Materials Overview of Iridates

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1 Materials Overview of Iridates Part I... Perovskite related structures -Metal-insulator transition in iridates- Tomohiro Takayama Max Planck Institute for Solid State Research

2 Energy Landscape why 5d oxides? Energy (K) 3d TM (Fe, Co, Ni, Cu..) 4f RE (Ce, Pr, Nd ) 5d TM (Re, Os, Ir, Pt ) Coulomb U Crystal field transfer t Spin-orbit coupling(soc) λ Coulomb U Spin-orbit coupling λ Crystal field Traditional playground for correlated electron physics Coulomb Spin-orbit coupling λ U Crystal field transfer t Interplay between U, t, and λ within close energy scale

3 Iridium oxide Sc Ti V Cr Mn Fe Co Ni Cu Zn Y Zr Nb Mo Tc Ru Rh Pd Ag Cd 77 Lu Hf Ta W Re Os Ir Pt Au Hg Ir 4+, 5d 5 (Ir 3+, Ir 5+, Ir 6+ also possible (but difficult)) Rh 3+ t 2g 6 Strong neutron absorber L-edge E(L 2 ) ~ 12.8 kev, E(L 3 ) ~11.2 kev ICSD-database... Number of reported compounds Cu-O: ~ 8,000, Mn-O: ~8,500 Co-O: ~ 4,700, Ru-O: ~ 1,600 Ir-O: ~ 480!

4 Iridates... From quantum spin liquid to Dirac/Weyl Spin-orbit Mott Weyl semimetal Topological Mott Ins. Kitaev Spin liquid Sr 2 IrO 4 Na 2 IrO 3 3D quantum spin liquid Topological Ins. A 2 Ir 2 O 7 Dirac electron Na 4 Ir 3 O 8 (111) perovskite SrIrO 3

5 Outline Part I... Perovskite and related structures - Metal-insulator transition in iridates- I. Ruddlesden Popper series From J eff = 1/2 Mott to spin-orbit induced semimetal II. Artificial Ruddlesden Popper Superlattice of [(SrIrO 3 )m, SrTiO 3 ] III. Hexagonal perovskite iridates & (111) oriented superlattice IV. Various perovskite-related iridates Part II... Iridates with edge-shared IrO 6 (various spin-liquid candidates) 2D, 3D honeycomb, Hyperkagome iridates

Perovskite ABO 3 structure A BO6 A ion (larger cation)... 12 coordination B ion (smaller cation).

6 Perovskite ABO 3 structure A BO6 A ion (larger cation) coordination B ion (smaller cation)... 6 coordination Corner-shared BO 6 network Goldschmidt s Tolerance factor 2 t < 1... BO 6 too large t > 1... A too large for the void t ~ ilmenite Distorted pv Tetra, ortho, monocli Ca-Ir-O Cubic pv Sr-Ir-O Hexagonal pv Ba-Ir-O

7 Layered perovskite...ruddlesden Popper series 1) Cut perovskite at (100) plane 3) Insert A O layer (ABO 3 ) n n: number of layers 2) Shift by (a/2, a/2) General formula: A O(ABO 3 ) n If A = A, A n+1 B n O 3n+1 (c.f. cut along (110) A 2 B 2 O 7 -type layered perovskite)

Ruddlesden Popper iridate Sr m+1 Ir m O 3m+1 Sr 4 Ir 3 O 10 Sr 3 Ir 2 O 7 Sr 2 IrO 4 m = 1 2 3

8 Ruddlesden Popper iridate Sr m+1 Ir m O 3m+1 Sr 4 Ir 3 O 10 Sr 3 Ir 2 O 7 Sr 2 IrO 4 m = High-pressure SrIrO 3 1) Larger coordination number for A-cation 2) Less tetragonal distortion

9 Outline I. Ruddlesden Popper series From J eff = 1/2 Mott to spin-orbit semimetal II. Artificial Ruddlesden Popper Superlattice of [(SrIrO 3 )m, SrTiO 3 ] III. Hexagonal perovskite iridates & (111) oriented superlattice IV. Various perovskite-related iridates

10 Unexpected magnetic insulator 5d Sr 2 IrO 4 IrO 2 Sr IrO 6 rotation ~ 11 Insulating B. J. Kim et al., Science (09) Canted AF K 2 NiF 4 -type structure Sr 2 CoO 4 Ferromagnetic metal Sr 2 RhO 4 Paramagnetic metal Sr 2 IrO 4 AF insulator G. Cao et al., PRB 57 (1998) Mott insulator despite widely extended 5d-orbital of Ir?

