Neutron-magnon interaction involving orbital transitions

In this paper we consider the two-magnon interaction of neutrons in magnetically coupled systems, namely ferromagnetic and ferrimagnetic crystals. The interaction mechanism is relevant to magnetic systems having magnetic atoms, the states of which allow orbital transitions due to interaction with neutrons. The formulation of the Heisenberg-type exchange interaction in terms of atomic states, which are perturbed owing to the scattering with neutrons, gives rise to the interaction terms. In effect they represent two-magnon Raman processes along with the scattering of neutrons. The calculations are carried out for ferromagnetic and ferrimagnetic systems The scattering cross sections are evaluated in terms of the matrix elements of the neutron-magnon interaction between the combined neutron-magnon states. The final expressions for the scattering cross sections, evaluated in the long-magnon-wavelength and low-temperature approximation, contain temperature T in different powers. The details of a similar calculation applicable to a simple antiferromagnet will be reported in a separate paper.