Spin-orbit effects in ferroelectric PbTiO3 under tensile strain

Abstract

We report a study based on first-principles calculations complemented by a tight-binding approach and a $\mathbit{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ model of the spin-orbit effects in epitaxially strained $\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_{3}$. The imposed biaxial tensile strain allows us to rotate the electrical polarization of $\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_{3}$ from out-of-plane to in-plane directions through structural phase transitions between a tetragonal, monoclinic, and orthorhombic phase. It is found that Ti $d$-state conduction bands exhibit two strong Rashba-like spin-splitting parameters of (1) 0.39 eV \AA{} at a tensile strain $\ensuremath{\eta}=1.55$% due to a polarization rotation in the monoclinic phase and (2) 1.08 eV \AA{} under large tensile strain of 3.8% due to band anticrossing in the orthorhombic phase. Remarkably, we also identified the presence of a quasipersistent spin texture for the band with a ${d}_{yz\ensuremath{-}zx}$ character in the orthorhombic phase. We then conclude that using strain could be an interesting way to tune the spin-orbit effects in ferroelectric materials with technological interests.