  The Casimir-Lifshitz torque between two biaxially polarizable anisotropic
planar slabs is shown to exhibit a non-trivial sign-reversal in its rotational
sense. The critical distance $a_c$ between the slabs that marks this reversal
is characterized by the frequency $\omega_c\!\sim \!c/2a_c$ 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. The
sign-reversal disappears in the nonretarded limit. Our perturbative result,
derived for the case when the differences in the relative polarizabilities are
small, matches excellently with the exact theory for uniaxial materials. We
illustrate our results for black phosphorus and phosphorene.
