Thermoelectric Materials and their Aplications

Thermoelectric Materials and their Aplications

1.   
               
PAUL SCHERRER INSTITUTPAUL SCHERRER INSTITUT
Electrical transport and magnetic
interactions in 3d and 5d transition
metal oxides
Laboratory for Developments and
Methods, Paul Scherrer Institute,
5232 Villigen PSI, Switzerland
[email protected]
Kazimierz Conder

2. For the past decades, a tremendous amount of effort
has been devoted to exploring the nature of 3d
transition metal oxides where various exotic states and
phenomena have emerged such as:
•high-Tc cuprate superconductivity
•colossal magnetoresistivity
•metal-insulator transitions
Motivation
It has been established that these states
and phenomena are caused by strong
cooperative interactions of spin, charge, and
orbital degrees of freedom.

3. 3
Lattice
Charge
order
Spin
order
Orbital
order
Spin, charge, orbital and lattice degrees of freedom in
strongly correlated electron systems
Higher cation charges:
•smaller radius
•smaller coord. numbers
Number of (unpaired)
electrons:
•spin
•charge
Occupied and
unoccupied orbitals
Bond anisotropy
Crystal field splitting
Jahn-Teller effect
Spin-orbit
interaction

4. Electrical properties of transition metal oxides
•The d-levels in most of the
transition metal oxides are partially
filled.
•According to band structure
calculations half of the known
binary compounds should be
conducting.
Empty or
completely filled
d-band (d
0
or d
10
)
Partly
filled
d-band

5. http://wps.prenhall.com/wps/media/objects/3085/3159106/blb2406.html
Energies of the d orbitals in
an octahedral crystal field.
Completely
filled orbitals:
d
6

Orbital interaction with the lattice
Orbitals are
nearby O
2-

Orbitals
are
between
O
2-

Octahedral crystal field

6. TiO- rutile
Ti
O
Ti
2+
3d
2
4s
0
metal
NiO- NaCl structureNi
2+
3d
8
4s
0
Is insulator!
Why not a metal?
Ni
O

7. CuO Cu
2+
3d
9
4s
0
CoO Co
2+
3d
7
4s
0
MnO Mn
2+
3d
5
4s
0
Cr
2
O
3
Cr
3+
3d
3
4s
0
Odd number of d electrons-
all this oxides should be
metals but are insulators
Whatever is the crystal
field splitting the
orbitals are not fully
occupied!!!
Why not metal?
3d
7
4s
23d
5
4s
2
3d
9
4s
23d
4
4s
2
Electron configurations
of elements

8. 8
Mott-Hubbard insulators
(on site repulsive electron force)
Sir Nevill
Francis Mot
Nobel Prize in
Physics 1977
•Most of the oxides show insulating behavior, implying that the d-
electrons are localized.
•Short-range Coulomb repulsion of electrons can prevent formation of
band states, stabilizing localized electron states.
W
W
U
Density of states
Upper Hubbard
band
Lower
Hubbard band
FL
Density of states
W FL
U
U<W U>W
Ni
2+
+ Ni
2+
→ Ni
3+
+ Ni
+

d
8
+ d
8
→ d
7
+ d
9
Correlation energy,
Hubbard U
Band width=W
small
large
Electron transfer
Coulomb repulsive
force
e
-

9. 9
Mott-Hubbard insulator
Charge Transfer insulator

10. 10
Electrons have not only charge but also spin!

11. 11
Magnetic order in transition metal oxides
Diamagnetism
Paramagnetism
Ferromagnetism
Antiferromagnetism
Ferrimagnetism

12. Magnetit (Fe
3
O
4
) inverse spinel.
Ferrimagnet.
Fe
2+
3d
6 Fe
3+
3d
5
Octahedral
coordination
Tetrahedral
coordination
Superexchange
Superexchange is a strong (usually)
antiferromagnetic coupling between
two nearest neighbor cations
through a non-magnetic anion.

•because of the Pauli Exclusion
Principle both spins on d and p
hybridized orbitals have to be
oriented antiparallel.
•this results in antiparallel
coupling with the neighbouring
metal cation as electrons on p-
orbital of oxygen are also
antiparallel oriented.
Pauli Exclusion Principle

13. Goodenough–Kanamori–Anderson Rules
d
z
2
d
x
2
−y
2
d
z
2
180
o
– Exchange between half
occupied or empty orbitals is
strong and antiferromagnetic
Ferromagnetic superexchange -
ferromagnetic when angle 90
o

14. 0.0 0.1 0.2 0.3
10
100
La
2-x
Sr
x
CuO
4
I
n
s
u
la
t
o
r
M
e
t
a
l
A
n
t
if
e
r
r
o
m
a
g
n
e
t
Superconductor
T
N
T
C
T
e
m
p
e
r
a
t
u
r
e

[
K
]
Sr-content x, (holes per CuO
2
-layer)
14
La, Sr
Cu
O
(LaBa)
2CuO
4 T
C=35K K.A. Müller und G.
Bednorz (IBM Rüschlikon 1986, Nobel price 1987)
High Temperature Superconductor: La
2-x
Sr
x
CuO
4
Undoped superconducting
cuprates are
antiferromagnetic Mott
insulators!

