Group theoretical methods are applied to a ferroelectric phase transition in barium aluminate $\left({\mathrm{BaAl}}_2{\mathrm{O}}_4\right).\mathrm{}$ The atomic displacements from x-ray-diffraction data are decomposed into four modes: a primary order parameter and three secondary order parameters. The spontaneous polarization $P_s$ is shown to arise from a secondary order parameter, resulting in a very small value of $P_s,$ as is typical of other improper ferroelectrics. Using a first-principles computational method, we show that the primary order parameter becomes unstable, and is driven to a nonzero value at the phase transition. Through coupling, the nonzero primary order parameter then drives the secondary order parameters to nonzero values as well.

• Received 21 June 2001

DOI:https://doi.org/10.1103/PhysRevB.65.064105