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 )

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

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:

Merits of NMR: local probe of electronic and magnetic features

• Site selected • Impurity phase isolated• Sensitive to the excitation near the Fermi-level

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

Simple resonance theory:

Zeeman energy: E = oh = nHo

Nuclear spin I: 2I +1 energy states

For I = 3/2,

(MHz)

H = 0 H = Ho

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

NMR frequency shifts:

0

0 00 (1 )

HK K

H

Site-IoNMR

signal

Site-II

(MHz)

Site-I

Site-II

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

(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

Satellite Lines:

I = 3/2

EFG = 0 EFG 0

o o+ Q/2o- Q/2o

27Al (I = 5/2) NMR powder pattern in Cr2AlC

76 77 78 79 80

27 A

l NM

R s

ignal

Frequency (MHz)

Cr2AlC

Spin-lattice relaxation time (T1):

M(t)

t

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

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

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.

Varian 300 Solid-State NMR

Home-built NMR probe-head(Top-loaded)

7.05 T superconducting magnet

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

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

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

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

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

Bulk magnetic susceptibility of BaCu2V2O8

Ghoshray et al. PRB 71 (2005)He et al. PRB 69 (2004)

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.

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 (%

)

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

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

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.

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

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).

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

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

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

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.