Spin-Orbit Physics Giving Rise to Novel Phases in Correlated Systems: Iridates and Related Materials

Recently, the effects of spin-orbit coupling (SOC) in correlated materials have become one of the most actively studied subjects in condensed matter physics, as correlations and SOC together can lead to the discovery of new phases. Examples include unconventional magnetism, spin liquids, and strongly correlated topological phases such as topological superconductivity. Among candidate materials, iridium oxides (iridates) have been an excellent playground to uncover such novel phenomena. In this review, we discuss recent progress in iridates and related materials, focusing on the basic concepts, relevant microscopic Hamiltonians, and unusual properties of iridates in perovskite- and honeycomb-based structures. Perspectives on SOC and correlation physics beyond iridates are also discussed.

[1]  Gang Cao,et al.  Weak ferromagnetism, metal-to-nonmetal transition, and negative differential resistivity in single-crystal Sr 2 IrO 4 , 1998 .

[2]  R. Valentí,et al.  Na2IrO3 as a molecular orbital crystal. , 2012, Physical review letters.

[3]  A. Vishwanath,et al.  Unified theory of spiral magnetism in the harmonic-honeycomb iridates α ,β , and γ Li 2 IrO 3 , 2014, 1408.3640.

[4]  G. Khaliullin.  Excitonic magnetism in Van Vleck-type d4 Mott insulators. , 2013, Physical review letters.

[5]  O. Korneta,et al.  Electron-dopedSr2IrO4−δ(0≤δ≤0.04): Evolution of a disorderedJeff=12Mott insulator into an exotic metallic state , 2010 .

[6]  H. Kee,et al.  Theory of metal-insulator transition in the family of perovskite iridium oxides , 2013 .

[7]  A. Vishwanath,et al.  Beyond Band Insulators: Topology of Semi-metals and Interacting Phases , 2013, 1301.0330.

[8]  D. Abanin,et al.  Interacting Weyl semimetals: characterization via the topological Hamiltonian and its breakdown. , 2014, Physical review letters.

[9]  G. Spinolo,et al.  Optical and transport properties of the magnetic semiconductor α‐RuCl3 , 1971 .

[10]  F. Lichtenberg,et al.  Superconductivity in a layered perovskite without copper , 1994, Nature.

[11]  J. Longo,et al.  Structure and properties of the high and low pressure forms of SrIrO3 , 1971 .

[12]  J. van den Brink,et al.  Crystal-field splitting and correlation effect on the electronic structure of A2IrO3. , 2012, Physical review letters.

[13]  A. Cook,et al.  Spin-orbit coupled j=1/2 iridium moments on the geometrically frustrated fcc lattice , 2015, 1502.01031.

[14]  Yong Baek Kim,et al.  Theory of magnetic phase diagrams in hyperhoneycomb and harmonic-honeycomb iridates , 2014, 1407.4125.

[15]  Ashvin Vishwanath,et al.  Subject Areas : Strongly Correlated Materials A Viewpoint on : Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates , 2011 .

[16]  L. Li,et al.  Evolution of Magnetism in the Single-Crystal Honeycomb Iridates (Na 1− x Li x ) 2 IrO 3 , 2013, 1307.2212.

[17]  J. Longo,et al.  High pressure synthesis of (ABX3) (AX)n compounds , 1972 .

[18]  S. Okamoto,et al.  Interface engineering of quantum Hall effects in digital transition metal oxide heterostructures. , 2011, Nature communications.

[19]  G. Sawatzky,et al.  Electron-electron interaction and localization in d and f transition metals. , 1988, Physical review. B, Condensed matter.

[20]  Yang Zhao,et al.  Magnetic order in α -RuCl 3 : A honeycomb-lattice quantum magnet with strong spin-orbit coupling , 2014, 1411.4610.

[21]  N. Perkins,et al.  Importance of anisotropic exchange interactions in honeycomb iridates: Minimal model for zigzag antiferromagnetic order in Na 2 IrO 3 , 2014, 1408.3647.

