Frequency dynamics of a chain of magnetized rotors: dumbbell model vs Landau-Lifshitz equation

During the past decades magnetic materials and structures that span several length scales have been of interest mainly due to their application in data storage and processing, flexible electronics, medicine, between others. From a microscopic point of view, these systems are typically studied using the Landau-Lifshitz equation (LLE), while approaches such as the dumbbell model are used to study macroscopic magnetic structures. In this work we use both the LLE and the dumbbell model to study spin chains of various lengths under the effect of a time dependent-magnetic field, allowing us to compare qualitatively the results obtained by both approaches. This has allowed us to identify and describe in detail several frequency modes that appear, with additional modes arising as the chain length increases. Moreover, we find that high frequency modes tend to be absorbed by lower frequency ones as the amplitude of the field increases. The results obtained in this work are of interest not only to better understand the behavior of the macroscopic spins chains, but also expands the available tools for qualitative studies of both macroscopic and microscopic versions of the studied system, or more complex structures such as junctions or lattices. This would allow to study the qualitative behavior of microscopic systems (e.g. nanoparticles) using macroscopic arrays of magnets, and vice versa.