Sr 2 IrO 4 as a J eff = 1/2 Spin-orbital Mott insulator e g t 2g xy yz zx Ir 4+ 5d 5 = = = 2 1 1 + + 10 Dq ~ 3 ev 2

, PRL 101 (2008) 076402 1 J eff 1/ 2 = ( xy, ± 1 2 ± yz, m1 2 + i zx, m1 2 ) 3 Complex phase i : recovery of

11 Sr 2 IrO 4 as a J eff = 1/2 Spin-orbital Mott insulator e g t 2g xy yz zx Ir 4+ 5d 5 = = = Dq ~ 3 ev L eff = -L = -1 0 eff S J eff = 1/2 = 1/2 picture xyj eff = 1/2 tetra λ SO ~ 0.5 ev yz, Jzx eff = 3/2 B. J. Kim et al., PRL 101 (2008) J eff 1/ 2 = ( xy, ± 1 2 ± yz, m1 2 + i zx, m1 2 ) 3 Complex phase i : recovery of orbital motion Sr 2 IrO 4 : Spin-orbital Mott insulator Need too large U Contrasted RXS scattering J eff = 1/2 state

12 Why J eff = 1/2 magnets interesting? Magnetic coupling between J eff = 1/2 (direct or via oxygen) J eff = 1/2 Jackeli & Khaliullin 1. Unique magnetic coupling Complex phase gives rise to interference effect Possible route for Kitaev spin liquid 2. Weak Mott insulator Vicinity to metal-insulator transition Charge fluctuation, long range hopping can be sizable 3. Ideal platform for synchrotron experiments L-edge of 5d elements in hard x-ray region RXS, RIXS and XMCD etc.

13 Isotropic Heisenberg AF expected for Sr 2 IrO 4 Ir O Ir : 180 (corner - sharing IrO 6 ) G. Jackeli and G. Khaliullin, PRL 102, (2009) Sr 2 IrO 4 Local axis Ir O Ir c IrO 6 rotation about c-axis y x Heisenberg + pseudodipolar interaction DM interaction Local axis rotated in accord with IrO 6 Isotropic Heisenberg Heisenberg AF despite with strong SOC??

2D isospin-correlation survives well above T N Diffuse scattering

T N T > T N 2D rod T < T N Bragg point 2D spin correlation

14 2D isospin-correlation survives well above T N Diffuse scattering observed by RXS Magnetic correlation above T N Contour plot in (h,0, l) plane S. Fujiyama Magnetic scattering above T N Sr 2 IrO 4 In-plane h T < T N T > T N 2D rod T < T N Bragg point 2D spin correlation survives above T N T > T N Even 20 K above T N, ξ a ~ 100a 0 (a 0 : Ir-Ir length) S. Fujiyama et al., PRL 108, (2012)

15 2D Heisenberg antiferromagnetism with J ~ 0.1 ev Magnetic correlation length by RXS Sr 2 IrO 4 2D Ising 2D Heisenberg 2D XY(BKT) S. Fujiyama et al., PRL 108, (2012) ab-plane: T-dependence: Heisenberg ξ = a 0.276a exp(1.25j / T ) M. Makivic and HQ Ding PRB 43, 3562 (1991) c-axis: critical divergence ξ c J ~ 0.1 ev {( T T N ) / TN} ν T N looks determined by inter-layer coupling S = 1/2 Heisenberg AF, J ~ 0.1 ev similar to La 2 CuO 4

16 More evidences for Heisenberg coupling Magnon dispersion studied by RIXS Analysis of high-temperature susceptibility J. Kim et al., PRL 108, (2012) T. Takayama et al., unpublished

