A Magnon Approach to Thermal Fluctuations in Mesospins

Systems consisting of single domain patterned magnetic elements, also mesospins, have proven to be a viable playground for studying ordering, phase transitions and dynamics at the mesoscale. One particularly interesting example of such a system is the 2D frustrated artificial spin ice (ASI). In analyzing and simulating the ASI, the mesospins are often approximated as point dipoles or ‘dumbbells’. When studying the effect of thermal fluctuations and thermally induced phase transitions however, the above description fails and leads to quantitative discrepancies. The reason behind this inaccuracy is rooted in the presence of an inner magnetic structure in the mesospins. Here, we address thermal fluctuations of mesospins by means of characterizing the spectrum of thermally excited magnons, and build a framework to study these excitations based on numerical simulations. We find that the spectrum of thermal magnons is discretized due to finite size effects, and that an important role is assigned to the fluctuations at the edges of the structure. The dynamics of these edge fluctuations is found to be governed by an energy barrier, which originates from the magnetic texture inside the mesospin.