  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.
