We show that the effective spin Hamiltonian used previously to describe the CuO planes of ${\mathrm{La}}_2$${\mathrm{CuO}}_4$ does not lead to a net ferromagnetic moment for CuO planes and hence does not describe the metamagnetic behavior seen experimentally. We construct for the first time a Hamiltonian from the symmetries of the crystal structure which does lead to metamagnetism. The linear spin-wave spectrum is also calculated. This work points to the necessity of constructing effective spin Hamiltonians for metamagnetic systems which have the same symmetries as the system they are to describe.

• Received 23 July 1990

DOI:https://doi.org/10.1103/PhysRevB.42.6509