Magnetic matter spin waves with “negative” group velocity

In this paper it is theoretically shown that in ferromagnetic films with in-plane magnetization there exist magnetic waves characterized by a “negative” group velocity. The group velocity is antiparallel to the phase velocity and to the propagation in-plane wave vector placed along the direction of the static magnetization and of the external magnetic field. These waves are volume spin waves and have backward character. When exchange effects are included this behavior is suppressed and the group velocity becomes “positive” and parallel to the phase velocity. Analytical expressions of the group velocity are given both for non-vanishing wave vector and in the resonant limit. Analogies and differences with electromagnetic waves propagating in backward-wave isotropic media are discussed.