17 Magnon Excitation Survives far above T N T = 20 K Sr 2 IrO 4 T N ~ 230 K SPring-8 BL11XU K. Ishii E i = kev (L 3 ), Q = (h, k, 32.5) T = 250 K q = (π, 0) T = 400 K AF correlation survives far above T N in IrO 2 planes

..no DM coupling J eff = 1/2 Mott like Sr 2 IrO 4, T N ~ 243 K J eff = 1/2

18 Ba 2 IrO 4... K 2 NiF 4 -type without IrO 6 rotation Ba 2 IrO 4 H. Okabe et al., PRB 83, (2011) Stabilized under high-pressure ~ 6 GPa No IrO 6 rotation...no DM coupling J eff = 1/2 Mott like Sr 2 IrO 4, T N ~ 243 K J eff = 1/2 character Basal plane AF order Moment along (110) S. Bossegia et al., PRL 110, (2013)

19 Distinct behavior under high-pressure Sr 2 IrO 4 remains insulating Ba 2 IrO 4 becomes metallic D. A. Zocco et al., J. Phys.: Condes. Matter 26, (2014). D. Orii et al., JKPS 63, 349 (2012) No Superconductivity observed... Due to the presence or absence of IrO 6 rotation?

20 Bi-layer iridate Sr 3 Ir 2 O 7 S. Fujiyama et al., PRB 86, (2012) Double IrO 2 layer -> increased bandwidth ρ shows an anomaly at magnetic order (~280 K) No weak-ferromagnetic moment along a-axis S. J. Moon et al., PRL 101, (2008) Band gap almost diminishes

Large magnon gap ~ 90 mev No single ion anisotropy expected in J eff = 1/2 Pseudodipolar term (~

21 Distinct magnetic structure and excitation spectra Magnetic structure Magnetic excitation spectra J eff = 1/2 robust Collinear AF Spin // c-axis Due to Pseudodipolar term? Large magnon gap ~ 90 mev No single ion anisotropy expected in J eff = 1/2 Pseudodipolar term (~ η = J H /U) enhanced at the border of MIT? J. W. Kim et al., PRL 109, (2012) J. Kim et al., PRL 109, (2012)

22 Metallic iridate realized at the end member SrIrO 3 Bandwidth control in Ruddlesden Popper Series Sr m+1 Ir m O 3m+1 SrIrO 3 m = Insulator to metal by increasing number of IrO 2 plane

23 Is SrIrO 3 a half-filled J eff = 1/2 metal? Sr 2 IrO 4 SrIrO 3? poor metal Perovskite SrIrO 3 Polycrystalline sample prepared under 5 GPa GdFeO 3 -type IrO 6 rotation & tilt Orthorhombic 2a c 2a c 2a c (a c : cubic unit cell) χ ~ emu/mol, γ ~ 2.2 mj/mol K 2 Large Wilson ratio R W ~ 10 Close to magnetism??

24 SrIrO 3 : not half-filled metal, but semi-metal! SrIrO 3 T-dependent R H non-linear ρ xy two carrier J eff = 1/2 half-filled picture n ~ cm -3 >> R H, S < 0 larger mobility for electrons Large Nernst ambipolar effect Estimate from R H n ~ cm -3

Is J eff = 1/2 picture valid in SrIrO 3?

, PRL 108, 177003 (2012) RIXS can detect Magnon, d-d

25 Is J eff = 1/2 picture valid in SrIrO 3? Elementary excitations studied by RIXS Ir L-edge 5d Sr 2 IrO 4 T = 20 K 2p Ir L 3 -edge ~ 11.2 kev J. Kim et al., PRL 108, (2012) RIXS can detect Magnon, d-d excitation, charge gap Peaks at same energy (~ 0.7 ev) J eff =3/2 to 1/2 intra-atomic d-d excitation seen in SrIrO 3

26 Semi-metal by band crossing and spin-orbit coupling GGA for SrIrO 3 GGA+SOC for SrIrO 3 M. Zeb and H. Y. Kee, PRB 86, (2012) 1/2 3/2 Band crossing around E F due to BZ folding Band splitting at the crossing points by SOC semi-metal Semi-metal protected by the Dirac node

