Dielectric response to the spin state transition in
LaCoO3-d Ceramics
Engineering Materials
Ceramics and Composites Laboratory
Rainer Schmidt
8th July 2008
Outline
Dielectric response to the spin state transition in LaCoO3-d Ceramics
Crystal Structure
Electronic Configuration and Magnetic Properties
Impedance Spectroscopy of LaCoO3-d Ceramics
Magneto-Electric Coupling
Conclusions
Crystal Structure
LaCoO3-d : Tilted Perovskite Structure
La3+:1.36 Å
O2-:
Ideal Perovskite
Shannon, Acta Cryst.A
32 (1976) p7518
1.4 Å
Co3+: 0.545 Å (LS)
0.61 Å (HS)
Tolerance factor:
LaCoO3-d was claimed to
contain oxygen vacancies
Radaelli & Cheong, Phys.Rev.B
66 (2002) p094408
t
R  R   1.003 LS  /
2 R  R 
O 2
O 2
La 3
Co 3
0.97 HS 
Crystal Structure
Tilted Perovskite Structure of LaCoO3-d
Looking down the b axis
Looking down the c axis
c
b
a
Rhombohedral Unit Cell
b
Space group:
Glazier notation:
Alexandrov notation:
R-3c (167)
a -a -a fff
a
Koehler & Wollan, J.Phys.Chem.Solids 2 (1957) p100
Goodenough, J.Phys.Chem.Solids 6 (1958) p287
Thornton et al. J.Solid State Chem. 61 (1986) p301
Electronic Configuration and Magnetic Properties
Co3+ : 3d6 configuration in an octahedral coordination
Co3+ : 3d6
eg
3d
Crystal field split - Hund’s coupling ~ 7 meV = 80 K
t2g
LS
HS
IS
S=0
S=2
S=1
Pauli’s rule: Two electrons can not occupy the same quantum state
Hund’s rule: Two Electrons prefer to half-occupy two degenerate orbitals
and paralell spin, rather than to fully occupy one orbital with
anti-paralell spin
Electronic Configuration and Magnetic Properties
High Spin State Model
Intermediate Spin State Model
Heikes et al. Physica (Amsterdam) 30 (1964) p1600
Jonker, J.Appl.Phys. 37 (1966) p1424
Raccah & Goodenough, Phys.Rev. 155 (1967) p932
Korotin et al., Phys.Rev.B 54 (1996) p5309
Radaelli & Cheong, Phys.Rev.B 66 (2002) p094408
Louca & Sarrao, Phys.Rev.Lett. 91 (2003) p155501
Ishikawa et al. Phys.Rev.Lett. 93 (2004) p136401
Haverkort et al., Phys.Rev.Lett. 97 (2006) p176405
Podlesnyak et al., Phys.Rev.Lett. 97 (2006) p247208
Klie et al., Phys.Rev.Lett. 99 (2007) p047203
Electronic Configuration and Magnetic Properties
50
100
150
200
250
300
350
Yamaguchi et al.,
Phys.Rev.B 53
(1996) R2926
Giblin et al.
Europhys.Lett. 70
(2005) p677
0.5
LaCoO3-d
Ts
0.3
Paramagnetism
0.3
0.2
0.2
0.1
0.5
0.4
0.4
0.1
0
50
100
150
200
250
300
350
0
50
100
150
200
250
300
350
7
30000000
2x10
7
20000000
1x10
7
3x10
1/c
"Curie-Tail" due to
a magnetic defect
structure called
magnetic polarons
or excitons
Magnetisation M in emu g
-1
0
Ts
0
50
100
10000000
Curie-Weiss plot
150
200
250
Temperature in Kelvin
300
350
2. Impedance Spectroscopy
Rainer Schmidt
Impedance Spectroscopy
Application of an Alternating Voltage Signal to a Sample:
U(w,t )=U0 cos(w t )
Measurement of the Alternating Current Response:
I(w,t ) = I0 cos(w t +d )
Time Dependent Definition of the Impedance:
ww t ) d 
U00 cos
cos(

U
ZZ(w,t, t ) 

II(w
w,t, t )
cosww
II00 cos(
t +t d )
UU( w,t
, t )
Time Independent Impedance:
Z Z*
w   Z exp (i idd )  Z '  iZ ''
Complex Relationship
Z  Z '  iZ '' 
1
iw C0  ' i ''
Equivalent Circuit Fitting of Impedance Spectra
Capacitance vs Frequency Plots
1
10
100
1000
10000 100000 1000000
1E7
1E-9
1E-9
c'0
2000000
bad fit
7
-1.0x10
100 K
1E-11
40 K
20 K
1E-12
0
10
10
1
0
2000000 4000000 6000
4000000 6000000 8000000 10000000
7
-1.0x10
Model 1
80 K
60 K
ginary part of specific impedance z''
1E-10
0
120 K
GB:
inary part of specific impedance z''
Specific capacitance c'
Electrode?
