material one expects the potential energy surface of the monolayer to be a double well the cation can reside on either side of the plane of anions but must overcome a significant barrier to go from one side to the other with the maximum energy corresponding to the fully planar configuration depending on the bulk crystal structure the potential energy surface may also include a third minimum between these two corresponding to an x m x orientation performing dft calculations we find a number of bistable mx 2 interfaces for example si mx 2 srtio 3 films with m ti fe ni and v and x s as and p have bistable interface structures and two stable film polarization states monolayers of the oxides pto 2 and zro 2 which in bulk crystallize in the cdi 2 and fluorite structures respectively also exhibit bistable behavior as does a monolayer of fluorite itself caf 2 perhaps the most promising interface structures are the latter two as epitaxial thin films of each can be grown successfully on silicon suggesting that growth of the proposed heterostructures will be experimentally feasible in fact thin 5 15 nm layers of epitaxial caf 2 have been used as a buffer layer in the growth of srtio 3 films on silicon as an example of this.