Exotic phases in Mott insulating Iridates with strong spin-orbit coupling: Phase diagram of the Kitaev-Heisenberg model in a magnetic field

Motivated by the recent proposal of a Mott insulating state with strong spin-orbit coupling for the Iridate Na$_{2}$IrO$_{3}$[1], we discuss the collective ground states of the effective Iridium moments in the presence of Heisenberg-Kitaev exchange interactions and a time-reversal symmetry breaking magnetic field. For a field pointing in the (111) direction we find a rich phase diagram with both symmetry breaking magnetically ordered phases as well as an unconventional topological phase which is stable over a small range of coupling parameters. Our numerical simulations further indicate two exotic multicritical points at the boundaries between these ordered phases, which we will discuss.\\[4pt] [1] J. Chaloupka, G. Jackeli, and G. Khaliullin, Phys. Rev. Lett. 105, 027204 (2010).