Magnetic Origin of the Tetragonal-Orthorhombic Phase Transition in the Cuprates

It is shown that a quasi two dimensional (layered) Heisenberg antiferromagnet with fully frustrated interplane couplings generically exhibits two thermal phase transitions with lowering temperature -- an upper transition (``order from disorder without order'') in which the lattice point-group symmetry is spontaneously broken, and a lower Ne{e}l transition at which spin-rotational symmetry is broken. We therefore suggest that it may primarily be the magnetic interactions between planes, rather than strains associated with a mismatch of ionic radii, that are responsible for the tetragonal to orthorhombic (T-O) structural phase transition seen in many of the cuprates.