Collective dynamics and ferromagnetic order in random planar arrays of magnetic granules

A dynamical study is done on existence and stability of ferromagnetically ordered ground state in a positionally disordered planar array of magnetic moments coupled only by dipolar forces. Starting from almost aligned ground state under a strong enough applied field, the excitation energy spectrum and related eigenmodes are found, permitting to develop a mean-field analysis of the static magnetization in function of magnetic field and temperature. In the limit of zero applied field, the stability conditions are obtained for the onset of in-plane spontaneous magnetization, manifesting a specific “order from disorder” mechanism.