Structural distortions and magnetic behavior of multiferroic Bi$_{1-x}$ Sm$_x$ Fe$_{0.94}$ Ti$_{0.06}$ O$_3$ (x = 0.1, 0.12) near the morphotropic phase boundary

High-resolution neutron powder diffraction, synchrotron x-ray diffraction, and magnetometry were used to investigate the structural and magnetic properties of Bi$_{1−𝑥}$⁢Sm$_𝑥$⁢Fe$_{0.94}$⁢Ti$_{0.06}$⁢O$_3$ (𝑥=0.1,0.12) perovskites near the morphotropic phase boundary. Both compositions exhibit coexisting rhombohedral (𝑅⁢3⁢𝑐 ) and antipolar orthorhombic (𝑃⁢𝑏⁢𝑎⁢𝑚 ) phases with nearly constant phase fractions in the temperature range of 1.5 to 300 K. Anomalous behavior of low temperature magnetic properties, including the change in the weak ferromagnetic state and exchange-bias effects, cannot be explained by tiny variations in the phase content. The magnetic response correlates with temperature-dependent local distortions of the FeO$_6$ octahedra, particularly tilting, rotation, and bond-angle variations occurred in the orthorhombic Pbam phase. The distortion parameter Δ shows a sharp increase at low temperatures, correlating with the evolution of magnetization. The local structural distortions strengthen Dzyaloshinskii-Moriya interactions, promoting spin canting and weak ferromagnetism. The results underscore the decisive role of nanoscale lattice distortions over the macroscopic phase transitions in controlling the magnetic ground state of Sm$^{3+}$ - and Ti$^{4+}$ -co-doped BiFeO$_3$ multiferroics.