Ferroelectricity
has recently been demonstrated in germanium-based
halide perovskites. We use first-principles-based simulations to study
4–18 nm CsGeBr3 films and develop a theory for ferroelectric
ultrathin films. The theory introduces (i) a local order parameter,
which identifies phase transitions into both monodomain and polydomain
phases, and (ii) a dipole pattern classifier, which allows efficient
and reliable identification of dipole patterns. Application of the
theory to both halides CsGeBr3 and CsGeI3 and
oxide BiFeO3 ultrathin ferroelectrics reveals two distinct
scenarios. First, the films transition into a monodomain phase below
the critical value of the residual depolarizing field. Above this
critical value, the second scenario occurs, and the film undergoes
a transition into a nanodomain phase. The two scenarios exhibit opposite
responses of Curie temperature to thickness reduction. Application
of a dipole pattern classifier reveals rich nanodomain phases in halide
films: nanostripes, labyrinths, zig-zags, pillars, and lego domains.