[22]  G. Jackeli,et al.  Mott insulators in the strong spin-orbit coupling limit: from Heisenberg to a quantum compass and Kitaev models. , 2008, Physical review letters.

[23]  S. Trebst,et al.  Weyl spin liquids. , 2014, Physical review letters.

[24]  A. Vishwanath,et al.  Charge transport in Weyl semimetals. , 2011, Physical review letters.

[25]  H. Kee,et al.  Generic spin model for the honeycomb iridates beyond the Kitaev limit. , 2013, Physical review letters.

[26]  R. Valentí,et al.  Effect of isoelectronic doping on the honeycomb-lattice iridate A 2 IrO 3 , 2013, 1312.0815.

[27]  A. Vishwanath,et al.  Doping a spin-orbit Mott insulator: Topological superconductivity from the Kitaev-Heisenberg model and possible application to (Na 2 /Li 2 )IrO 3 , 2011, 1109.4155.

[28]  Jianzhou Zhao,et al.  Anomalous High-Energy Waterfall-Like Electronic Structure in 5 d Transition Metal Oxide Sr2IrO4 with a Strong Spin-Orbit Coupling , 2015, Scientific Reports.

[29]  Xiao-Liang Qi,et al.  Possible proximity of the Mott insulating iridate Na2IrO3 to a topological phase: Phase diagram of the Heisenberg-Kitaev model in a magnetic field , 2011, 1101.1145.

[30]  Zohar Nussinov,et al.  Compass models: Theory and physical motivations , 2015 .

[31]  H. Hafiz,et al.  Fermi Arcs vs. Fermi Pockets in Electron-doped Perovskite Iridates , 2015, Scientific Reports.

[32]  L. Balents,et al.  Topological nodal semimetals , 2011, 1110.1089.

[33]  B. J. Kim,et al.  Dimensionality driven spin-flop transition in layered iridates. , 2012, Physical review letters.

[34]  M Zahid Hasan,et al.  Three-Dimensional Topological Insulators , 2010, Annual Review of Condensed Matter Physics.

[35]  A. Said,et al.  Magnetic excitation spectrum of Na2IrO3 probed with resonant inelastic x-ray scattering , 2013, 1304.4484.

[36]  H. Hwang,et al.  BASIC NOTIONS , 2022 .

[37]  T. Noh,et al.  Dimensionality-controlled insulator-metal transition and correlated metallic state in 5d transition metal oxides Sr n+1Ir nO3n+1 (n=1, 2, and infinity). , 2008, Physical review letters.

[38]  S. Mandal,et al.  Exactly solvable Kitaev model in three dimensions , 2007, 0801.0229.

[39]  Persistent semi-metal-like nature of epitaxial perovskite CaIrO3 thin films , 2015, 1502.01261.

[40]  B. J. Kim,et al.  Isospin Dynamics in Sr2IrO4 : Forging Links to Cuprate Superconductivity , 2011, 1110.0759.

[41]  S. Cheong,et al.  Spin waves and revised crystal structure of honeycomb iridate Na2IrO3. , 2012, Physical review letters.

[42]  V. Durairaj,et al.  Partial antiferromagnetism in spin-chainSr5Rh4O12,Ca5Ir3O12, andCa4IrO6single crystals , 2006, cond-mat/0612642.

[43]  C. Lacroix,et al.  Pyrochlore Antiferromagnet: A Three-Dimensional Quantum Spin Liquid , 1998, cond-mat/9807407.

[44]  B. Bauer,et al.  Spin-orbit physics of j =1/2 Mott insulators on the triangular lattice , 2014, 1409.6972.

[45]  A. Vishwanath,et al.  Noncoplanar and counterrotating incommensurate magnetic order stabilized by Kitaev interactions in γ-Li(2)IrO(3). , 2014, Physical review letters.

[46]  B. J. Kim,et al.  Direct evidence for dominant bond-directional interactions in a honeycomb lattice iridate Na2IrO3 , 2015, Nature Physics.

