  Graphene nanodisk is a graphene derivative with a closed edge. The trigonal
zigzag nanodisk with size $N$ has $N$-fold degenerated zero-energy states. A
nanodisk can be interpletted as a quantum dot with an internal degree of
freedom. The grand state of nanodisk has been argued to be a quasi-ferromagnet,
which is a ferromagnetic-like states with a finite but very long life time. We
investigate the spin-filter effects in the system made of nanodisks and leads
based on the master equation. The finite-size effect on spin filter is
intriguing due to a reaction from the polarization of incoming current to a
quasi-ferromagnet. Analyzing the relaxation process with the use of the
Landau-Lifshitz-Gilbert equation, we explore the response to four types of
incoming currents, namely, unpolarized current, perfectly polarized current,
partially polarized current and pulse polarized current. We propose some
applications for spintronics, such as spin memory, spin amplifier, spin valve,
spin-field-effect transistor and spin diode.
