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Study of the magnetic anisotropy in a planar model of the La2CuO4

We study the anisotropy energy in a planar model for the Cu-O layers of the La2CuO4 investigated in previous works. The Tight-Binding (TB) potential of the model was extended out of the validity region with the purpose of incorporate it in the potential. Next, the spin-orbit operator was considered in the Hartree Fock solution of the full HF problem. It follows that in spite of the fact that the extended potential possesses the square symmetry of the crystalline structure, the anisotropy energy vanishes in its purely 2D formulation. The result indicates that for the prediction by the model of the observed non vanishing magnetic anisotropy at zero doping and temperature in La2CuO4, its formulation requires of a 3D representation of its Wannier orbitals and the use of d like orbitals. The consideration of more realistic 3D character of the model, by including multiple CuO planes, also could be important due to the argued absence of long range order in 2D.