  Nonlinear spintronics has significant attention as it combines nonlinear
dynamics with spintronics, opening up new possibilities beyond linear
responses. A recent theoretical work [Cong et al., Phys. Rev. Lett. 130, 166302
(2023)] predicts the nonlinear generation of spin density [nonlinear spin
Edelstein effect (NSEE)] in centrosymmetric metals based on symmetry analysis
combined with first principle calculation. However, its microscopic mechanism
remains unclear. This paper focuses on the fundamental role of orbital degrees
of freedom for the nonlinear generation in centrosymmetric systems. Using a
combination of tight-binding model and density functional theory calculations,
we demonstrate that nonlinear orbital density can arise independently of
spin-orbit coupling. In contrast, spin density follows through spin-orbit
coupling. We further elucidate the microscopic mechanism responsible for this
phenomenon, which involves the NSEE induced by electric-field-induced orbital
Rashba texture. We also find that the NSEE is significantly influenced by the
energy level broadening and that most materials previously predicted to exhibit
strong NSEE exhibit negligible NSEE for the energy level broadening of the
order of room temperature but demonstrate substantial NSEE only when the energy
level broadening is reduced. In addition, we also explore the potential
applications of the nonlinear orbital and spin Edelstein effect for field-free
switching.

Materials Science