Chirality Ordering of Chiral Spin Liquids

We study the effect of introducing a weak antiferromagnetic interplanar exchange coupling in the two dimensional frustrated Heisenberg model. We show that a ferromagnetic(FM) ordering of chirality - {\it i.e.}, same chirality on adjacent planes - is energetically favoured, thus leading to bulk violation of the discrete symmetries parity($P$) and time reversal($T$).