Next to Leading Order Spin(1)Spin(1) Effects in the Motion of   Inspiralling Compact Binaries
  Using effective field theory techniques we compute the next to leading order Spin(1)Spin(1) terms in the potential of spinning compact objects at third Post-Newtonian order, including sub-leading self-induced finite size effects. This result represents the last ingredient to complete the relevant spin potentials to 3PN order from which the equations of motion follow via a canonical formalism. As an example we include the precession equation. 
Rafael A. Porto and Ira Z. Rothstein