15. Double-exchange mechanism
Magnetic exchange that may arise between
ions on different oxidation states!
•Electron from oxygen orbital jumps
to Mn
4+
cation, its vacant orbital
can then be filled by an electron
from Mn
3+
.
•Electron has moved between the
neighboring metal ions, retaining its
spin.
•The electron movement from one
cation to another is “easier” when
spin direction has not to be
changed (Hund's rules).
Mn
3+
d
4
Mn
4+
d
3
O
2-
2p

16. 16
Ferromagnetic
Metal
Paramagnetic
Insulator
La
1-x
Ca
x
MnO
3
.

Double exchange mechanism.
The electron movement from
one cation to another is
“easier” when spin direction
has not to be changed
Note that no oxygen sites are
shown!

17. 17
A.P. Ramirez, J. Phys.: Condens.
Matter., 9 (1997) 8171
CMR (colossal magnetoresistance) La
0.75
Ca
0.25
MnO
3

T
c
)(
)()0(
HR
HRHR
R


Magnetoresistance is defined as
the relative change of resistances
at different magnetic field
Tc
Ferromagnetic
Metal
Paramagnetic
Insulator

18. ✓
4d and 5d orbitals are more extended than 3d’s

✓
reduced on-site Coulomb interaction strength

✓
sensitive to lattice distortion, magnetic order, etc.

✓
spin-orbit (SO) coupling much stronger
5d vs. 3d transition metal oxides

19. PRB, 74 (2006) 113104
•4d and 5d orbitals are more extended than
3d’s
•Reduced Coulomb interaction
Heungsik Kim et al., Frontiers
in Condensed Matter Physics,
KIAS, Seoul, 2009
Insulator
Metal
Insulator

20. Sr
2IrO
4
Under the octahedral
symmetry the 5d states
are split into t
5
2g
and e
g

orbital states. The
system would become a
metal with partially filled
wide t
2g
band.
PRL 101, 076402 (2008)
J
eff
= |S – L| is an
effective total
angular momentum
defined in the t
2g
manifold with the
spin S and the orbital
angular L momenta.
An unrealistically large
U>> W could lead to a
Mott insulator. However,
a reasonable U cannot lead
to an insulating state as
already 4d Sr
2
RhO
4
is a
normal metal.
By a strong Spin-Orbit
(SO) coupling
the t
2g
band splits into
effective total angular
momentum J
eff=1/2
doublet and J
eff=3/2
quartet bands.
The J
eff=1/2 spin-orbit
states form a narrow band
so that even small U opens
a Mott gap, making it a
Mott insulator
The formation of the
J
eff
bands due to the
large SO coupling
energy explains why
Sr
2
IrO
4
is insulating
while Sr
2
RhO
4
is
metallic.

21. Opposite directions of electronic orbital
motions around a nucleus occur with the same
probability, and thereby cancel each other.
Interaction between the electron's spin and the magnetic field
generated by the electron's orbit around the nucleus.
Spin and orbital motion have the same directions.
The spin-orbit correlation suppresses the transfer
of electrons to neighboring atoms making Sr
2
IrO
4

an insulator.

22. 22
Na
2
IrO
3
and Li
2
IrO
3
Kitaev-Heisenberg model
Crystal structure of
Na
2IrO
3
monoclinic space
group C 2/m
PRB 88, 035107 (2013)
Iridium
honeycomb layers
stacked along the
monoclinic c axis
For both Na
2
IrO
3
and Li
2
IrO
3
a
honeycomb structure is observed
enabling a realization of the
exactly solvable spin model with
spin liquid ground state proposed
by Kitaev.

23. 23
J
1=0 J
2=0J
1=2J
2
Heisenberg exchangeKitaev exchange
A Spin Liquid (Figure Credits: Francis Pratt, STFC)
Na
2
IrO
3
and Li
2
IrO
3
Kitaev-Heisenberg model
J>0 ferromagnetic
J<0 antiferromagnetic
PRL 105, 027204 (2010)

24. 24
Na
2
IrO
3
and Li
2
IrO
3
Kitaev-Heisenberg model
A Spin Liquid (Figure Credits: Francis Pratt, STFC)
•Na
2
IrO
3
and Li
2
IrO
3
order
magnetically at 15K
•I was suggested (PRB 84, 100406
(2011)) that the reduction of the
chemical pressure along the c-
axis can induce spin glass
behavior.
•This can be achieved either by
exerting pressure in the ab
plane or substituting Na by
smaller Li ions.

25. •Antiferromagnetic transition around 15K
for the parent compound Na
2
IrO
3
.
•This is suppressed for the doped sample.
K. Rolfs, S. Toth, E. Pomjakushina, D.
Sheptyakov, K. Conder, to be
published
Na
2-xLi
xIrO
3 with x = 0, 0.05, 0.1 and 0.15
Magnetization measurements of
Na
1.9Li
0.1IrO
3 in 0.1T. Real and imaginary
part of the AC susceptibility measured
at different frequencies.
The cusp is frequency
dependent which is
characteristic for the
spin-glass phase
Na
1.95
Li
0.05
IrO
3
Na
2IrO
3
G
l
a
s
s
y

s
t
a
t
e
For higher doping
spin-glass state

26. 26
Conclusions
Electrical transport
properties in transition
metals (Mott insulators):
•crystal field splitting
•Coulomb repulsion
Colossal
magnetoresistivity:
•crystal field splitting
•orbital order
5d iridates:
•crystal field splitting
•spin-orbit interaction

27. 27