Dyson Maleev transformation in ferromagnets with single ion planar anisotropy

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Abstract
We show that the Dyson Maleev (DM) transformation can be applied to the Heisenberg ferromagnet with single ion planar anisotropy, although the resulting bilinear part of the bosonic equivalent normally ordered Hamiltonian is not hermitian. With respect to the approaches adopted up to this moment, that is, the Holstein Primakoff (HP) transformation and the matching matrix elements (MME) method, the DM transformation offers relevant advantages because it generates a finite number of interaction potentials, so we are able to obtain the second-order perturbation contributions of the excitation energy, a practically impossible result to get in the HP and MME frame. In this communication we discuss the problem and show the main results; details of the very long, cumbersome calculations will be given elsewhere.