It has previously been proposed , , that symmetry lowering in the Aurivillius phases (see SI section 3) is caused by tilting of the oxygen octahedra around the a-axis (tilt mode designated by the irreducible representation (irrep) notation 𝑋 3 + ), rotations of the oxygen octahedra around the c-axis (irreps 𝑋 2 + , 𝑋 1 -), (shown in SI Figure ), and the polar cation motions along the a-axis (irrep 𝛤 5 -), which when coupled together contribute to a material's ferroelectric ground state.