  Hafnia (HfO$_2$)-based thin films have promising applications in nanoscale
electronic devices due to their robust ferroelectricity and integration with
silicon. However, HfO$_2$ has various stable and metastable polymorphs with
quite similar structures and energies. Identifying and stabilizing the
ferroelectric functional phases of HfO$_2$ have attracted intensive research
interest in recent years. In this work, first-principles calculations on
(111)-oriented HfO$_2$ are used to discover that imposing an in-plane shear
strain on the tetragonal phase induces a nonpolar to polar phase transition.
This in-plane shear-induced polar phase is shown to be an epitaxial distortion
of a known metastable ferroelectric $Pnm2_1$ phase of HfO$_2$. It is proposed
that this ferroelectric $Pnm2_1$ phase can account for the recently observed
ferroelectricity in the (111)-oriented HfO$_2$-based thin film [Nature
Materials 17, 1095-1100 (2018)]. Further investigation of this second
functional ferroelectric phase in HfO$_2$ could potentially improve the
performances of HfO$_2$-based films in logic and memory devices.
