1. Dielectric response to the spin state transition in LaCoO3-d Ceramics
Engineering Materials
Ceramics and Composites Laboratory
Rainer Schmidt
8th July 2008

2. Dielectric response to the spin state transition in LaCoO3-d Ceramics
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

3. contain oxygen vacancies
Crystal Structure
LaCoO3-d : Tilted Perovskite Structure
La3+:1.36 Å
Shannon, Acta Cryst.A
32 (1976) p7518
O2-: 1.4 Å
Co3+: Å (LS)
0.61 Å (HS)
Ideal Perovskite
Tolerance factor:
LaCoO3-d was claimed to
contain oxygen vacancies
Radaelli & Cheong, Phys.Rev.B
66 (2002) p094408

4. Tilted Perovskite Structure of LaCoO3-d
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 a
Space group: R-3c (167)
Glazier notation: a - a - a -
Alexandrov notation: f f f
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

5. Co3+ : 3d6 configuration in an octahedral coordination
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

6. Intermediate Spin State Model
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

7. LaCoO3-d Paramagnetism "Curie-Tail" due to a magnetic defect
Electronic Configuration and Magnetic Properties
LaCoO3-d
Paramagnetism
"Curie-Tail" due to
a magnetic defect
structure called
magnetic polarons
or excitons
1/c
Yamaguchi et al.,
Phys.Rev.B 53
(1996) R2926
Giblin et al.
Europhys.Lett. 70
(2005) p677

8. Impedance Spectroscopy
2. Impedance Spectroscopy Rainer Schmidt
Impedance Spectroscopy
Application of an Alternating Voltage Signal to a Sample:
Measurement of the Alternating Current Response:
U(w,t )=U0 cos(w t )
I(w,t ) = I0 cos(w t +d )
Time Dependent Definition of the Impedance:
Time Independent Impedance:
U(w,t ) U0 cos(w t )
I(w,t ) I0 cos(w t + d )
Z(w,t )
(id ) Z*
Complex Relationship

9. Capacitance vs Frequency Plots
Equivalent Circuit Fitting of Impedance Spectra
Capacitance vs Frequency Plots
bad fit
Two plateaus indicate
GB and bulk relaxations

10. Equivalent Circuit Fitting of Impedance Spectra
M '' & Z '' vs Frequency Plots

11. - Z '' vs Z ' Plots Low frequency Z’:
Equivalent Circuit Fitting of Impedance Spectra
- Z '' vs Z ' Plots
Low frequency Z’:

12. Z '' / Z '' (max) vs Frequency Plots at Various Temperatures
Equivalent Circuit Fitting of Impedance Spectra
Z '' / Z '' (max) vs Frequency Plots at Various Temperatures

13. Strong Magneto-Electric Coupling of Magnetic Polarons
No Magneto-Electric Coupling at the Spin-State Transition Ts Ts

14. Equivalent Circuit Fitting of Impedance Spectra
C1, C2, R1, R2 vs Temperature
Grain Boundary 2
Grain Boundary 1
Bulk

15. 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

16. Acknowledgments University of Durham, Department of Physics
Ian Terry, Sean Giblin
University of Durham, Department of Physics
Chris Leighton
University of Minneapolis, Department of Chemical
Engineering and Materials Science