Dimensionality Driven Spin-Flop Transition in Layered Iridates
  Using resonant x-ray diffraction, we observe an easy c-axis collinear antiferromagnetic structure for the bilayer Sr$_3$Ir$_2$O$_7$, a significant contrast to the single layer Sr$_2$IrO$_4$ with in-plane canted moments. Based on a microscopic model Hamiltonian, we show that the observed spin-flop transition as a function of number of IrO$_2$ layers is due to strong competition among intra- and inter-layer bond-directional pseudo-dipolar interactions of the spin-orbit entangled $J_{eff}$=1/2 moments. With this we unravel the origin of anisotropic exchange interactions in a Mott insulator in the strong spin-orbit coupling regime, which holds the key to the various types of unconventional magnetism proposed in 5$d$ transition metal oxides. 
J. W. Kim, Y. Choi, Jungho Kim, J. F. Mitchell, G. Jackeli, M.   Daghofer, J. van den Brink, G. Khaliullin, and B. J. Kim
cond-mat.str-el