Acoustical and optical spin modes of multilayers with ferromagnetic and antiferromagnetic coupling

A study of the in-phase ("acoustical") and of the out-of-phase ("optical") spin modes in layered ferromagnetic structures with both ferromagnetic and antiferromagnetic coupling is presented, in particular for the system Fe(20 Angstrom)/Cr(20 Angstrom)/Fe(20 Angstrom)/Cr(9 Angstrom)/Fe(100 Angstrom). A calculation of the dynamic magnetization, assumed constant in each film, gives an explanation of the behavior of the two kinds of modes at differen t magnetic fields. The "acoustical" mode is the lowest frequency one fur lo w applied fields, but its frequency switches with that of the "optical" mod es at higher fields. It is found that the system exhibits soft modes as a f unction of the applied field. One of these is a Goldstone mode.