Electrical transport and magnetic interactions in 3d and 5d transition metal oxides

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
kazimierz.conder@psi.ch
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 (d0 or d10)
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:
d6
Orbital interaction with the lattice
Orbitals are
nearby O2-
Orbitals
are
between
O2-
Octahedral crystal field

6. TiO- rutile
Ti
O
Ti2+ 3d24s0
metal
NiO- NaCl structure Ni2+ 3d84s0
Is insulator!
Why not a metal?
Ni
O

7. CuO Cu2+ 3d94s0
CoO Co2+ 3d74s0
MnO Mn2+ 3d54s0
Cr2O3 Cr3+ 3d34s0
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?
3d74s23d54s2 3d94s23d44s2 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
Ni2+ + Ni2+ → Ni3+ + Ni+
d8 + d8 → d7 + d9
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 (Fe3O4) inverse spinel.
Ferrimagnet.
Fe2+ 3d6 Fe3+ 3d5
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
dz
2
dx
2
−y
2
dz
2
180o – Exchange between half
occupied or empty orbitals is
strong and antiferromagnetic
Ferromagnetic superexchange -
ferromagnetic when angle 90o

14. 0.0 0.1 0.2 0.3
10
100
La2-x
Srx
CuO4
Insulator
Metal
Antiferromagnet
Superconductor
TN
TC
Temperature[K]
Sr-content x, (holes per CuO2
-layer)
14
La, Sr
Cu
O
(LaBa)2CuO4 TC=35K K.A. Müller und G.
Bednorz (IBM Rüschlikon 1986, Nobel price 1987)
High Temperature Superconductor: La2-xSrxCuO4
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+ d4 Mn 4+ d3
O2- 2p

16. 16
Ferromagnetic
Metal
Paramagnetic
Insulator
La1-xCaxMnO3. 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) La0.75Ca0.25MnO3
Tc
)(
)()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. Sr2IrO4
Under the octahedral
symmetry the 5d states
are split into t5
2g and eg
orbital states. The
system would become a
metal with partially filled
wide t2g band.
PRL 101, 076402 (2008)
Jeff = |S – L| is an
effective total
angular momentum
defined in the t2g
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 Sr2RhO4 is a
normal metal.
By a strong Spin-Orbit
(SO) coupling
the t2g band splits into
effective total angular
momentum Jeff=1/2
doublet and Jeff=3/2
quartet bands.
The Jeff=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
Jeff bands due to the
large SO coupling
energy explains why
Sr2IrO4 is insulating
while Sr2RhO4 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 Sr2IrO4
an insulator.

22. 22
Na2IrO3 and Li2IrO3 Kitaev-Heisenberg model
Crystal structure of Na2IrO3
monoclinic space
group C 2/m
PRB 88, 035107 (2013)
Iridium
honeycomb layers
stacked along the
monoclinic c axis
For both Na2IrO3 and Li2IrO3 a
honeycomb structure is observed
enabling a realization of the
exactly solvable spin model with
spin liquid ground state proposed
by Kitaev.

23. 23
J1=0 J2=0J1=2J2
Heisenberg exchangeKitaev exchange
A Spin Liquid (Figure Credits: Francis Pratt, STFC)
Na2IrO3 and Li2IrO3 Kitaev-Heisenberg model
J>0 ferromagnetic
J<0 antiferromagnetic
PRL 105, 027204 (2010)

24. 24
Na2IrO3 and Li2IrO3 Kitaev-Heisenberg model
A Spin Liquid (Figure Credits: Francis Pratt, STFC)
• Na2IrO3 and Li2IrO3 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 Na2IrO3.
• This is suppressed for the doped sample.
K. Rolfs, S. Toth, E. Pomjakushina, D.
Sheptyakov, K. Conder, to be published
Na2-xLixIrO3 with x = 0, 0.05, 0.1 and 0.15
Magnetization measurements of
Na1.9Li0.1IrO3 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
Na1.95Li0.05IrO3
Na2IrO3
Glassystate
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