27 Dirac dispersion & magnetotransport ARPES Y. F. Nie at al., PRL 114, (2015) Dirac-dispersion in electron band Identified. Non-quadratic dependence B 1.5? T. Takayama et al., unpublished Large longitudinal MR not related with Lorentz force

28 Carrier doping onto J eff = 1/2 Mott Sr 2 IrO 4 Chemical doping (controversial...) Ionic liquid gating C. Lu et al., PRB 91, (2015) A. De la Torre et al., arxiv: X. Chen et al., arxiv: O. B. Korneta et al., PRB 82, (2010) J. Ravichandran et al., arxiv: No metallic state realized

29 Fermi arc & d-wave gap opening? Surface electron-doping by K-deposition SC gap? by STM Y. K. Kim et al., Science 345, 187 (2014) Y. J. Yan et al., arxiv:

30 Metal-insulator transition in (Sr 1-x La x ) 3 Ir 2 O 7 Bulk MIT occurs by La doping ARPES x = st order phase boundary A. de la Torre et al., PRL 113, (2014) x = J. He et al., Sci. Rep. 5, 8533 (2015) T. Hogan et al., PRL 114, (2015) Electron pocket observed

31 Outline I. Ruddlesden Popper series From J eff = 1/2 Mott to spin-orbit semimetal II. Artificial Ruddlesden Popper Superlattice of [(SrIrO 3 ) m, SrTiO 3 ] III. Hexagonal perovskite iridates & (111) oriented superlattice IV. Various perovskite-related iridates

32 How spin-orbital Mott evolves into a semi-metal? J eff = 1/2 Mott (from half-filled) Intermediate phase: Sr 4 Ir 3 O 10 Semi-metal (almost band ins.) Resistivity (poly) Magnetic susceptibility (poly) 4SrCO 3 +3IrO 2 (precursor) 1100, 5GPa for 1h Only polycrystal available Not clean (inter-growth??) More sophisticated way to trace MIT?

33 How spin-orbital Mott evolves into a semi-metal? J eff = 1/2 Mott (from half-filled) Bulk crystal RP series Sr n+1 Ir n O 3n+1 limited materials Semi-metal (almost band ins.) Super-lattice [(SrIrO 3 ) m, SrTiO 3 ](001) on-demand sequence J. Matsuno SrIrO 3 SrTiO 3 n = 1 2 m = 1 m = 2 Artificial Ruddlesden Popper series! J. Matsuno et al., PRL 114, (2015)

34 Superlattice reproduced (semi-)metal - insulator evolution Metal-insulator change with inserting SrTiO 3 layers m Bulk J. Matsuno et al., PRL 114, (2015) [(SrIrO 3 ) m, SrTiO 3 ](001) (m: number of SrIrO 3 layers)

, PRL 114, 247209 (2015) MIT appears at m = 3 accompanying

35 Magnetic insulator to semi-metal m =... Semi-metal as like bulk J. Matsuno et al., PRL 114, (2015) MIT appears at m = 3 accompanying appearance of magnetism Large in-plane moment appears in m = 1 and 2 m = 1 strongly insulating above T c... Mott insulator?

36 Up-up-down-down in-plane moments in Sr 2 IrO 4 Sr 2 IrO 4 AF and metamagnetism H = 0 1st IrO 2 layer 2nd IrO 2 layer Canted moment In-plane moment appears due to IrO 6 rotation & DM interaction Up-up-down-down configuration of in-plane moment Ground state: AF magnetism Metamagnetic transition by in-plane field 3rd IrO 2 layer 4th IrO 2 layer M ~ 0.07 µ B /Ir

37 Weak ferromagnetism in m = 1 superlattice SrIrO 3 /SrTiO 3 /SrIrO 3 /SrTiO 3 Weak Ferromagnetism 1st IrO 2 layer TiO 2 layer Canted moment 2nd IrO 2 layer TiO 2 layer m = 1 ground state: weak ferro Ir-O-Ti-O-Ir coupling along c-axis FM irrespective of Ir-O-Ti FM or AF parallel canting moment M ~ 0.02 µ B /Ir smaller than Sr 2 IrO 4 smaller rotation & m = 1 essentially reproduces the nature of Sr 2 IrO 4

