Low-frequency signature of magnetization nutation in nanomagnets

In this work, we show that surface anisotropy in nanomagnets induces a nutational motion of their magnetization at various frequencies, the lowest of which can be described by the macrospin model whose dynamics is governed by an effective energy potential. We derive analytical expressions for the precession and nutation frequencies and amplitudes as functions of the size of the nanomagnet and its atomistic parameters, such as the exchange coupling and the onsite anisotropy. Our analytical model predicts a reduction of the precession frequency with increased surface anisotropy. We also simulate the dynamics of the corresponding atomistic many-spin system and compare the results with the effective model. We thereby show that the first nutation mode induced by the finite size and surface anisotropy occurs at a frequency that is four times larger than the precession frequency, thus lending itself to a relatively easy detection by standard experiments of magnetic resonance.