  We study numerically the low-temperature electronic transport properties of a
single-ion magnet with uniaxial and transverse spin anisotropies. We find clear
signatures of a Kondo effect caused by the presence of a transverse
(zero-field) anisotropy in the molecule. Upon applying a transverse magnetic
field to the single-ion magnet, we observe oscillations of the Kondo effect due
to the presence of diabolical (degeneracy) points of the energy spectrum of the
molecule caused by a geometrical phase interference effects similar to those
observed in the quantum tunneling of multi-ion molecular nanomagnets. The
field-induced lifting of the ground state degeneracy competes with the
interference modulation, resulting in some cases in a suppression of the Kondo
peak.
