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

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 kazimierz.conder@psi.ch

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-Tccupratesuperconductivity • 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 Spin order Crystal field splitting Jahn-Teller effect • Number of (unpaired) • electrons: • spin • charge • Higher cation charges: • smaller radius • smaller coord. numbers Occupied and unoccupied orbitals Bond anisotropy Lattice Spin-orbit interaction Charge order Orbital order

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. 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

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

7. CuO Cu2+ 3d94s0 CoO Co2+ 3d74s0 MnO Mn2+ 3d54s0 Cr2O3 Cr3+ 3d34s0 Electron configurations of elements 3d44s2 3d94s2 3d54s2 3d74s2 Why not metal? Whatever is the crystal field splitting the orbitals are not fully occupied!!! Odd number of d electrons- all this oxides should be metals but areinsulators

8. Mott-Hubbard insulators (on site repulsive electron force) Sir Nevill Francis MotNobel Prize in Physics 1977 Band width=W Correlation energy, Hubbard U e- large Electron transfer Coulomb repulsive force Ni2+ + Ni2+ → Ni3+ + Ni+ d8 + d8 → d7 + d9 small U W FL U>W U<W Density of states Upper Hubbard band W FL U Lower Hubbard band 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. Density of 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 Octahedral coordination Tetrahedral coordination Magnetit (Fe3O4) inverse spinel. Ferrimagnet.

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

14. Cu O La, Sr High Temperature Superconductor:La2-xSrxCuO4 (LaBa)2CuO4 TC=35K K.A. Müller und G. Bednorz(IBM Rüschlikon 1986, Nobel price 1987) 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 Mn4+ cation, its vacant orbital can then be filled by an electron from Mn3+. • Electron has moved between the neighboring metal ions, retaining its spin. • The electron movement from one cationto another is “easier” when spin direction has not to be changed (Hund's rules). O2- 2p Mn4+ d3 Mn3+ d4

16. Ferromagnetic Metal Paramagnetic Insulator La1-xCaxMnO3.Double exchangemechanism. 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. CMR (colossal magnetoresistance) La0.75Ca0.25MnO3 Tc 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. 4d and 5d orbitals are more extended than 3d’s • Reduced Coulomb interaction Insulator Metal Insulator HeungsikKim et al., Frontiers in Condensed Matter Physics, KIAS, Seoul, 2009 PRB, 74 (2006) 113104

20. Sr2IrO4 Under the octahedral symmetry the 5d states are split into t52gand eg orbital states. The system would become a metal with partially filled wide t2gband. 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 t2gband splits into effective total angular momentum Jeff=1/2 doublet andJeff=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 Sr2IrO4isinsulatingwhileSr2RhO4ismetallic. 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, 076402 (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 Li2IrO3Kitaev-Heisenberg model Crystal structure of Na2IrO3 For both Na2IrO3 and Li2IrO3 a honeycomb structure is observed enabling arealization 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)

23. Na2IrO3 and Li2IrO3Kitaev-Heisenberg model Heisenberg exchange Kitaev exchange J>0 ferromagnetic J<0 antiferromagnetic A Spin Liquid (FigureCredits: Francis Pratt, STFC) J1=0 J1=2J2 J2=0 PRL 105, 027204 (2010)

24. Na2IrO3 and Li2IrO3Kitaev-Heisenberg model • Na2IrO3and 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. A Spin Liquid (FigureCredits: Francis Pratt, STFC)

25. Na2-xLixIrO3with 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 15Kfor the parent compound Na2IrO3. • This is suppressed for the doped sample. Glassystate 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, tobepublished

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