Tuning ferromagnetic BaFe 2 ( PO 4 ) 2 through a high Chern number topological phase

There is strong interest in discovering or designing wide-gap Chern insulators. Here we follow a Chern insulator to trivial Mott insulator transition versus interaction strength $U$ in a honeycomb-lattice Fe-based transition-metal oxide, discovering that a spin-orbit coupling energy scale $\ensuremath{\xi}=40$ meV can produce and maintain a topologically entangled Chern insulating state against large band structure changes arising from an interaction strength $U$ up to 60 times as large. Within the Chern phase the minimum gap switches from the zone corner $K$ to the zone center $\mathrm{\ensuremath{\Gamma}}$ while maintaining the topological structure. At a critical strength ${U}_{c}$, the continuous evolution of the electronic structure encounters a gap closing then reopening, upon which the system reverts to a trivial Mott insulating phase. This Chern insulator phase of honeycomb lattice ${\mathrm{Fe}}^{2+}\phantom{\rule{4pt}{0ex}}{\mathrm{BaFe}}_{2}$(${\mathrm{PO}}_{4}$)${}_{2}$ corresponds to a large Chern number $\mathcal{C}\phantom{\rule{0.28em}{0ex}}=\phantom{\rule{0.28em}{0ex}}\ensuremath{-}3$ that will provide enhanced anomalous Hall conductivity due to the associated three edge states threading through the bulk gap of 80 meV.