Sign of the coupling betweenT-violating ground states in second-order perturbation theory

We consider the coupling between two T-violating systems by a non-T-violating interaction. We show that the configuration in which the signs of the T breaking in the two systems are opposite generally has lower energy. In the context of those theories of the cuprate superconductors which postulate breaking of T invariance in the ${\mathrm{CuO}}_2$ planes, a crude estimate of the Coulomb-induced ‘‘antiferromagnetic’’ coupling for reasonable domain sizes indicates that it is an ‘‘edge’’ effect but at least competitive with the ‘‘ferromagnetic’’ one due to Josephson and magnetic effects.