[47]  R. Harlow,et al.  Single crystal structure determination of double layered strontium iridium oxide [Sr3Ir2O7] , 1994 .

[48]  M. Lumsden,et al.  Jeff=12Mott spin-orbit insulating state close to the cubic limit inCa4IrO6 , 2013, 1309.5411.

[49]  T. Smidt,et al.  Realization of a three-dimensional spin–anisotropic harmonic honeycomb iridate , 2014, Nature Communications.

[50]  H. Takagi,et al.  Weak antiferromagnetism of J eff = 1 2 band in bilayer iridate Sr 3 Ir 2 O 7 , 2012, 1207.7151.

[51]  R. Nandkishore,et al.  Weyl semimetals with short-range interactions , 2013, 1311.7133.

[52]  Yong Baek Kim,et al.  Heisenberg-Kitaev model on the hyperhoneycomb lattice , 2013, 1308.6592.

[53]  D. Khomskii,et al.  Orbitally induced Peierls state in spinels. , 2004, Physical review letters.

[54]  R. Yu,et al.  High-pressure synthesis of orthorhombic SrIrO3 perovskite and its positive magnetoresistance , 2008 .

[55]  Yong Baek Kim,et al.  Topological spinon semimetals and gapless boundary states in three dimensions. , 2014, Physical review letters.

[56]  W. E. Gardner,et al.  X-Ray, infrared, and magnetic studies of α- and β-ruthenium trichloride , 1967 .

[57]  A. Bombardi,et al.  Unconventional magnetic order on the hyperhoneycomb Kitaev lattice inβ−Li2IrO3: Full solution via magnetic resonant x-ray diffraction , 2014, 1408.0246.

[58]  Antoine Georges,et al.  Strong Correlations from Hund’s Coupling , 2012, 1207.3033.

[59]  D. Machin,et al.  Ternary and quaternary oxides of ruthenium and iridium , 1978 .

[60]  Roland Ward,et al.  The Preparation of a Strontium-Iridium Oxide Sr2IrO41,2 , 1957 .

[61]  S. Sakai,et al.  Phase-Sensitive Observation of a Spin-Orbital Mott State in Sr2IrO4 , 2009, Science.

[62]  R. Moessner,et al.  Topology and interactions in a frustrated slab: tuning from Weyl semimetals to C>1 fractional Chern insulators. , 2014, Physical review letters.

[63]  X. Qi,et al.  Topological insulators and superconductors , 2010, 1008.2026.

[64]  B. J. Kim,et al.  Large spin-wave energy gap in the bilayer iridate Sr3Ir2O7: evidence for enhanced dipolar interactions near the mott metal-insulator transition. , 2012, Physical review letters.

[65]  A. Damascelli,et al.  Na2IrO3 as a novel relativistic Mott insulator with a 340-meV gap. , 2012, Physical review letters.

[66]  A. Santoro,et al.  Neutron Powder Diffraction Study of the Crystal Structures of Sr2RuO4 and Sr2IrO4 at Room Temperature and at 10 K , 1994 .

[67]  Pollini.  Electronic properties of the narrow-band material alpha -RuCl3. , 1996, Physical review. B, Condensed matter.

[68]  N. Perkins,et al.  Critical properties of the Kitaev-Heisenberg model. , 2012, Physical review letters.

[69]  D. Baldomir,et al.  Ab initiostudy ofZ2topological phases in perovskite (111) (SrTiO3)7/(SrIrO3)2and (KTaO3)7/(KPtO3)2multilayers , 2013, 1306.2238.

[70]  Gang Cao,et al.  Observation of a metal-to-insulator transition with both Mott-Hubbard and Slater characteristics in Sr2IrO4 from time-resolved photocarrier dynamics , 2012 .

[71]  L. Li,et al.  Novel magnetism of Ir5+(5d4) Ions in the double perovskite Sr2YIrO6. , 2013, Physical review letters.

[72]  S. Matsuura,et al.  Protected boundary states in gapless topological phases , 2012, 1212.2673.

