| The configurations of lowest energy of a system of pseudo-spins S = 1/2 forming a simple cubic lattice are analysed by considering the most general interaction, between nearest neighbours, allowed by a fourfold symmetry of the bond : Hij = J∥ Siz Sjz + J (Six Sjx + Siy Sjy) for a pair (i, j) oriented along the z axis. In zero external field, the most stable configuration is either ferromagnetic when J∥ and J are both negative, or antiferromagnetic in the other cases; in the latter situation various antiferromagnetic configurations are obtained depending on the signs of J∥ and J. For all these configurations, derived in a classical way, the spin wave spectrum is calculated in order to check the magnetic stability of the system as well as to evaluate the quantum ground state energy and the mean spin deviation in this ground state. It is also shown that when J∥ = — J < 0, the antiferromagnetic ground configuration is an eigenstate of the total Hamiltonian. Thus a new three dimensional magnetic system, whose ground state is known exactly, is obtained. |
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