Quantum-mechanical approximation to the ground state of cerous magnesium nitrate

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Abstract
In this paper we perform a complete quantum-mechanical calculation of the ground-state energy of a system of spins 1/2 that are coupled by dipole-dipole forces. The only hypothesis used is the assumption that the ground state has two times the periodicity of the underlying magnetic lattice. This paper is the application to a specific crystal of results derived in a preceding paper. The Hamiltonian is decomposed in eight invariant pieces each with its own coupling constant. The basis wave functions are decomposed according to the eight one-dimensional representations of the permutation group that leaves the cluster invariant. The results are given in the form of tables applicable to any compound that has the spins situated on a Bravais lattice. The calculation is applied to cerous magnesium nitrate and we show that the results for the lowest state of each representation are leading to a spectrum that is different from the results obtained with the classical or Hartree method. Although the lowest state is still the same antiferromagnetic configuration, it turns out now that this state lies barely below the ferromagnetic state; the order in which the ferromagnetic and antiferromagnetic levels appear is different from the order obtained in a classical calculation.