38 Electronic structure of superlattices Single layer Large FS Magnetic Insulator with large gap Bilayer Semi-metal Marginally insulating J. Matsuno et al., PRL 114, (2015)

39 Outline I. Ruddlesden Popper series From J eff = 1/2 Mott to spin-orbit semimetal II. Artificial Ruddlesden Popper Superlattice of [(SrIrO3)m, SrTiO3] III. Hexagonal perovskite iridates & (111) oriented superlattice IV. Various perovskite-related iridates

40 Another form of AIrO 3...hexagonal perovskite 6M-SrIrO 3 ambient pressure phase IrO 6 connected by corner and face sharing Tolerance factor t ~ 0.99 Reported as non-fermi-liquid correlated metal... G. Cao et al., PRB 76, (2007)

with O 2- B: occupy octahedral void between AO3 layers (AO3 layer) (B layer) Layer III I -

41 How to see cubic perovskite See perovskite along (111) direction AO 3 B AO 3 B AO 3 B AO 3 B Stacking of AO3 layers O 2- B cation A (111) A: large ion size, make close-packed layer with O 2- B: occupy octahedral void between AO3 layers (AO3 layer) (B layer) Layer III I - I II III I II III I II III I II III - iii i ii iii i ii iii i ii iii i Corner shared BO 6 (ccp)

42 How to see hexagonal perovskite When tolerance factor t > 1 (large A and/or small B), B-O bonds cannot connect each other within AO3 lattice. Stacking of AO3 layers Combination of two stacking pattern O 2- B cation A (AO3) -I II I II III II III I III - I- (B) iii iii iii i i i ii ii ii Unit cell (AO3) -I II III I III II I II III - I- (B) iii i ii ii i iii iii i ii Unit cell 2H BaNiO Layer 3 -type III (AO3) -I II I II I II I II - (B) iii iii iii iii iii iii iii (hcp)

43 Variation of hexagonal perovskite 2H 9H J. M. Longo, Mat. Res. Bull. 3, 687 (1968) 6H (3c) Cubic perovskite High-pressure Face-sharing BO 6... Repulsion between cations larger BO 6 High-pressure leads to more corner-shared network

44 Magnetic insulator BaIrO 3 9M structure Phase transition T c ~ 180 K 25 9M-type BaIrO 3 20 Ba ρ (mωcm) Ir 3 O 12 Ambient pressure phase Ir 3 O 12 unit connect along c-axis M (emu/mol) Temperature (K) H = 1 T Resistivity increases below T c Weak ferromagnetic below T c Also G. Cao et al., Solid state com. 113, 657- (2000)

113, 657- (2000) Clear magnetic order below T c ~ 180 K M. L. Brooks et al.

45 CDW(SDW), Canted AF or FM?? Non-linear I-V µsr XMCD T < T c, non-linear conduction... Charge density wave? G. Cao et al., Solid state com. 113, 657- (2000) Clear magnetic order below T c ~ 180 K M. L. Brooks et al., PRB 71, (R) (2005) <L z >/<s z > = 2.8(2) Sizable orbital moment Spin-orbital Mott? M. A. Languna-Marco et al., PRL 105, (2010) No CDW q-vector, Magnetic Bragg peak identified to date

46 Ferromagnetic metal 5M-BaIrO 3 5M BaIrO 3 Stabilized under narrow pressure range around 4 GPa -(IrO 6 )-(Ir 2 O 9 )-(Ir 2 O 9 )- sequence Weak moment ~ µ B /Ir Small anomaly in C/T J. -G. Cheng et al., PRB 80, (2009)

47 6M Sr(Ba)IrO 3 : semimetal Monoclinic SrIrO 3 BaIrO 3 6M-type R H < 0 R H < 0 S > 0 S > 0 ambient pressure phase synthesized P > 5 GPa n ~ cm n ~ cm -3 Negative Hall and Positive Seebeck represent two-types of carriers

3~4 GPa -(IrO 6 )-(Ir 2 O 9 )-(Ir 2 O 9 )- Magnetic insulator Ferromagnetic metal The nature of

