Quantum atomistic approach for interacting spins

The phenomenological Landau theory of the spin precession has been used to reproduce the out-of-equilibrium properties of many magnetic systems. However, such an approach suffers from some serious limitations. The main reason is that the spin and the angular momentum of the atoms are described by the classical theory of the angular momentum. We derive a discrete model that extends the Landau theory to the quantum mechanical framework. Our approach is based on the application of the quantification procedure to the classical Hamiltonian of an array of interacting spins. The connection with the classical dynamics is discussed.