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The structural and magnetic effects of non-magnetic vanadium (V) doping in helimagnetic SrFeO$_{3-\delta}$ (SFO) are investigated, focusing on up to 3% substitution at the Fe site. Structural analysis from X-ray diffraction (XRD) and Raman spectroscopy, supported by phonon mode calculations, reveals that pure SFO exists as a mixed tetragonal-orthorhombic phase, while V-doped samples exhibit an emerging cubic phase alongside tetragonal symmetry. Magnetic hysteresis (M-H) loops show notable ferromagnetic behavior within the antiferromagnetic matrix, persisting even at room temperature. Temperature-dependent magnetization measurements indicate a Neel temperature (TN ) shift from 70K to 55K, along with increased magnetization differences in field-cooled (FC) and zero field-cooled (ZFC) data, reflecting heightened magnetic frustration due to competing FM/AFM exchange interactions. X-ray photoelectron spectroscopy (XPS) and X-ray absorption near-edge structure (XANES) analyses reveal a rise in Fe$^{3+}$ and V$^{5+}$ states, affecting oxygen vacancy distributions and corresponding structural shifts seen in XRD and Raman results. The multivalent Fe$^{3+}$/Fe$^{4+}$ and V$^{4+}$/V$^{5+}$ states enhance double-exchange (DE) and super-exchange (SE) interactions (Fe$^{3+}$-O-Fe$^{4+}$ and Fe$^{3+}$-O-V$^{5+}$), promoting ferromagnetism. Frequency-dependent magnetization studies display a subtle susceptibility peak shift, indicating spin-glass-like behavior in V-doped samples.

Materials with magnetoelectric coupling (MEC) between ferroic orders at room temperature are extremely important in modern technology and physics. BaTiO$_3$ is a robust ferroelectric in which several doping have led to MEC. However, often MEC depends on the amount of substitution. In a series of (1-x)BaTiO$_{3.}$(x)CaMnO$_3$ (x=0,0.03, 0.06, 0.09), MEC was only observed in (0.97)BaTiO$_{3.}$(0.03)CaMnO$_3$. The structural modifications with changing substitution reveal a reduced Ti-O-Ti angle for this sample which is the most ferromagnetic in nature. A mixed phase of tetragonal P4mm and hexagonal P6$_3$/mmc space groups of BaTiO$_3$ is observed in the substituted samples, with nominal contribution of the hexagonal phase for x=0.03. A valence state study using XPS and XANES reveals the presence of enhanced proportion of Mn3+ ions in the sample which support a Jahn-Teller distortion, thereby supporting the ferroelectricity for x=0.03. Indirect and direct evidences of MEC was obtained from magnetodielectric and magnetoelectric measurements. A magnetocapacitance of 0.4% was observed with a dc magnetic field of 4kOe at 10kHz, while magnetoelectric coupling coefficient, $\alpha_{\rm ME} \sim 88$ mVcm$^{-1}$Oe$^{-1}$ was obtained for dc magnetic field of 600 Oe and a 10Hz ac field of 40 Oe. Such MEC was not observed for higher substitution which emphasizes the sensitivity of the structural properties on substitution.