PAUL SCHERRER INSTITUT
Electrical transport and magnetic
interactions in 3d and 5d transition
metal oxides
Kazimierz Conder
Laboratory for Developments and
Methods, Paul Scherrer Institute,
5232 Villigen PSI, Switzerland
kazimierz.conder@psi.ch
Motivation
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
It has been established that these states
and phenomena are caused by strong
cooperative interactions of spin, charge, and
orbital degrees of freedom.
Spin, charge, orbital and lattice degrees of freedom in
strongly correlated electron systems
Spin
order
Crystal field splitting
Jahn-Teller effect
Number of (unpaired)
electrons:
• spin
• charge
Lattice
Spin-orbit
interaction
Higher cation charges:
• smaller radius
• smaller coord. numbers
Charge
order
Orbital
order
Bond anisotropy
Occupied and
unoccupied orbitals
3
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.
Partly
filled
d-band
Empty or
completely filled
d-band (d0 or d10)
Orbital interaction with the lattice
Octahedral crystal field
Orbitals are
nearby O2-
Orbitals
are
between
O2-
Completely
filled orbitals:
d6
Energies of the d orbitals in
an octahedral crystal field.
http://wps.prenhall.com/wps/media/objects/3085/3159106/blb2406.html
TiO- rutile
Ti
Ti2+ 3d24s0
O
metal
NiO- NaCl structure Ni2+ 3d84s0
Ni
O
Is insulator!
Why not a metal?
Why not metal?
CuO
Cu2+ 3d94s0
CoO
Co2+ 3d74s0
MnO
Mn2+ 3d54s0
Cr2O3
Cr3+ 3d34s0
Whatever is the crystal
field splitting the orbitals
are not fully occupied!!!
Odd number of d electronsall this oxides should be
metals but are insulators
3d44s2
3d54s2
Electron configurations
3d74s2
3d94s2 of elements
Mott-Hubbard insulators
Sir Nevill
Francis Mot
(on site repulsive electron force)
Nobel Prize in
Physics 1977
Correlation energy,
Hubbard U
Band width=W
e-
large
+
→
+
d8 + d8 → d7 + d9
Ni2+
small
Ni2+
Ni3+
Ni+
U>W
U<W
U
W
Electron transfer
Coulomb repulsive
force
Upper Hubbard
band
W
FL
FL
Lower
Hubbard band
W
Density of states
U
Density of states
•Most of the oxides show insulating behavior, implying that the delectrons are localized.
•Short-range Coulomb repulsion of electrons can prevent formation of
band states, stabilizing localized electron states.
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Mott-Hubbard insulator
Charge Transfer insulator
9
Electrons have not only charge but also spin!
10
Magnetic order in transition metal oxides
Diamagnetism
Paramagnetism
Ferromagnetism
Antiferromagnetism
Ferrimagnetism
11
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 porbital of oxygen are also
antiparallel oriented.
Fe2+ 3d6
Fe3+ 3d5
Pauli Exclusion Principle
Octahedral
coordination
Tetrahedral
coordination
Magnetit (Fe3O4) inverse spinel.
Ferrimagnet.
Goodenough–Kanamori–Anderson Rules
dx2−y2
dz 2
dz2
180o – Exchange between half
occupied or empty orbitals is
strong and antiferromagnetic
Ferromagnetic superexchange ferromagnetic when angle 90o
High Temperature Superconductor: La2-xSrxCuO4
(LaBa)2CuO4 TC=35K K.A. Müller und G.
Bednorz (IBM Rüschlikon 1986, Nobel price 1987)
Cu
TC
Metal
TN
Insulator
100
Antiferromagnet
La, Sr
Temperature [K]
O
La2-xSrxCuO4
Superconductor
10
0.0
0.1
0.2
0.3
Sr-content x, (holes per CuO2-layer)
Undoped superconducting
cuprates are
antiferromagnetic Mott
insulators!
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Double-exchange mechanism
Magnetic exchange that may arise between
ions on different oxidation states!
O2- 2p
Mn 3+ d4
Mn 4+ d3
• 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).
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!
Ferromagnetic
Metal
Paramagnetic
Insulator
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CMR (colossal magnetoresistance) La0.75Ca0.25MnO3
Tc
Ferromagnetic
Metal
Tc
Magnetoresistance is defined as
the relative change of resistances
at different magnetic field
Paramagnetic
Insulator
R 
R ( H  0)  R ( H )
R(H )
A.P. Ramirez, J. Phys.: Condens.
Matter., 9 (1997) 8171
17
5d vs. 3d transition metal oxides
✓ 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
• 4d and 5d orbitals are more extended than 3d’s
• Reduced Coulomb interaction
Insulator
Metal
Insulator
PRB, 74 (2006) 113104
Heungsik Kim et al., Frontiers
in Condensed Matter Physics,
KIAS, Seoul, 2009
Sr2IrO4
Under the octahedral
symmetry the 5d states
are split into t52g and eg
orbital states. The
system would become a
metal with partially filled
wide t2g band.
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.
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.
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.
PRL 101, 076402 (2008)
Interaction between the electron's spin and the magnetic field
generated by the electron's orbit around the nucleus.
Opposite directions of electronic orbital
motions around a nucleus occur with the same
probability, and thereby cancel each other.
Spin and orbital motion have the same directions.
The spin-orbit correlation suppresses the transfer
of electrons to neighboring atoms making Sr2IrO4
an insulator.
Na2IrO3 and Li2IrO3 Kitaev-Heisenberg model
Crystal structure of Na2IrO3
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.
monoclinic space
group C 2/m
Iridium
honeycomb layers
stacked along the
monoclinic c axis
PRB 88, 035107 (2013)
22
Na2IrO3 and Li2IrO3 Kitaev-Heisenberg model
Kitaev exchange
Heisenberg exchange
J>0 ferromagnetic
J<0 antiferromagnetic
A Spin Liquid (Figure Credits: Francis Pratt, STFC)
J1=0
J1=2J2
J2=0
PRL 105, 027204 (2010)
23
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 caxis can induce spin glass
behavior.
• This can be achieved either by
exerting pressure in the ab
plane or substituting Na by
smaller Li ions.
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Na2-xLixIrO3 with x = 0, 0.05, 0.1 and 0.15
For higher doping
spin-glass state
Na2IrO3
Na1.95Li0.05IrO3
Glassy state
The cusp is frequency
dependent which is
characteristic for the
spin-glass phase
• Antiferromagnetic transition around 15K
for the parent compound Na2IrO3.
• This is suppressed for the doped sample.
Magnetization measurements of
Na1.9Li0.1IrO3 in 0.1T. Real and
imaginary part of the AC susceptibility
measured at different frequencies.
K. Rolfs, S. Toth, E. Pomjakushina, D.
Sheptyakov, K. Conder, to be published
Conclusions
5d iridates:
• crystal field splitting
• spin-orbit interaction
Electrical transport
properties in transition
metals (Mott insulators):
• crystal field splitting
• Coulomb repulsion
Colossal
magnetoresistivity:
• crystal field splitting
• orbital order
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