Electronic and magnetic properties of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Ba</mml:mi> <mml:mi>x</mml:mi> </mml:msub> <mml:msub> <mml:mi>Sr</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>−</mml:mo> <

The electronic and magnetic properties of 3d-3d double perovskite oxides ${\mathrm{Ba}}_{x}{\mathrm{Sr}}_{2\ensuremath{-}x}{\mathrm{TiFeO}}_{6}$ (BSTF) have been studied using a combined experimental and theoretical approach. The magnetic behavior of ${\mathrm{Ba}}_{x}{\mathrm{Sr}}_{2\ensuremath{-}x}{\mathrm{TiFeO}}_{6}$ has been investigated by EPR spectroscopy (5 to 650 K), M"ossbauer spectroscopy (78 to 300 K), and magnetometry (5 to 315 K). The temperature dependence of the EPR linewidth shows two minima for all samples (in the temperature range 100--200 K), implying structural changes in the local environment arising from the ${\mathrm{Fe}}^{3+}$ and ${\mathrm{Fe}}^{4+}$ ions. The two types of iron ions ${\mathrm{Fe}}^{3+}$ and ${\mathrm{Fe}}^{4+}$ are indicated by M"ossbauer spectroscopy and their percentage in the samples were estimated. An antiferromagnetic phase transition is indicated by a negative Curie-Weiss temperature, which we found in our magnetic susceptibility studies with temperature by adjusting three distinct magnetic fields (0.1, 1, and 10 kOe) in ${\mathrm{Ba}}_{x}{\mathrm{Sr}}_{2\ensuremath{-}x}{\mathrm{TiFeO}}_{6}$, and these transition temperatures were also estimated. However, a type 5 ordered $\mathrm{Pm}\overline{3}\phantom{\rule{0.16em}{0ex}}\mathrm{m}$ structure with AFM-1 type alignment of spin moment on the two inequivalent Fe-1 and Fe-2 atoms has been found to be the magnetic ground state from density functional theory-based calculations. The coexistence of different charge states of Fe (${\mathrm{Fe}}^{3+}$ and ${\mathrm{Fe}}^{4+}$) has been validated from theoretical calculations. The exchange interaction calculations show a long-range antiferromagnetic ordering with a competing weak ferromagnetic interaction.