IXS 2013, Aug. 15, 2013, Stanford
RIXS study of
honeycomb iridates
Young-June Kim
University of Toronto
Acknowledgements
Toronto
H. Gretarsson
Samples
J. P. Clancy
Argonne+Brookhaven
Jungho Kim
Diego Casa
Mary Upton
Ayman Said
Thomas Gog
John Hill
Xuerong Liu
Emil Bozin
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: Na2IrO3
 Kitaev interaction
 Orbital excitations
 Magnetic excitations + Phonons
Future directions
Theoretical motivation
Mott
Insulator
?
U/t
Metal
Topological
(Band) Insulator
l/t
Adapted from Pesin & Balents, Nature Physics 6, 376 (2010)
Why iridates?
U
l
Physics of Ir4+ (5d5) in cubic CEF
Ir4+ (5d5)
eg
CEF
t2g
(leff = “-1”)
jeff = 1/2
SO jeff = 3/2
B.J. Kim et al, PRL (2008)
Iridate materials
A2Ir2O7
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)
A2IrO3
Srn+1IrnO3n+1
Candidate for Topological
Jeff=1/2 spin orbital
Insulator, Kitaev-Heisenberg
Mott insulator, possible
Model:
high-temperature
Shitade et al, PRL (2009),
superconductivity
Chaloupka et al, PRL (2010),
BJ Kim et al, PRL (2008)
Choi et al, PRL (2012)
BJ Kim et al, Science (2009)
Comin et al., PRL (2012)
J. Kim et al, PRL (2012)
Gretarsson et al, PRL (2013)
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 Resonant Inelastic X-ray Scattering
(RIXS) as a viable scattering technique for
elementary excitations (Ament et al. RMP 83, 705
(2011)





Magnons in La2CuO4 (Braicovich et al. PRL 2009)
Paramagnons in cuprates (Le Tacon et al. Nat. Phys. 2011)
Triplons in spin ladders Sr14Cu24O41 (Schlappa et al. PRL
2009)
Orbitons in spin chain Sr2CuO3 (Schlappa et al. Nature
2012)
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




Sr2IrO4 Jungho Kim et al. PRL 108, 177003 (2012).
Sr3Ir2O7 Jungho Kim et al. PRL 109, 157402 (2012).
Sr3IrCuO6 Xuerong Liu et al., PRL 109, 157401 (2012).
Na2IrO3 Gretarsson et al., PRL 110, 076402 (2013);
PRB 87, 220407 (2013).



Na4Ir3O8 Xuerong Liu et al.
Eu2Ir2O7 L. Hozoi et al., submitted
Sr2(Ir,Rh)O4, J. P. Clancy, NEXT TALK
Ei dependence
Outline
1.
2.

RIXS and iridates - an overview
 Why are we studying Iridates?
 RIXS
 Materials
Quantum compass model and honeycomb
lattice iridates: Na2IrO3
 Kitaev interaction
H. Gretarsson et al. PRL 110, 076402 (2013)
 Spin-orbital
excitations
H. Gretarsson
et al. PRB 87, 220407 (R) (2013)
 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 (jeff=1/2)
Jackeli and Khaliullin PRL 2009
A2IrO3 (A=Na, Li)
Li2IrO3 powder
Na2IrO3 crystal
~2x2 mm2
Singh, Gegenwart


Honeycomb lattice of Ir4+
Heisenberg-Kitaev model?
However…
F. Ye et al., PRB 85 180403 (2012)
Ir4+ (5d5)
eg
CEF
t2g
(leff = 1)
jeff = 1/2
jeff = 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 2nd and 3rd nearest neighbor interaction
 Antiferromagnetic Kitaev term
More RIXS data
Resonance behavior Na2IrO3
Elastic + shoulder
Temperature dependence
Ca2+5xY2−5xCu5O10
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
Na2IrO3
 Jeff=1/2 description works well
 Magnetic excitation around 30-40 meV – Kitaev
energy scale?
 Phonons
Future directions
 Pressure
 Thin Films
 Time-resolved