Strain control of magnetic structure in layered iridates via strong orbital-lattice coupling

We have studied from first principles the structural, electronic, and magnetic properties of the layered-perovskite iridates A$_2$IrO$_4$ and A$_3$Ir$_2$O$_7$ (A=Sr,Ba) as a function of epitaxial strain. In most of perovskite iridates, due to their large spin-orbit coupling and cubic crystal field, ground state could be described by an effective total angular momentum state $J_{\rm eff}=1/2$ within $t_{2g}$ manifold. In contrary to what is usually assumed, we find that $d_{x^2-y^2}$ orbital plays a crucial role to determine a magnetic ground state of iridates if the cubic crystal field is not big enough compared to band width. For instance Ba$_2$IrO$_4$ with tensile strain induces a situation in which magnetization is reversed. Our first-principles results show how A-site cation, dimensionallity, and strain are correlated with the band width and crystal field to control magnetic ground states.