48 Metal-insulator transition in hexagonal iridates 9M BaIrO 3 C2/m 5M BaIrO 3 C2/m 6M Sr(Ba)IrO 3, C2/c Ir 3 O 12 Ambient pressure phase -(Ir 3 O 12 )-(Ir 3 O 12 )-(Ir 3 O 12 )- Intermediate phase 3~4 GPa -(IrO 6 )-(Ir 2 O 9 )-(Ir 2 O 9 )- Magnetic insulator Ferromagnetic metal The nature of transition unclear (Mott, SDW, etc.) High pressure phase > 5 GPa -(IrO 6 )-(Ir 2 O 9 )-(IrO 6 )- Semi-metal

49 Electronic structure of 6M-SrIrO 3 A. Yaresko Ir2 at Ir 2 O 9 Ir1 at single IrO 6

50 Dirac cones above and below E F A. Yaresko

51 Honeycomb physics involved? Hopping between Ir1 and Ir2 (via O 2p) is stronger. Hopping between Ir2 is week Layered quasi-2d? Ir1 and Ir2 form honeycomb-like lattice in ab-plane

52 Topological Ins. by (111) bi-layer bi-layer SrIrO 3... Topological insulator Bi-layer perovskite along (111) regarded as buckled honeycomb Layer potential, next-nearest hopping can open a gap.

Fabrication of (111) superlattice (111) Oriented thin-film on

SrIrO 3... 6M thin-film (incl. face-share) obtained CaIrO 3.

5 IrO 3 (CSIO) gives the best results Superlattice [CSIO 2m,

53 Fabrication of (111) superlattice (111) Oriented thin-film on STO... Difficulty due to polar surface (SrO 3 ) 4- & Ti 4+ SrIrO M thin-film (incl. face-share) obtained CaIrO 3... Relaxed due to lattice mismatch D. Hirai Ca 0.5 Sr 0.5 IrO 3 (CSIO) gives the best results Superlattice [CSIO 2m, STO 2 ] k m = 1 m = 2 D. Hirai et al., APL Materials 3, (2015)

54 Metal-insulator transition in (111) superlattice Like (001) superlattice, MIT takes place by thickness change (m = 1, 2: ρ too high to measure ρ xy ) D. Hirai et al., APL Materials 3, (2015) For small m, the superlattice is magnetic insulator. Not TI, correlation effect must be considered.

55 Outline of Lectures I. Ruddlesden Popper series From J eff = 1/2 Mott to Dirac semimetal II. Artificial Ruddlesden Popper Superlattice of [(SrIrO3)m, SrTiO3] III. Hexagonal perovskite iridates & (111) oriented superlattice IV. Various perovskite-related iridates

56 Other perovskite related structures Perovskite can accommodate multiple A or B ions Y. Shimakawa et al., J. Phys. Condens. Matter 26, (2014)

Double perovskite A 2 BB O 6... Frustration?

10 IrO 6 M. Wakeshima et al., J. Mater. Chem.

57 Double perovskite A 2 BB O 6... Frustration? A: Sr 2+, Ba 2+ B 4+, B 4+ Ba 2 Ce 4+ IrO 6 e.g. Sr 2 CeIrO 6, Ba 2 CeIrO 6 A: Ln 3+ B 4+, B 2+ e.g. La 2 MgIrO 6, La 2 ZnIrO 6 T N ~ 17 K Θ W ~ -177 K f ~ 10 IrO 6 M. Wakeshima et al., J. Mater. Chem. 10, 419 (2000) Frustrated? Distorted, P2 1 /n FCC lattice Also, K 2 IrCl 6 etc.

58 Double perovskite... Ir-O-O-Ir Kitaev? La 2 BIrO 6 (B = Mg, Zn) T N ~ 12 K Θ W ~ -24 K T c ~ 7.5 K Θ W ~ -3 K Less frustrated... A-type AF G. X. Cao et al., PRB 87, (2013) Ir-O-O-Ir Kitaev interaction dominant? A. A. Aczel et al., arxiv:

59 Ordered hexagonal PV... Spin liquid candidate Spin-liquid behavior in Ba 3 IrTi 2 O 9 Θ W ~ -133 K 6M-type stacking T. Dey et al., PRB 86, (2012) Ir occupies face-sharing octahedra ~7% of site-mixing at Ti(3) ~37% site mixing between Ir(1) and Ti(2) Ir-O-O-Ir bond... Kitaev exchange in triangular lattice?