[73]  T. Senthil,et al.  Twisted Hubbard model for Sr2IrO4: magnetism and possible high temperature superconductivity. , 2010, Physical review letters.

[74]  M. Schmidt,et al.  Anisotropic Ru3+ 4d5 magnetism in the α-RuCl3 honeycomb system: Susceptibility, specific heat, and zero-field NMR , 2014, 1411.6515.

[75]  M. Randeria,et al.  Novel magnetic state in d 4 Mott insulators , 2013, 1311.2823.

[76]  Naoto Nagaosa,et al.  Doping a Mott insulator: Physics of high-temperature superconductivity , 2004, cond-mat/0410445.

[77]  S. Manni,et al.  Effect of nonmagnetic dilution in the honeycomb-lattice iridates Na 2 IrO 3 and Li 2 IrO 3 , 2014, 1404.4253.

[78]  Jan Kunes,et al.  Quantum spin Hall effect in a transition metal oxide Na2IrO3. , 2008, Physical review letters.

[79]  T. Berlijn,et al.  Long-range magnetic ordering in Na 2 IrO 3 , 2011, 1104.4046.

[80]  G. Jackeli,et al.  Zigzag magnetic order in the iridium oxide Na2IrO3. , 2013, Physical review letters.

[81]  Yogesh Singh,et al.  Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A2IrO3. , 2011, Physical review letters.

[82]  N. B. Brookes,et al.  Spin-Orbit Coupling in the Mott Insulator Ca2RuO4 , 2001 .

[83]  Yusuke Nomura,et al.  First-principles study of the honeycomb-lattice iridates Na2IrO3 in the presence of strong spin-orbit interaction and electron correlations. , 2014, Physical review letters.

[84]  S. Chi,et al.  Direct evidence of a zigzag spin-chain structure in the honeycomb lattice: A neutron and x-ray diffraction investigation of single-crystal Na2IrO3 , 2012, 1202.3995.

[85]  H. Kee,et al.  α-RuCl3: A spin-orbit assisted Mott insulator on a honeycomb lattice , 2014, 1403.0883.

[86]  A. Vishwanath,et al.  Three-dimensional quantum spin liquids in models of harmonic-honeycomb iridates and phase diagram in an infinite- D approximation , 2013, 1309.1171.

[87]  J. Goodenough,et al.  Ruthenium double perovskites: Transport and magnetic properties , 2004 .

[88]  Liang Fu,et al.  Topological crystalline insulators. , 2010, Physical review letters.

[89]  S. J. Moon,et al.  The electronic structure of epitaxially stabilized 5d perovskite Ca(1-x)Sr(x)IrO3 (x = 0, 0.5, and 1) thin films: the role of strong spin-orbit coupling. , 2009, Journal of physics. Condensed matter : an Institute of Physics journal.

[90]  I. Terasaki,et al.  Insight on the electronic state of Sr2IrO4 revealed by cationic substitutions , 2008 .

[91]  S. Trebst,et al.  Quantum spin liquid with a Majorana Fermi surface on the three-dimensional hyperoctagon lattice , 2014, 1401.7678.

[92]  G. Jackeli,et al.  Kitaev-Heisenberg model on a honeycomb lattice: possible exotic phases in iridium oxides A2IrO3. , 2010, Physical review letters.

[93]  H. Kee,et al.  Topological phases in iridium oxide superlattices: Quantized anomalous charge or valley Hall insulators , 2014, 1406.4884.

[94]  Y. Narumi,et al.  Successive magnetic phase transitions in α − RuCl 3 : XY-like frustrated magnet on the honeycomb lattice , 2015, 1503.03591.

[95]  Jaejun Yu,et al.  Novel Jeff=1/2 Mott state induced by relativistic spin-orbit coupling in Sr2IrO4. , 2008, Physical review letters.

[96]  H. Takagi,et al.  Spin-liquid state in the S=1/2 hyperkagome antiferromagnet Na4Ir3O8. , 2007, Physical review letters.

