  Tunnel transport of interacting spin-polarized electrons through a
single-level vibrating quantum dot in external magnetic field is studied. By
using density matrix method, the current-voltage characteristics and the
dependence of conductance on temperature of a single-electron transistor were
calculated. We found that a lifting of Coulomb blockade in external magnetic
field happens in stages. The Franck-Condon steps associated with inelastic
electron tunneling in our case are doubled due to contribution of two
Zeeman-split levels in electron transport. The doubling of steps can be also
observed in the presence of Coulomb interaction. For strong electron-vibron
interaction the temperature dependence of conductance is shown to be
non-monotonic and anomalous growth of conductance maximum weakly depends both
on the Coulomb strength and the external magnetic field.
