2
( )( ) ( )h12831312
22
n1 += II
qQecosmmm
powder pattern (I=3/2)
nn-2A1 n-A1 n+A1 n+2A1
A1=1/4e2qQ/
n16A2/9 n+A2/n
2nd oeder splitting of central transition for powder pattern spectruim
( )( )
( )( )
0
22
22
222
01/21/2
12432
649
cos-19cos-1
h
h
qQeII
IA
A
+
=
+=
=0
=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
n16A2/9 n+A2/n
Central transition lineOpposite?!
40
NMR spectrum
signal (A)
H
signal (B)
(1) sweep ( H=constant;H0)
spectrumMagnetic field sweep and frequency sweep
H0
() (constant; 0
signal (A)
H
signal (B)
0
Opposite!!Need to pay attentions !!
41
Hyperfine field at nuclear site
These give additional field (Hhf) at nuclear site-> shift in spectrum (NMR shift
0 0+
Fermi contact
Dipole interaction
orbital interaction
S-electron2)0(3
8 sheFH =
( ) 53
* 3rr
H ediprrss
= h
3* 1
rH eorb lh=
Core-poratizationinteraction ( ) =
iii
ecpH
22 )0()0(3
8 sh
=hf
In the material, nuclear experiences additional field due to hyperfine interaction
3d system~-100kOe/B
S
Hint
42
between NMR shift and magnetic susceptibility
H=Hz+Hhf
Hamiltonian
Hz=Hzeeman (H=H0)
Hhf=Hdipole+HFermi+Hcore-polarization+..=AIS A: hyperfine coupling constant
)( hf0 HHIH n += h ASH =hfNMR shift originates from thermal average value of Hhf
=ASince is expressed by (thermal average value of electron magnetization),
=AA (=AH0)
Knight shift is given by K = Hhf/H = AH/H A
K is proportional to
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)
total(T)=spin(T)+orb++impurity Ktotal(T)=Kspin(T)+Korb
What is ground state ? Spin singlet ? or magnetic?
From the NMR measurements, increase of 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
44
Example of K- plot
K-plot K A/NB,
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 (
%)
(emu/g)
Good linear relationK is proportional to
Hyperfine coupling constant can be estimated from the slope
BNA
ddK
=
Ahf =3.3 /B
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 istransferred hyperfine field
45
NMR in simple metal
1) NMR shift (Knight shift)K=(A/B)paulisince pauli is expressed by (1/2)g2B2NEf2
2)Nuclear spin lattice relaxation time T1Relaxation mechanism
scattering of free electron from k,> to k,> nuclear spin can flop from state
Pauli paramagnetism pauliNo electron correlation
Simple metal (like Cu and Al and so on)
( ) ( ) ( ){ } ( )
+ = kkkk
N EEkfkfsIAT 11
,
222
1
hh
( ) ( ){ } ( )Fk EETkfTkkfkf =
= BB
1
( ){ } TkNgAT FN B
2222
1
)(1 hh
=
1/T1 is proportional to T
T1T= constant
K is independent of T( ){ }FB Ng
AK 22
=
46
Korringa relation
Skg
kTKT
=
=
2
B
NB
2
B
NB2
1
441
h
h
h
( ){ } TkNgAT FN B
2222
1
)(1 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 22
=
47
Modified Korringa relation
Skg
kTKT
=
=
2
B
NB
2
B
NB2
1
441
h
h
h
Korringa Relation
Modified Korringa Relation
K>1AF spin correlationK
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.
=AA0
hfIHH nh=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=NHint
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 10
M12 cluster a
b
c
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)
S
Hint
Core- polarization
Mn4+(3B) : Hint ~ 22.0T
Mn3+(4B) : Hint ~ 26.4T
Mn3+(4B) : 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
N=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)
res= N 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 = -JSSNeel state
E=-J/4
Single state E=3J/4
J
54
NMR example
Both systems have a energy gap in spin excitation
T-dependence of K (NMR shift)
K~~(1/T)exp(-/ for spin dimerK~~(1/T0.5)exp(-/ for spin ladder
can be estimated
55
NMR example
1/T1~exp(-/
can be estimated fromT-dependence of T1
T175 K (for dimer)T1 =60 K (for ladder)
K74 K (for dimer)K =30 K (for ladder)
56
NMR example
K ~00
Comparison of K and T1 gives information about q-dependence of (q)
1/T1TK = exp(-T1/kT/exp(-K/kT for dimerif KT1, 1/T1TK should be constant
1/T1TK = exp(-T1/kT/exp(-K/kT/T0.5 for ladderif KT1, 1/T1TK should increase at low T
Observation of decrease -> this is due to T1>K
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 (
) 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
Knight shift 1/T1
TT 1/1
TT 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(-/
S-wave SC !
Decrease of spin susceptibilityT-dependence of 1/T1
63
NMR example (Superconductor)
Ru(Cu)
Sr
O
RuO2
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
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
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
NMR studies in High Tc Cuprates)
1/T1T shows CW behavior
1/T1T~1/(T+a)1/T1 ~T3
q
q
Q
Evidence of AF spin correlationsK is almost T-independent
68
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
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
Hloc
( )H H e e
Gi
G
rG
G r=
+
0
2
2 2
2 2
1
0 .999 1.000 1.001 1 .002
C
B
A
( ) ( )( )f h h H rS
= r d2
H /H 0
ABC
CoreSaddleCenter
Redfield patternpenetration depth: coherence length type II SC
70
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
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 )
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
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) /2=2.193MHz/T
Q=0.4410-24 (cm2)
99Ru (I=5/2) /2 =1.954MHz/T
Q=0.0710-24 (cm2)
Observation of Ru-NMR signal (below TC) magnetic ordering of Ru spins
Hzeeman>>HQuad
Hint=584kOe , Q=15MHz
K. Kumagai, Y. Furukawa et al., PRB 63 (2001)180509
73
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
74
Novel superconductors
newly discovered LaOFeAsCo(K)-doped BaFe2As2 system
Prof. Canfields 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
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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 == Bmagnetic moment of electron
gN:g-factor (2.0023)
201092.02
==cm
e
eB
h
H0 = 0 H0 0
Sz= 1/2
Sz = -1/2
(erg/G)
In the magnetic field of H
HSgE zBe == H
Bohr magneton
Hgh B=
e/2=28.02 /c.f., Proton N/2=42.577/
~ 28 Tesla
S band ~3.2GHz ~9 cmX-band ~9.5 ~3 K-band ~24 ~1.2J (Q)-band ~34 ~ 0.9-ban ~90 ~0.3
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ESR
Advantage of high frequency (magnetic filed) increase of resolutionincrease of sensitivitysimplification of the spectra and of their assignment
Magnetic field up to 2 ; 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) |/|~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
82
ESR
pulsed ESR
nano-second controlled system is required!
Short T1 -> short T2 (spin echo T2)
/2 pulse pulse Spin echo signal
If T2 is less than 1 should be less than 1
JEOL (Japan)
83
ESR
What can one get information from ESRinvestigation 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]Br89H2O
Eight Fe3+ (S=5/2) ions are almost coplanar
Strong AF interaction between Fe3+ spinsa total spin S=10 ground state
(S=5/26-5/22=10)
HS ++= Byxz SSEDS g)(222
Spin Hamiltonian for the S=10 ground state
medium
hard axis
91
E
H = 0
E
m = 0
m = 1 0m = - 1 0
Energy levels for 21 sublevels in S=10 ground state
~27K
mHDmE Bm g~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 ++= Byxz SSEDS g)(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
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