recent nmr results in ncku c. s. lue ( 呂欽山 ) department of physics, national cheng kung...
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Recent NMR Results in NCKU
C. S. Lue (呂欽山 )
Department of Physics,
National Cheng Kung University
(國立成功大學物理系 )
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Outline:
I: Fundamental NMR principles:
(i) NMR frequency shifts
(ii) Quadrupole interactions
(ii) Spin-lattice relaxation rates
II: Studied systems:
(i) 27Al NMR study of electronic structure of Al3M
(ii) 51V NMR study of spin gap nature of BaCu2V2O8
(iii) 51V NMR study of pseudogap characteristics of Fe2VAl
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Bulk Properties: collective response of the system to an external perturbation
• Electronic property: = E/J• Magnetic property: = M/H• Thermal property: C = U/T• Optical property:
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Merits of NMR: local probe of electronic and magnetic features
• Site selected • Impurity phase isolated• Sensitive to the excitation near the Fermi-level
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Central transition 71Ga NMR line shape in NbGa3
91.6 91.7 91.8 91.9
71G
a NM
R sig
nals
Frequency (MHz)
Ga-II
Ga-I
D022 crystal structure
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Simple resonance theory:
Zeeman energy: E = oh = nHo
Nuclear spin I: 2I +1 energy states
For I = 3/2,
(MHz)
H = 0 H = Ho
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NMR in Solids:
3 3
8( )
32
( )[ ] ]
3[m B n s r
r r s s l
r rH I
(i) Magnetic hyperfine interactions: couplings between nuclear magnetic moment n and electronic magnetic moment e
Fermi-contact dipolar orbitals-like e- non-s-character e-
Ks Kan Korb
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NMR frequency shifts:
0
0 00 (1 )
HK K
H
Site-IoNMR
signal
Site-II
(MHz)
Site-I
Site-II
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NMR Shift & Magnetic susceptibility
(a) Simple metals: (s-electrons)
(b) d-electron based materials:
Note: Bulk diamagnetic term L does not enter because of the small hyperfine field.
ss hf sK H
total s d VV L
s d orbtotal hf s hf d hf VVK H H H
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(ii) Electric hyperfine interactions: couplings between nuclear quadrupole moment eQ and electric field gradient
(For I > 1/2 in the non-cubic environments with axial symmetry )
+q +q
-q
-q
-q
-q
+q+q
2 2 2
3Quadrupole fr
[ (3 )] [3 ( 1)]4 (2
equency
1) 4 (2 1)
2 (2 1)
zzQ zz z m
zzQ
eQVeQH V I I E m
eQV
I II I I
I h
I
I
-q
-q -q
-q
+q-q +q +q
Ea > Eb
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Satellite Lines:
I = 3/2
EFG = 0 EFG 0
o o+ Q/2o- Q/2o
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27Al (I = 5/2) NMR powder pattern in Cr2AlC
76 77 78 79 80
27 A
l NM
R s
ignal
Frequency (MHz)
Cr2AlC
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Spin-lattice relaxation time (T1):
M(t)
t
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Recovery curve of 11B in ZrB2
0.1 1 10 100-0.8
-0.4
0.0
0.4
0.8
del (ms)
ZrB2
T= 300 K
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T1 & Electronic origins
2
2
1
1
2
From a simple scattering theory
1( ) ( )[1
For a simple paramagneti
( )]
( )[1 ( )]
c
~
metal
1( )
( )
e n
F
F
i V j D E f E f E dE
D ET
T
f E f E E
1 11 1
1
1 1 1 11 1 1 1
(a) Simple metals:
( -electrons dominated)
Korringa relation
(b) -electron mate
( )
constant ( )
( )
rials
)
:
( ) (
s
s orb d
T T
TT
T
d
T
s
T T
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Magnetic dipolar broadening of rigid lattices:
(Simplest case: cubic)r ~ 2A and ~ 10-3 B
Hloc ~ /r3 ~ 1 gauss
Ho = 1 T = 104 gauss
Hloc /Ho = /o ~ 10-4
If o ~ 10 - 100 MHz,
intrinsic line width
~ 1 - 10 kHz
Motional narrowing: motional effects narrow the line width in normal liquids.
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Varian 300 Solid-State NMR
Home-built NMR probe-head(Top-loaded)
7.05 T superconducting magnet
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D023-type Al3Zr & Al3Hf
Potential aerospace applications:High melting point
Low mass density
Large elastic modulus
Shortage: Poor ductility
Interesting issues: Electronic properties
Structural stability
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27Al NMR central transitions of Al3Zr & Al3Hf
Central transition line shapes: Anisotropic Knight shift &
Quadrupole effects
High-frequency peak: Al-III
Low-frequency part: Al-I & Al-II
78.39 78.42 78.45 78.48 78.51
27A
l NM
R s
igna
l (ar
b. u
nits
)
Frequency (MHz)
Al3Hf
Al3Zr
27K=0
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Satellite lines for the three Al sites in Al3Zr and Al3Hf
77 78 79 80
S
pin-
echo
inte
gral
(ar
b. u
nits
)
Frequency (MHz)
Al-II
Al-I
Al-III
Al3Zr
77 78 79 80
Al-I
Al-III
Spi
n-ec
ho in
tegr
al (
arb.
uni
ts)
Frequency (MHz)
Al3Hf
Al-II
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Partial 27Al NMR results of Al3Zr & Al3Hf
6 2
1
1Using 1.9 10 gauss for Al and experimental 2 [ ] ( )
hf
s shf sB n Fh D Ek
TTH H
Alloy Al-I Al-II Al-III Total
Al3Zr 0.0147 0.0146 0.0223 0.0172
Al3Hf 0.0145 0.0232 0.0304 0.0227
Smaller Fermi-level DOS in Al3Zr → Al3Zr is more stable than Al3Hf with respect to the D023 structure, consistent with the fact that Al3Hf becomes more favorable with D022 as T > 650 C.
