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Abstract

BiFeO$_3$ is a multiferroic material featuring ferroelectricity and noncollinear antiferromagnetism. Definitive and efficient control of the characteristic spin texture of BiFeO$_3$ is attractive for emerging quantum devices. In this regard, crystal-field $d\rightarrow d$ excitations localized on Fe atomic sites in BiFeO$_3$ provide an avenue for manipulation of the spin texture as they induce a complex interplay among the spin, charge, and lattice degrees of freedom. In this work, the \textit{ab initio} \textit{GW}-BSE method is used to characterize these excitations within an excitonic picture. We find that the $d-d$ transitions appear as strongly bound, chiral, spin-flip excitons deep within the electronic band gap as a result of the intricate competition between the lattice potential, the antiferromagnetic ordering, the spin-orbit coupling, and the electron-hole interaction. Most crucially, these excitons are composed of electron-hole pairs with opposite spins that constitute almost all of their $\pm \hbar$ total angular momentum. These excitons of specific angular momentum can be selectively excited using circularly polarized light, consequently modulating the local magnetic moment.