[97]  H. Takagi,et al.  Engineering a Spin-Orbital Magnetic Insulator by Tailoring Superlattices. , 2014, Physical review letters.

[98]  O. Korneta,et al.  Lattice-driven magnetoresistivity and metal-insulator transition in single-layered iridates , 2011, 1106.2381.

[99]  A. Bostwick,et al.  Fermi arcs in a doped pseudospin-1/2 Heisenberg antiferromagnet , 2014, Science.

[100]  Y. Singh,et al.  Antiferromagnetic Mott insulating state in single crystals of the hexagonal lattice material Na2IrO3 , 2010, 1006.0437.

[101]  H. Takagi,et al.  Hyperhoneycomb Iridate β-Li2IrO3 as a platform for Kitaev magnetism. , 2014, Physical review letters.

[102]  H. Kee,et al.  Kitaev magnetism in honeycomb RuCl 3 with intermediate spin-orbit coupling , 2014, 1411.6623.

[103]  Yong Baek Kim,et al.  Non-Fermi-liquid and topological states with strong spin-orbit coupling. , 2012, Physical review letters.

[104]  F. Ye,et al.  Lattice-Tuned Magnetism of Ru$^{4+}$(4d$^{4})$ Ions in Single-Crystals of the Layered Honeycomb Ruthenates: Li$_{2}$RuO$_{3}$ and Na$_{2}$RuO$_{3}$ , 2014, 1408.5441.

[105]  M. Crawford,et al.  Anomalous magnetic and transport behavior in the magnetic insulator Sr 3 Ir 2 O 7 , 2002 .

[106]  G. Khaliullin,et al.  Hidden symmetries of the extended Kitaev-Heisenberg model:Implications for the honeycomb-lattice iridates A2IrO3 , 2015, 1502.02587.

[107]  A. Ruegg,et al.  Topological phases in layered pyrochlore oxide thin films along the [111] direction , 2012, 1211.0562.

[108]  Shou-Cheng Zhang,et al.  Charge Density Waves and Axion Strings from Weyl Semimetals , 2012, 1207.5234.

[109]  H. Kee,et al.  Topological crystalline metal in orthorhombic perovskite iridates , 2014, Nature Communications.

[110]  Leon Balents,et al.  My title , 2013 .

[111]  Yong Baek Kim,et al.  Odd-parity triplet superconducting phase in multiorbital materials with a strong spin-orbit coupling: application to doped Sr₂IrO₄. , 2014, Physical review letters.

[112]  Alexei Kitaev,et al.  Anyons in an exactly solved model and beyond , 2005, cond-mat/0506438.

[113]  Y. Motome,et al.  Vaporization of Kitaev spin liquids. , 2014, Physical review letters.

[114]  Bohm-Jung Yang,et al.  Emergent topological phenomena in thin films of pyrochlore iridates. , 2014, Physical review letters.

[115]  H. Kandpal,et al.  Kitaev interactions between j = 1/2 moments in honeycomb Na2IrO3 are large and ferromagnetic: insights from ab initio quantum chemistry calculations , 2013, 1312.7437.

[116]  M. Gingras,et al.  Quantum spin ice: a search for gapless quantum spin liquids in pyrochlore magnets , 2013, Reports on progress in physics. Physical Society.

[117]  H. Matsuhata,et al.  Canted antiferromagnetic ground state in Sr3Ir2O7 , 2007 .

[118]  S. Trebst,et al.  Finite-temperature phase diagram of the Heisenberg-Kitaev model , 2011, 1105.2005.

[119]  Yoshio Kobayashi,et al.  Moessbauer spectroscopy and magnetization studies of .alpha.- and .beta.-ruthenium trichloride , 1992 .

[120]  R. Arita,et al.  {\it Ab initio} Studies on the Interplay between Spin-Orbit Interaction and Coulomb Correlation in Sr$_2$IrO$_4$ and Ba$_2$IrO$_4$ , 2011, 1107.0835.