M\"ossbauer parameters of $^{57}$Fe substituents in the topological insulator $Bi_2Se_3$

$^{57}$Fe M\"ossbauer spectroscopy can probe several \emph{local} structural, electronic and magnetic properties of Fe-containing systems. However, to establish a direct relationship between these properties and a system's geometric structure, the experimental M\"ossbauer parameters need to be analyzed \emph{via} electronic structure calculations. Herein, structural, electronic and magnetic effects of iron substituents in the topological insulator $Bi_2Se_3$, as uniquely probed by $^{57}$Fe M\"ossbauer spectroscopy, have been determined \emph{via} spin-polarized electronic structure calculations. The iron ion substituents, of \emph{nominal} Fe$^{3+}(S = 5/2)$ oxidation and spin state, are unequivocally shown to substitute Bi$^{3+}$ sites in epitaxial $Bi_2Se_3$ thin-films used for M\"ossbauer measurements. Concomitant with iron substitution, \emph{localized} structural rearrangements take place whereby the longer Bi-Se bonds of the native system are replaced by significantly shorter Fe-Se counterparts in the Fe-containing system. The resulting distorted-octahedral environment about substituent iron ions gives rise to characteristic M\"ossbauer parameters ($\delta_{Fe} \approx$ 0.51 mm/s, $\Delta E_{Q} \approx$ 0.20 mm/s) which have been calculated in excellent agreement with measured values for Fe-doped $Bi_2Se_3$ thin films. Consistent with a substituent Fe$^{3+}$ ion's \emph{nominal} high-spin electronic configuration ($t_{2g}^{\uparrow \uparrow \uparrow} e_g^{\uparrow \uparrow}$), an Fe-centered spin density has been established which, nevertheless, extends towards neighboring Se atoms \emph{via} direct Fe-Se bonding and concomitant Fe(d)-Se(p) hybridization.