  We derive the general form of the non-trivial geometric phase resulting from
the unique combination of point group and time reversal symmetries. This phase
arises e.g. when a magnetic adatom is adsorbed on a non-magnetic C$_n$ crystal
surface, where $n$ denotes the fold of the principal axis. The energetic
ordering and the relevant quantum numbers of the eigenstates are entirely
determined by this quantity. Moreover, this phase allows to conveniently
predict the protection mechanism of any prepared state, shedding light onto a
large number of experiments and allowing a classification scheme. Owing to its
robustness this geometric phase also has great relevance for a large number of
applications in quantum computing, where topologically protected states bearing
long relaxation times are highly desired.
