  We present a theoretical description of the thermopower due to
magnon-assisted tunneling in a mesoscopic tunnel junction between two
ferromagnetic metals. The thermopower is generated in the course of thermal
equilibration between two baths of magnons, mediated by electrons. For a
junction between two ferromagnets with antiparallel polarizations, the ability
of magnon-assisted tunneling to create thermopower $S_{AP}$ depends on the
difference between the size $\Pi_{\uparrow, \downarrow}$ of the majority and
minority band Fermi surfaces and it is proportional to a temperature dependent
factor $(k_{B}T/\omega_{D})^{3/2}$ where $\omega_{D}$ is the magnon Debye
energy. The latter factor reflects the fractional change in the net
magnetization of the reservoirs due to thermal magnons at temperature $T$
(Bloch's $T^{3/2}$ law). In contrast, the contribution of magnon-assisted
tunneling to the thermopower $S_P$ of a junction with parallel polarizations is
negligible. As the relative polarizations of ferromagnetic layers can be
manipulated by an external magnetic field, a large difference $\Delta S =
S_{AP} - S_P \approx S_{AP} \sim - (k_B/e) f (\Pi_{\uparrow},\Pi_{\downarrow})
(k_BT/\omega_{D})^{3/2}$ results in a magnetothermopower effect. This
magnetothermopower effect becomes giant in the extreme case of a junction
between two half-metallic ferromagnets, $\Delta S \sim - k_B/e$.
