First-principles study of bilayer polymeric manganese phthalocyanine

We study bilayer manganese phthalocyanine (MnPc) molecules and MnPc polymeric sheets using first-principles simulations with a focus on the magnetic interactions between Mn atoms. We find that the most stable position of the upper layer with respect to the lower layer is shifted about $1/8$ of a lattice vector from the center of the bottom layer along the direction toward a nearest-neighbor N atom. The magnetic ground state is the N\'eel antiferromagnetic (AFM) configuration within a layer and ferromagnetic (FM) between Mn atoms in adjacent layers. In this state, the system becomes a semiconductor with an indirect band gap of $11\phantom{\rule{0.16em}{0ex}}\text{meV}$. The strongest interaction is the interlayer coupling between the closest Mn atoms. A maximally localized Wannier analysis suggests that the dominant coupling pathway is Mn-(N,C)-Mn rather than a direct Mn-Mn coupling. The maximum calculated magnetic anisotropy energy is found to be $1.0\phantom{\rule{0.16em}{0ex}}\text{meV}$ per Mn atom. We also find that the bilayer molecule shows a significant stacking angle change from FM to AFM configurations accompanied by a change of orbital filling ordering.