1.                  
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 1

2. 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.

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

4. Empty or completely filled d-band (d0 or d10)
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. Orbital interaction with the lattice
Octahedral crystal field
Energies of the d orbitals in an octahedral crystal field.
Completely filled orbitals: d6
Orbitals are nearby O2-
Orbitals are between O2-

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

7. Why not metal? CuO Cu2+ 3d94s0 CoO Co2+ 3d74s0 MnO Mn2+ 3d54s0
Whatever is the crystal field splitting the orbitals are not fully occupied!!!
CuO Cu2+ 3d94s0
CoO Co2+ 3d74s0
MnO Mn2+ 3d54s0
Cr2O Cr3+ 3d34s0
Odd number of d electrons-
all this oxides should be metals but are insulators
3d74s2
3d54s2
3d94s2
3d44s2
Electron configurations
of elements

8. Mott-Hubbard insulators (on site repulsive electron force)
Sir Nevill Francis Mot Nobel Prize in Physics 1977
Ni2+ + Ni2+ → Ni3+ + Ni+
d8 + d8 → d7 + d9
Correlation energy, Hubbard U
Band width=W
small
large
Electron transfer
Coulomb repulsive
force e- W U
Density of states
Upper Hubbard band
Lower
Hubbard band FL
U<W
U>W
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.

9. Mott-Hubbard insulator Charge Transfer insulator

10. Electrons have not only charge but also spin!

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

12. Pauli Exclusion Principle
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.
Fe3+ 3d5
Fe2+ 3d6
Pauli Exclusion Principle
Octahedral
coordination
Tetrahedral
coordination
Magnetit (Fe3O4) inverse spinel.
Ferrimagnet.

13. Goodenough–Kanamori–Anderson Rules
dz2
dx2−y2
180o – Exchange between half occupied or empty orbitals is strong and antiferromagnetic
Ferromagnetic superexchange - ferromagnetic when angle 90o

14. High Temperature Superconductor: La2-xSrxCuO4
(LaBa)2CuO4 TC=35K K.A. Müller und G. Bednorz (IBM Rüschlikon 1986, Nobel price 1987)
La, Sr Cu O
Undoped superconducting cuprates are antiferromagnetic Mott insulators! 14

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).
O2- 2p
Mn 3+ d4
Mn 4+ d3

16. 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

17. CMR (colossal magnetoresistance) La0.75Ca0.25MnO3Tc Tc
Magnetoresistance is defined as the relative change of resistances at different magnetic field
Paramagnetic
Insulator
Ferromagnetic
Metal
A.P. Ramirez, J. Phys.: Condens. Matter., 9 (1997) 8171

18. 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

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

20. 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.
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.
Jeff = |S – L| is an effective total angular momentum defined in the t2g manifold with the spin S and the orbital angular L momenta.
PRL 101, (2008)

21. 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.

22. 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, (2013)

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

24. Na2IrO3 and Li2IrO3 Kitaev-Heisenberg model
Na2IrO3 and Li2IrO3 order magnetically at 15K
I was suggested (PRB 84, (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.
A Spin Liquid (Figure Credits: Francis Pratt, STFC)

25. Na2-xLixIrO3 with x = 0, 0.05, 0.1 and 0.15
For higher doping spin-glass state
Na2IrO3
Na1.95Li0.05IrO3
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.
Glassy state
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

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