Anomalous enhancement of Neel temperature and magnetic coupling for Bi$_{\mathrm{0.9}}$Ca$_{\mathrm{0.1}}$FeO$_{\mathrm{3-\delta }}$ and Bi$_{\mathrm{0.9}}$Pb$_{\mathrm{0.1}}$FeO$_{\mathrm{3-\delta }}$

Temperature dependent neutron diffraction patterns of the Ca-doped BiFeO$_{\mathrm{3\thinspace }}$and Pb-doped BiFeO$_{\mathrm{3}}$ show that their Neel temperatures (T$_{\mathrm{N}})$ increase to 710 K and 680 K, while pure BiFeO$_{\mathrm{3}}$ has a T$_{\mathrm{N}}$ \textasciitilde 643 K. X-ray absorption spectra clearly shows that there is no evidence of mixed valence states despite divalent cation doping in trivalent Bi-sites. X-ray photoemission spectroscopy study revealed that divalent doping has introduced oxygen vacancies in the system. Oxygen deficiency plays a significant role in contracting Fe-O bond length in Fe-O$_{\mathrm{6}}$ octahedra and hence increasing the Fe-O-Fe bond angle in Bi$_{\mathrm{0.9}}$Ca$_{\mathrm{0.1}}$FeO$_{\mathrm{3-\delta }}$ and Bi$_{\mathrm{0.9}}$Pb$_{\mathrm{0.1}}$FeO$_{\mathrm{3-\delta }}$. The decreased Fe-O bond length and increased Fe-O-Fe bond angle favors the Goodenough-Kanamori-Anderson (GKA) coupling. The GKA coupling increases the magnetic interaction between the spins and hence increases the T$_{\mathrm{N}}$. Additionally, doping of divalent cations (Ca$^{\mathrm{2+}}$ and Pb$^{\mathrm{2+}})$ results in the destruction of cycloidal spin structure and formation of a simple antiferromagnetic (AFM) structure. This structure can easily be canted near the heterogeneous interface with a ferromagnetic layer to induce the Dzyaloshinskii-Moriya (DM) interaction and enhance the magneto-electric (M-E) coupling.