  Waiting time distribution and the zero-frequency full counting statistics of
unidirectional electron transport through a double quantum dot molecule
attached to spin-polarized leads are analyzed using the quantum master
equation. The waiting time distribution exhibits a non-trivial dependence on
the value of the exchange coupling between the dots and the gradient of the
applied magnetic field, which reveals the oscillations between the spin states
of the molecule. The zero-frequency full counting statistics, on the other
hand, is independent of the aforementioned quantities, thus giving no insight
into the internal dynamics. The fact that the waiting time distribution and the
zero-frequency full counting statistics give a non-equivalent information is
associated with two factors. Firstly, it can be explained by the sensitivity to
different timescales of the dynamics of the system. Secondly, it is associated
with the presence of the correlation between subsequent waiting times, which
makes the renewal theory, relating the full counting statistics and the waiting
time distribution, not longer applicable. The study highlights the particular
usefulness of the waiting time distribution for the analysis of the internal
dynamics of mesoscopic systems.
