IXS 2013, Aug. 15, 2013, Stanford

RIXS study of honeycomb iridates

Young-June Kim University of Toronto

Acknowledgements Toronto H. Gretarsson J. P. Clancy Argonne+Brookhaven Jungho Kim Diego Casa Mary Upton Ayman Said Thomas Gog John Hill Xuerong Liu Emil Bozin Samples Yogesh Singh (IISER Mohali) Philip Gegenwart (Gottingen) S.-W. Cheong (Rutgers) G. Cao (U. Kentucky) K. H. Kim (Seoul National U) Theory Jeroen van den Brink (Dresden) Liviu Hozoi (Dresden) Vamshi Katukuri (Dresden) Yong Baek Kim (Toronto) Hae Young Kee (Toronto) Arun Paramekanti (Toronto) Heungsik Kim (Seoul) Jaejun Yu (Seoul)

Outline 1.

2.

   RIXS and iridates - an overview Why are we studying Iridates?

RIXS  Materials  Quantum compass model and honeycomb lattice iridates: Na 2 IrO 3 Kitaev interaction   Orbital excitations Magnetic excitations + Phonons Future directions

Theoretical motivation

U/t

Mott Insulator ?

Metal Topological (Band) Insulator l

/t

Adapted from Pesin & Balents, Nature Physics 6, 376 (2010)

U

Why iridates?

l

Physics of Ir 4+ (5d 5 ) in cubic CEF Ir 4+ (5d 5 ) e g CEF t 2g j eff = 1/2 (

l eff

= “-1”) SO j eff = 3/2

B.J. Kim et al, PRL (2008)

Iridate materials

A 2 Ir 2 O 7 A 2 IrO 3 Sr n+1 Ir n O 3n+1

Candidate for Topological Insulator, Weyl Semi-Metal , Metallic Spin Liquid:

Yanagishima et al. JPSJ (2001) Yang et al, PRB (2010), Wan et al, PRB (2011), Witczak-Krempa et al, PRB (2012) Nakatsuji et al, PRL (2006)

Candidate for Topological Insulator, Kitaev-Heisenberg Model :

Shitade et al, PRL (2009), Chaloupka et al, PRL (2010), Choi et al, PRL (2012) Comin et al., PRL (2012) Gretarsson et al, PRL (2013)

J eff =1/2 spin orbital Mott insulator, possible high-temperature superconductivity

BJ Kim et al, PRL (2008) BJ Kim et al, Science (2009) J. Kim et al, PRL (2012) Wang et al, PRL (2011)

Why RIXS?

   Neutron scattering is very difficult  Large neutron absorption cross-section of Ir  Large single crystal sample unavailable ($$) Emergence of (2011)

Resonant Inelastic X-ray Scattering

(RIXS) as a viable scattering technique for elementary excitations (Ament et al. RMP 83, 705     Magnons in La 2 CuO 4 Paramagnons (Braicovich et al. PRL 2009) in cuprates (Le Tacon et al. Nat. Phys. 2011) Triplons 2009) Orbitons 2012) in spin ladders Sr 14 Cu 24 O 41 in spin chain Sr 2 CuO 3 (Schlappa et al. PRL (Schlappa et al. Nature Looking for problems to study with hard x-ray L3 edge RIXS  Iridates

Iridate RIXS: The beginning ~ 1 eV Energy resolution

Progress in energy resolution Insulating cuprates: Cu K-edge 1 eV Hill et al. PRL 1998 0.4 eV Kim et al. PRL 2002 0.1 eV Ellis et al. PRB 2008

MERIX spectrometer Si(844) Analyzer Diego Casa Ayman Said Yuri Shvydko

MERIX: workhorse        Sr 2 IrO 4 Sr 3 Ir 2 O 7 Jungho Kim et al. PRL 108 , 177003 (2012).

Jungho Kim et al. PRL 109 , 157402 (2012).

Sr 3 IrCuO 6 Na 2 IrO 3 Xuerong Liu et al., PRL 109 , 157401 (2012).

Gretarsson et al., PRL 110 , 076402 (2013); PRB 87 , 220407 (2013).

Na 4 Ir 3 O 8 Eu 2 Ir 2 O 7 Xuerong Liu et al.

L. Hozoi et al., submitted Sr 2 (Ir,Rh)O 4 , J. P. Clancy, NEXT TALK

Ei dependence

Outline 1.

2.

   RIXS and iridates - an overview Why are we studying Iridates?

RIXS    Quantum compass model and honeycomb lattice iridates: Na 2 IrO 3 Kitaev interaction Spin-orbital excitations  Materials Magnetic excitations Future directions

Kitaev’s compass model Kitaev, Ann. Phys. 2006 Nussinov and van den Brink arXiv:1303.5922

1. Interactions are bond dependent 2. Honeycomb lattice    Exactly solvable model Spin liquid ground state (frustration) Topological quantum computing

Bond-dependent interaction Kugel and Khomskii, Sov. Phys. JETP 37, 725 (1973)   Orbital character is needed for bond-dependent interaction Isospins (j eff =1/2) Jackeli and Khaliullin PRL 2009

A 2 IrO 3 (A=Na, Li)

Li 2 IrO 3 Na 2 IrO 3 powder crystal ~2x2 mm 2

  Honeycomb lattice of Ir 4+ Heisenberg-Kitaev model? Singh, Gegenwart

However… F. Ye et al., PRB 85 180403 (2012) Ir 4+ (5d 5 ) e g CEF t 2g (

l eff

= 1) j eff = 1/2 j eff = 3/2 3 2 l Need to look at CEF excitations  RIXS

RIXS spectra

Momentum dependence

RIXS spectra Quatum Chemical calculation: van den Brink group

However… Chaloupka, Jackeli, and Khaliullin PRL 2010 X. Liu, et al., PRB (2011) Experimental structure    Phase diagram of NN Heisenberg-Kitaev model No zig-zag phase! Still a lot of confusion about the Hamiltonian  Large 2 nd and 3 rd nearest neighbor interaction  Antiferromagnetic Kitaev term

More RIXS data

Resonance behavior Na 2 IrO 3

Elastic + shoulder

Temperature dependence Ca 2+5x Y 2 − 5x Cu 5 O 10 W. S. Lee et al. arXiv:1301.4267

Momentum dependence

Magnetic dispersion Chaloupka et al., PRL 110, 097204 (2013) • • • Need a large energy scale Kitaev term?

AF or FM?

Magnetic excitation (neutron) S. K. Choi, R. Coldea, et al., PRL 108, 127204 (2012)

Conclusions    RIXS is a powerful experimental probe for studying magnetism of iridates Na 2 IrO 3  J eff =1/2 description works well  Magnetic excitation around 30-40 meV – Kitaev energy scale?

 Phonons Future directions  Pressure   Thin Films Time-resolved