  We theoretically investigate the thermoelectric and spin thermoelectric
properties of a T-shaped double quantum dot strongly coupled to two
ferromagnetic leads, focusing on transport regime where the system exhibits the
two-stage Kondo effect. We study the dependence of the (spin) Seebeck
coefficient, the corresponding power factor and the figure of merit on
temperature, leads' spin polarization and dot level position. We show that the
thermal conductance fulfills a modified Wiedemann-Franz law. We also
demonstrate that the spin thermopower is enhanced at temperatures corresponding
to the second stage of Kondo screening. Very interestingly, the
spin-thermoelectric response of the system is found to be highly sensitive to
the spin polarization of the leads. In some cases spin polarization of the
order of 1% is sufficient for a strong spin Seebeck effect to occur. This is
explained as a consequence of the interplay between the two-stage Kondo effect
and the exchange field induced in the double quantum dot. All calculations are
performed with the aid of numerical renormalization group technique.
