Confined magnon dispersion in ferromagnetic and antiferromagnetic thin films in a second quantization approach: the case of Fe and NiO

We present a methodology based on the calculation of the inelastic scattering from magnons via the spin scattering function in confined geometries such as thin films using a second quantization formalism, for both ferromagnetic and antiferromagnetic materials. The case studies are chosen with an aim to demonstrate the effects of film thickness and crystal orientation on magnon modes, using bcc Fe(100) and NiO with (100) and (111) crystallographic orientations as prototypical systems. Due to the quantization of the quasi-momentum we observe a granularity in the inelastic spectra in the reciprocal space path reflecting the orientation of the thin film. This approach also allows to capture softer modes that appear due to the partial interaction of magnetic moments close to the surface in a thin film geometry, in addition to bulk modes. The softer modes are also affected by crystallographic orientations as illustrated by the different surface-related peaks of NiO magnon density of states at approximately ~ 65 meV for (100) and ~ 42 meV for (111). Additionally, we explore the role of anisotropy on magnon modes, revealing that introducing anisotropy to both Fe and NiO films increases the overall hardness of the magnon modes. The introduction of a surface anisotropy produces a shift of the surface-related magnon DOS peak to higher energies with increased surface anisotropy, and in some cases leading to surface confined mode.