  It is shown that, upon the electron quantum transport via the nanostructure
containing a spin dimer, the spin-flip processes caused by the s-f exchange
interaction between electron and dimer spins lead to the Fano resonance
effects. An applied magnetic field eliminates degeneracy of the upper triplet
states of the dimer, changes the conditions for implementation of the Fano
resonances and antiresonances, and induces the new Fano resonance and
antiresonance. It results in the occurrence of a sharp peak and dip in the
energy dependence of transmittance. These effects strongly modify the
current--voltage characteristic of the spin-dimer structure in a magnetic field
and form giant magnetoresistance.
