Unveiling the Origin of the Basal-plane Antiferromagnetism in the $J_{\mathrm{eff}}=$1/2 Mott Insulator Ba$_{\mathrm{2}}$IrO$_{\mathrm{4}}$: A Density Functional and Model Hamiltonian Study

Based on the density functional theory and our new model Hamiltonian, we have studied the basal-plane antiferromagnetism in the novel $J_{\mathrm{eff}}=$1/2 Mott insulator Ba$_{\mathrm{2}}$IrO$_{\mathrm{4}}$. By comparing the magnetic properties of the bulk Ba$_{\mathrm{2}}$IrO$_{\mathrm{4}}$ with those of the single-layer Ba$_{\mathrm{2}}$IrO$_{\mathrm{4}}$, we demonstrate unambiguously that the basal-plane antiferromagnetism is caused by the intralyer magnetic interactions rather than by the previously proposed interlayer ones. In order to reveal the origin of the basal-plane antiferromagnetism, we propose a new model Hamiltonian by adding the single ion anisotropy and pseudo-quadrupole interactions into the general bilinear pseudo-spin Hamiltonian. The obtained magnetic interaction parameters indicate that the single ion anisotropy and pseudo-quadrupole interactions are unexpectedly strong. Systematical Monte Carlo simulations demonstrate that the basal-plane antiferromagnetism is caused by the isotropic Heisenberg, bond-dependent Kitaev and pseudo-quadrupole interactions. Our results show for the first time that the single ion anisotropy and pseudo-quadrupole interaction can play significant roles in establishing the exotic magnetism in the $J_{\mathrm{eff}}=$1/2 Mott insulator.