R2
6
-8.0x10
C2
GB
6
-6.0x10
Element
R2
C2
2
3
46
5
10
10-4.0x10
10 R1 10
CPE1-T
Frequency fCPE1-P
in Hz
C1
R1
Two plateaus indicate
GB
and bulk relaxations
1E-10
Model
Model1 2
6
-8.0x10
CPE1
R2
R2
R1
R1
C2
C2
CPE1
C1
1E-11
C1
Bulk Element
-6.0x10
R2
Bulk:
Element
6
GB
GB
C1
Bulk
Bulk
Element
Value
R2
1.2614E05
Value
Error1.344E-09
%C2
1.2614E05
R1
N/A 3.4609E05
1.344E-09
C1
N/A 1.936E-12
3.4609E05
N/A
2.931E-09
N/A Data File:
0.54747
Circuit Mo
N/A C:\SheffieldP
1.936E-12
Mode:
N/A Run
Fitting /
6
Maximum
Maximum
100
-2.0x10 Data
File: Iterations:
Optimizat
Optimization
Iterations:
0
Increasing
Circuit Model File:
C:\SheffieldPro
Type of F
Increasing
C:\SheffieldProject\AC_Impedance_Spectroscopy\L
Type of Fitting:
Complex
Mode:
Run Type
Fittingof/ W
S
frequency
Freedom
Free(+)
Freedom
Freedom
Value
Error
Free(+)
R2C2
Free(+)
c'∞
Free(+)
1.2614E05
N/A
Free(+)
C2R1 1E-12
Free(+)
Free(+)
1.344E-09
N/A Free(+)
6 C1
R1
Free(+)
6
7
-4.0x10
3.4609E05
N/A
10Free(+)10
CPE1-T
Free(+)
Free(+)
2.931E-09
N/A
Data
File:
CPE1-P
Free(+)
Free(+)
0.54747
N/A
Circuit
Model
File:
C1
Free(+)
Free(+)
1.936E-12
N/A
Mode:
GB relaxation peakGB relaxation peak
K
-2.0x10 Data60
File:
6
Circuit Model File:
60 K
R1+R2
Equivalent Circuit Fitting of Impedance Spectra
M '' & Z '' vs Frequency Plots
1
2
10
3
4
10
5
10
10
6
10
6
11
-3.0x10
2.0x10
Grain Boundary
6
-2.5x10
Bulk
11
1.5x10
6
-2.0x10
fmax=1/(2 ·R2·C2)
6
-1.5x10
11
1.0x10
fmax=1/(2 ·R1·C1)
6
-1.0x10
10
5.0x10
5
-5.0x10
60 Kelvin
2
10
3
10
4
10
Frequency f in Hz
0
0.0
1
10
Imaginary part of modulus M '' /
Imaginary part of specific impedance z''
10
0.0
5
10
6
10
Equivalent Circuit Fitting of Impedance Spectra
- 0Z '' vs
Z ' Plots
2000000 4000000
Imaginary impedance z'' in
8000000 10000000
7
-10000000
cm
-1.0x10
6000000
60 Kelvin
-8.0x10
6
-8000000
Low frequency Z’:
-6.0x10
6
-6000000
lim z ' ( f )  R1  R2;
-4.0x10
6
-2.0x10
6
f 0
GB relaxation peak
-4000000
R1+R2
-2000000
Increasing
frequency
Bulk
0.0
0.0
6
2.0x10
4.0x10
0
6
6.0x10
6
Real impedance z' in
8.0x10
cm
6
1.0x10
7
Equivalent Circuit Fitting of Impedance Spectra
Z '' / Z '' (max) vs Frequency Plots at Various Temperatures
Imaginary specific impedance z'' / z''max
10
100
40K
1000
10000
60K
100000
100K
80K
1.0
1000000
1E7
120K
1.0
0.8
0.6
0.8
GB1
GB2
0.6
0.4
0.4
0.2
0.2
0.0
1
10
0.0
2
10
3
10
4
10
5
10
Frequency in Hz
6
10
7
10
7
2x10
Magneto-Electric Coupling
-2
6x10
7
2x10Polarons
Strong Magneto-Electric Coupling of Magnetic
7
-2
1x10
5x10
r
22
0.30
20
0.25
0.20
18
0.15
-1
16
Magnetisation M in emu g
No Magneto-Electric
Spin-State Transition Ts
20
30 Coupling
40 at the 50
Temperature in Kelvin
20
40
60
80
100
24
0.35
Ts
Bulk relative permittivity
1/
1/
3x10
6x10
0.10
20
40
60
80
Temperature in Kelvin
100
Equivalent Circuit Fitting of Impedance Spectra
C1, C2, R1, R2 vs Temperature
20
40
60
80
100
120
1E-8
123
0.35
0.40
Temperature in Kelvin
90
66
51
39
31
0.45
24
1E-9
17.5
/T
GrainBoundary
Boundary22
Grain
0.5
1E-9
]
20.0
1E-10
1E-10
Grain
Grain Boundary
Boundary 11
1E-11
1E-11
Resistivity ln [
Specific capacitance in F/cm
1E-8
0.30
15.0
12.5
10.0
7.5
Bulk
Dielectric
Bulk
1E-12
1E-12
20
40
60
80
100
Temperature in Kelvin
120
Bulk
Grain Boundary 1
5.0
GB1
GB2
0.30
0.35
1/T
0.40
0.25
in 1/K
0.25
0.45
Conclusions
Conclusions
No Clear Magneto-Electric Coupling at the
Spin State Transition in LaCoO3-d
Stronger Magneto-Electric Coupling with the
Magnetic Polaron Defect Structure
The GB Relaxation Splits at the Spin State
Transition
The Second GB Relaxation Shows Typical
GB Capacitance and is not an Electrode
Interface Effect
Acknowledgments
Acknowledgments
Ian Terry, Sean Giblin
University of Durham, Department of Physics
Chris Leighton
University of Minneapolis, Department of Chemical
Engineering and Materials Science