Emergence of half-metallic ferromagnetism in transition metal substituted Na$_{0.5}$Bi$_{0.5}$TiO$_3$

The multifunctional materials with prominent properties such as electrical, ferroelectric, magnetic, optical and magneto-optical are of keen interest to several practical implications. In the roadmap of designing such materials, in the present work, using density functional theory based first-principles calculations, we have investigated the functional properties of transition metal substituted-NBT. Our calculations predict the emergence of half-metallic ferromagnetism in the system. A nonzero magnetic moment of 1.49 $\mu_{\rm B}/{\rm f.u.}$ is obtained for 25\% concentration of Ni. Our data on optical properties for pure NBT is in excellent agreement with available theory and experiments. For Ni-NBT, we observed a diverging nature of static dielectric constant, which could be attributed to the induced metallic character in the material. Our simulations on MOKE predict a significant Kerr signal of 0.7$^\circ$ for 6.25\% Ni-concentration.