Spin-orbit entanglement in Mott insulating oxides:   Unusual interactions and
possible exotic phases
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Over the last few years, there has been an upsurge of interest in materials
in which exotic states may emerge as the result of relativistic spin-orbit
interactions. We will discuss insulating iridium oxides from this perspective.
We show that the strong spin-orbit coupling, through the entanglement of spin
and orbital spaces, leads to a variety of interesting Hamiltonians ranging
from the Heisenberg model to the Kitaev or quantum compass models,
for different lattice geometries [1]. Based on these effective
Hamiltonians, we present a comprehensive theoretical study [3,4] of the rich
phase behavior and dynamics observed in layered iridium oxides such as
tetragonal Sr2IrO4 and Sr3Ir2O7 and hexagonal A2IrO3 (A=Na, Li).
We suggest that the hexagonal iridates might be close to the
Kitaev spin-liquid state. We also discuss the layered tetragonal vanadate
Sr2VO4 and argue  that magnetically-hidden octupolar order, driven
by spin-orbit coupling, is realized in this compound [2].
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[1] G.Jackeli and G.Khaliullin, Phys.Rev.Lett. 102, 017205 (2009).
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[2] G.Jackeli and G.Khaliullin, Phys.Rev.Lett. 103, 067205 (2009).
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[3] J.Chaloupka, G.Jackeli, and G.Khaliullin, Phys.Rev.Lett. 105,
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027204 (2010).
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[4] J.Chaloupka, G.Jackeli, and G.Khaliullin, Phys.Rev.Lett. 110,
097204 (2013).