  We present the result of the quadratic-in-spin interaction Hamiltonian for
binary systems of rotating compact objects with generic spins, up to NNNLO
corrections within the post-Newtonian expansion. The calculation is performed
by employing the effective field theory diagrammatic approach, and it involves
Feynman integrals up to three loops, evaluated within the dimensional
regularization scheme. The gauge-invariant binding energy and the scattering
angle, in special kinematic regimes and spin configurations, are explicitly
derived. The results extend our earlier study on the spin-orbit interaction
effects.