Fermi-level s-DOS (states/eV atom) for each Al crystallographic site
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Oxidation states: Magnetic Cu2+ (S = ½)
Nonmagnetic V5+
Spin chains:CuO4 square plaquette +
edge-sharing V(I)O4 tetrahedra
Alternating coupling ratio J2/J1 = 0.2
Spin gap = 230 K
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Bulk magnetic susceptibility of BaCu2V2O8
Ghoshray et al. PRB 71 (2005)He et al. PRB 69 (2004)
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Models for the S=1/2 one-dimensional spin chain compounds
1. Alternating-chain model
2. Dimer-chain model
/1( ) T
spin T eT
/
1( )
(3 )spin TT
T e
J1
J2
J J
J1J1
J JJ
From the analyses of the bulk susceptibility and heat capacity, He et al. concluded that the alternating chain model is more suitable for the understanding of the gap characteristics of BaCu2V2O8.
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51V NMR investigation of BaCu2V2O8
50 100 150 200 250 300
0.0
0.1
0.2
0.3
0.4
T (K)
V-I V-II
Kob
s (%
)
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T-dependent NMR shifts of BaCu2V2O8
0.003 0.006 0.009 0.012 0.015
10-3
10-2
10-1
(c)K (II) = 370 K
Ksp
inT
0.5 (
K0.5)
1/T (K-1)
(c)K (I) = 360 K
0.003 0.006 0.009 0.012 0.015
0.01
0.1
1
(d)K (II) = 470 K
Ksp
inT
(K
)
1/T (K-1)
(d)K (I) = 460 K
/1( ) T
spinK T eT
/
1( )
(3 )spin TK T
T e
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T-dependent NMR T1 of BaCu2V2O8
0.003 0.006 0.009 0.012
1
10
1/T
1 (s-1
)
1/T (K-1)
(c)R (II) = 440 K
0.003 0.006 0.009 0.012
1
10
1/T
1 (s
-1)
1/T (K-1)
(d)R (II) = 450 K
/
1
1 TeT
/1
1 1
(3 )TT T e
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NMR parameters of BaCu2V2O8
Alternating-chain model:
K(I) = 360 K
K(II) = 370 K
R(II) = 440 K
For V-II, R/K ~ 1.2
Dimer-chain model:
K(I) = 460 K
K(II) = 470 K
R(II) = 450 K
For V-II, R/K ~ 1
Summary: Both models seem to be suitable for the understanding of the spin gap nature in BaCu2V2O8.
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L21 Heusler-type Fe2VAl
• Transport: semi-conducting behavior
• Magnetism: paramagnetic behavior (Pauli or Van-Vleck?)
• Low-T specific heat:
possible 3d heavy fermion = 14 mJ/mol K2
mass enhancement m*/m ~ 20 -70)
• LiV2O4: 3d heavy fermion?
• FeSi: 3d Kondo insulator
22 ( )
3 B Fk D E
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Theoretical calculations on Fe2VAl
• G. Y. Guo, G. A. Botton, and Y. Nishino, J. Phys.: Condens. Matter 10, L119 (1998).
• D. J. Singh and I. I. Mazin, Phys. Rev. B 57, 14352 (1998).
• R. Weht and W. E. Pickett, Phys. Rev. B 58, 6855 (1998).
• M. Weinert and R. E. Watson, Phys. Rev. B 58, 9732 (1998).
• A. Bansil, S. Kaprzyk, P. E. Mijnarends, and J. Tobola, Phys. Rev. B 60, 13396 (1999).
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1. Narrow NMR line width:
nonmagnetic
2. NMR shifts:
For 51V, Ko= 0.61% is not likely due
to the Pauli paramagnetism.
→ Van-Vleck mechanism dominated
Band splitting: Eg ~ 0.22 eV
/ 2( ) g BE k T
o T eKK T
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T-dependent NMR T1 of Fe2VAl
Eg ~ 0.27 eV
Low-T data:
V partial Fermi-level DOS
D(EF) = 0.023 states/eV atom
Total Fermi-level DOS
D(EF) = 0.055 states/eV atom
→ Semi-metallic characteristics
/ 22
1
1g BE k TbT eaT
T
2
1
12 [ ] (
1)
3( )
hf Fd
B nhk H D ETT
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1. Sample-dependent heat capacity
2. Solid line: C(T) = T +T3+T5
Small = 1.5 mJ/mol K2
3. Magnetic cluster induced low-T
upturn in
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Field-dependent specific heat in Fe2VAl
2 2 (2 1)2
2 (2 1) 2[ (2 1) ]( 1) ( 1)
,
3( 1) 3.7
20.0037 per formula unit
x J x
B x J x
B
B
B B
x e x eC Nk J
e e
g Hx
k T
J g J J
N
• Multi-level Schottky anomaly:
Conclusions: the reported enhancement is not intrinsic → Fe2VAl is a false d-electron heavy fermion.