Magnetic properties of $Sr_2IrO_4$ a $DFT$ stud

$Sr_2IrO_4$ is a magnetic insulator with a small $Ir$-magnetic moment [1]. $IrO_4$ rotations (due to the $I41/acd$ space group) allow non-collinear magnetic ordering, thus this material could have weak ferromagnetism (non-collinear antiferromagnetically ordered $Ir$ magnetic moments); other possible explanation is band-magnetism. Simple $DFT$ calculations give a non-magnetic conductor. Intra-atomic electron repulsion can generate magnetic moments in the $d$-orbitals (via the Hubbard $U$ ($U_H$)), but due to extended character of these $5d$-orbitals the $U_H$ should be quite small. $Sr_2IrO_4$ is analyzed with the $WIEN2k$ package. Different magnetic configurations with varying $U_H$ are calculated in order to try to explain the observed magnetic behaviour. [1] C Cos\'io-Castaneda, G Taviz\'on, A Baeza and R Escudero, \textit{J. Phys.: Cond. Matter} \textbf{19} (2007) 446210