Low dimensional structures comprised of ferroelectric (FE) PbTiO$_3$ (PTO) and quantum paraelectric SrTiO$_3$ (STO) are hosts to complex polarization textures such as polar waves, flux-closure domains and polar skyrmion phases. Density functional theory (DFT) simulations can provide insight into this order, but, are limited by the computational effort needed to simulate the thousands of required atoms. To relieve this issue, we use the novel multi-site support function (MSSF) method within DFT to reduce the solution time for the electronic groundstate whilst preserving high accuracy. Using MSSFs, we simulate thin PTO films on STO substrates with system sizes $>2000$ atoms. In the ultrathin limit, the polar wave texture with cylindrical chiral bubbles emerges as an intermediate phase between full flux closure domains and in-plane polarization. This is driven by an internal bias field born of the compositionally broken inversion symmetry in the [001] direction. Since the exact nature of this bias field depends sensitively on the film boundary conditions, this informs a new principle of design for manipulating chiral order on the nanoscale through the careful choice of substrate, surface termination or use of overlayers. Antiferrodistortive (AFD) order locally interacts with these polar textures giving rise to strong FE/AFD coupling at the PbO terminated surface driving a $p(2 times Lambda)$ surface reconstruction. This offers another pathway for the local control of ferroelectricity.
تحميل البحث