Influence of the next-nearest neighbor exchange interaction on the thin-film spin‐wave spectrum

• NNN interaction character can be identified from the spin wave resonance intensity order.
• The order of modes can be reversed due to in-plane spin-wave propagation.
• This mode reversal requires antiferromagnetic (AFM) dynamical coupling.
• The dynamical coupling can be AFM even if both NN and NNN exchange interactions are ferromagnetic.

We study the order of modes in the spin‐wave spectrum of a ferromagnetic thin film. In our calculations we use the Heisenberg model taking into account the exchange interaction between the nearest (NN) and next-nearest (NNN) neighbors and including the single-ion anisotropy term. We elucidate the effect of the NNN exchange coupling on both the spectrum of propagating spin waves and the spin‐wave resonance (SWR) spectrum. We show that with sufficiently strong antiferromagnetic NNN interaction the order of modes in the spin‐wave spectrum is reversed at the center of the Brillouin zone, with the lowest mode optic and the highest one acoustic. This effect allows to infer the character of the NNN interaction from the resonance peak intensity pattern in the SWR spectrum. We also show that the reversed order of modes can be related to in-plane spin‐wave propagation. Surprisingly, this dynamic reversal can occur even if both the NN and NNN exchange interactions are ferromagnetic. This effect should be observed in Brillouin light scattering and spin-polarized electron energy loss spectra as a collapse, followed by a spectrum with a reversed intensity pattern with changing wave-vector length.