  We theoretically analyze the spectrum of a magnetic molecule when its charge
and spin can couple to the molecular vibrations. More specifically, we show
that the interplay between charge-vibron and spin-vibron coupling leads to a
renormalization of the magnetic anisotropy parameters of the molecule. This
effect is discussed for a model device consisting of an individual magnetic
molecule embedded in a junction. We study the transport properties of the
device and illustrate how the differential conductance is affected by the
vibrationally induced renormalization of the magnetic anisotropy. Depending on
the total molecular spin and the bare (intrinsic) magnetic anisotropy, the
induced modulation can lead to visible shifts and crossings in the spectrum,
and it can even be the cause of a transport blockade. It is therefore of
particular interest to use mechanically controllable break junctions, since in
such a case, the relevant coupling between the molecular spin and vibrations
can be controlled via deformations of the molecule when stretching or
compressing the junction.
