Fig. 1: Ferroelectric and magnetic ground state of La substituted BiFeO₃.

Effective Hamiltonian calculated (a) magnetic ground state energy of the spin cycloid and G-type antiferromagnetic phase in BiFeO₃ and Bi_0.85La_0.15FeO₃. R3c represents uniform, and M1 and M2 represent modulated polar configurations (“Methods”). A spin cycloid exists in the ground state of BiFeO₃ whereas a complex mixed state becomes increasingly stable in Bi_0.85La_0.15FeO₃ thin films due to the decreasing energy difference between the two magnetic configurations. Complex state (shaded area) is defined as the mixed state of the spin cycloid and G-type canted antiferromagnetic phase. The dotted lines represent the average energy of the two systems in the complex state configuration. b Schematic of the energy landscape of the BiFeO₃ and Bi_0.85La_0.15FeO₃ where the ground state of magnetic textures such as G-type antiferromagnet and spin cycloid phases in the two systems is described. Red arrows form the spin cycloid in the ground state of BiFeO₃ with the ΔU energy barrier, whereas the complex state is formed in Bi_0.85La_0.15FeO₃ due to the reduced energy barrier on La substitution. Green up/down arrows represent the polarization in the double well structure. c, d High angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) images and polar vector mapping in BiFeO₃ and Bi_0.85La_0.15FeO₃. Insets are the schematics of the estimated polarization direction in the unit cell of BiFeO₃ and Bi_0.85La_0.15FeO₃. Colored arrows indicate the direction as well as the magnitude of the atomic displacement vector vis-à-vis polarization. The average polarization is no longer along [111] after La-substitution. The scale bar is 1 nm. e–h Ferroelectric domain (PFM) and corresponding magnetic texture (iso-B NV images) of BiFeO₃/Bi_0.85La_0.15FeO₃ in the pristine state. In (h), two types of contrast are visible: the stripe-like contrast from the spin cycloid phase, and the more uniform contrast from a canted antiferromagnetic (AFM) phase.