Weak ferromagnetism in the low-temperature tetragonal phase of the cuprates

The criterion for the existence of weak ferromagnetism in the low-temperature distorted phases of (Formula presented)(Formula presented)-type compounds is derived on the basis of a general superexchange Hamiltonian. It is found that a ferromagnetic canting out of the (Formula presented) planes is excluded in the pure low-temperature tetragonal phase. The anisotropic superexchange interactions between the copper spins are obtained from a Hubbard model which includes all copper 3d and oxygen 2p orbitals, and all on-site Coulomb matrix elements. The results apply when the oxygen octahedra surrounding each copper have tetragonal symmetry. Explicit expressions for the net ferromagnetic moment and the in-plane and the out-of-plane gaps in the spin-wave spectrum are derived and estimated in terms of the microscopic parameters of the cuprates.