Distance-Dependent Sign Reversal in the Casimir-Lifshitz Torque.

The Casimir-Lifshitz torque between two biaxially polarizable anisotropic planar slabs is shown to exhibit a nontrivial sign reversal in its rotational sense. The critical distance a_{c} between the slabs that marks this reversal is characterized by the frequency ω_{c}∼c/2a_{c} at which the in-planar polarizabilities along the two principal axes are equal. The two materials seek to align their principal axes of polarizabilities in one direction below a_{c}, while above a_{c} their axes try to align rotated perpendicular relative to their previous minimum energy orientation.