60 Ordered hexagonal PV... J eff = 1/2 singlet? Spin singlet formation in Ba 3 BiIr 2 O 9 Ir 4+ Bi 4+ Sudden drop of χ at T* ~ 74 K Spin gap opening in dimers Ir 4+ makes Ir 2 O 9 dimers Ir-Ir distance increases below T*?? W. Miller at al, JACS 134, 3265 (2012)

61 A-site ordered perovskite AA 3 B 4 O 12 A :12 4 coordination 2a 0 x 2a 0 x 2a 0 Cubic Im-3 (No. 204) Z=2 X Y Z A A B O ~0.18 ~ CaCu 3 M 4 O 12 M 4+ RE 3+ Cu 3 M 4 O 12 M a~8 A Slide from M. Isobe

62 Overview of ACu 3 B 4 O 12 B :3d ACu 2+ 3Ti 4 O 12 A = Ca 2+ Magnetic insulator ACu 2+ 3V 4 O 12 ACu 2+ 3Cr 4 O 12 A = Ca 2+,Sr 2+ ACu 2+ 3Mn 4 O 12 ACu 2+ 3Fe 4 O 12 A = Na +, Ca 2+, Y 3+ Pauli paramagnetic metal Pauli paramagnetic metal A= R 3+ Partial charge transfer AF metal A= Bi 3+ charge disproportionation Ferri metal A = Ca 2+ Ferrimagnetic semiconductor A= Bi 3+, R 3+ Ferromagnetic metal A = Ca 2+,Sr 2+ A= Bi 3+, R 3+ charge disproportionation or charge transfer Ferri semiconductor AF insulator ACu 2+ 3Co 4 O 12 (ACu 3+ 3Co 4 O 12 ) A = Ca 2+ Pauli para metal A= La 3+ low-spin insulator Slide from M. Isobe

63 New heavy fermion oxide? CaCu 3 Ir 4 O 12 Upturn of C/T at low temp. γ ~ 120 mj/ir-mol K 2 Curie-Weiss Cu 2+ 3d seems localized But deviates below T* ~ 80 K. Below T*, ρ shows pronounced decrease Hybridization of Cu 3d & Ir 5d? J. G. Cheng et al., PRL 111, (2013)

Along a, edge-share Along c, corner-share MgSiO 3.

64 Post-perovskite... High-pressure phase of PV Post-perovskite... High-pressure phase of perovskite CaIrO 3 Mg 2 SiO 4 MgSiO 3 From SPring-8 webpage Along a, edge-share Along c, corner-share MgSiO 3... Perovskite to post-perovskite around 120 GPa, 2500 K S. Murakami et al., Science 304, 855 (2004) For CaIrO 3, this transition occurs around 4 GPa, 1200 K

65 Post-perovskite CaIrO 3... Kitaev & Heisenberg Ca 1-x Na x IrO 3...MIT takes place Along a, edge-share Along c, corner-share Canted AF AF coupling along c FM alignment along a Coexistence of Heisenberg & Kitaev coupling? K. Ohgushi et al., PRB 74, (2006) K. Ohgushi et al., PRL 110, (2013)

66 Summary Perovskite iridates Structural flexibility (controlled by ionic size or pressure)... Systematic evolution of crystal and electronic structure provide opportunity to trace metal-insulator transition. The metallic iridates at the one end are Dirac semi-metals? Possibility of various new materials in the ordered structure

Giniyat Khaliullin Max Planck Institute for Solid State Research, Stuttgart

Mott insulators with strong spin-orbit coupling Giniyat Khaliullin Max Planck Institute for Solid State Research, Stuttgart LS driven unusual ground states & excitations motivated by: Sr 2 IrO 4 Na 2 IrO