Antagonism between polar displacements and Rashba phenomena in strained SrTiO₃

Spintronic exploits the spin degree of freedom in addition to the charge of carriers, yielding numerous applications in data storage for instance [Nat. Mater. 6, 813 (2007)]. An alternative pathway toward lower power spintronics exists and exploits the spin-orbit interaction (SOI) of non-magnetic materials through the Spin Hall Effect (SHE) [Phys. Lett. 13, 467 (1971); Science 306, 1910 (2004)] and inverse Spin Hall Effect (ISHE) Nat. Commun. 3, 629 (2012); Phys. Rev. Lett. 96, 246601 (2006)]. More recently, a promising pathway toward efficient spin-charge current interconversion has been identified and uses a peculiar interplay between polar displacements and SOI: when inversion symmetry is broken, such as at interfaces, surfaces or in ferroelectric compounds, the polar displacements can yield a Rashba interaction lifting the degeneracy of bands according to their spin [JETP Lett. 39, 78 (1984)]. The efficiency of the conversion is related to the Rashba parameter, usually assumed to depend directly on the spin-orbit interaction and polar displacements amplitude.



In this study, we use SrTiO_3, a prototypical compound allowing Rashba phenomena [Nat. Mater. 15, 1261 (2016)], for studying the interplay between polar displacements and Rashba interaction on the basis of first-principles Density Functional Theory simulations. Within ferroelectric phases reached under compressive strain, we reveal an unexpected suppression of Rashba effects when polar displacements amplitude increases. By inspecting the role of individual lattice distortions, this surprising behavior is ascribed to the suppression of Ti t_2g orbital degeneracies induced by the polar displacements. In turn, it weakens the spin-orbit interaction amplitude and hence Rashba effects. This antagonism observed in SrTiO₃ thus highlights that a large electric field is not necessarily a prerequisite for reaching a sizable Rashba parameter and that the latter quantity might be bounded to a upper value.