From Rashba Ferroelectrics to exotic spin textures: the role of spin-orbit coupling in cross-coupling phenomena

During the last couple of decades, the spin-orbit interaction has played an increasingly crucial role in condensed matter physics, thanks to its relevance as a rich microscopic mechanism from the fundamental point of view and as a driving force for innovative spintronic applications on the technological side. After a general overview on spin-orbit coupling (SOC), I will discuss two non-trivial aspects where this relativistic interaction gives rise to novel and exotic phenomena in multifunctional materials. First, I will focus on the ab-initio modelling of (non-magnetic) ferroelectric semiconductors, where SOC leads to a tight link between Rashba spin-splitting, spin-texture and electric polarization, with the appealing perspective of electric-field control of spin-degrees of freedom and long-sought integration of spintronics with ferroelectricity. Second, I will discuss first-principles results for 2D magnets, where SOC can play a relevant role in the emergence of multiferroicity as well as of a large anisotropic exchange coupling. The latter is also put forward as a novel and alternative mechanism that can possibly give rise to topologically non-trivial spin configurations even in centrosymmetric systems.