  A two-sublattice spin-fermion model of ferrimagnetic spinel, with spin-$1/2$
itinerant electrons at the sublattice $A$ site and spin-$s$ localized electrons
at the sublattice $B$ site is considered. The exchange between itinerant and
localized electrons is antiferromanetic. As a result the external magnetic
field, applied along the magnetization of the localized electrons, compensates
the Zeeman splitting due to the spin-fermion exchange and magnon-fermion
interaction induces spin anti-parallel p-wave superconductivity which coexists
with magnetism. We have obtained five characteristic values of the applied
field (in units of energy) $H_{cr1}<H_3<H_0<H_4<H_{cr2}$. At $H_0$ the external
magnetic field compensates the Zeeman splitting. When $H_{cr1}<H<H_{cr2}$ the
spin antiparallel p-wave superconductivity with $T_{1u}$ configuration coexists
with magnetism. The superconductor to normal magnet transition at finite
temperature is second order when $H$ runs the interval $(H_3,H_4)$. It is an
abrupt transition when $H_{cr1}<H<H_3$ or $H_4<H<H_{cr2}$. This is proved
calculating the temperature dependence of the gap for three different values of
the external magnetic field $H_{cr1}<H<H_3$, $H_4<H<H_{cr2}$ and $H=H_0$. In
the first two cases the abrupt fall to zero of the gap at superconducting
critical temperature shows that the superconductor to normal magnet transition
is first order. The Hubbard term (Coulomb repulsion), in a weak coupling
regime, does not affect significantly the magnon induced superconductivity.
Relying on the above results one can formulate a recipe for preparing a
superconductor from ferrimagnetic spinel: i) hydrostatic pressure above the
critical value of insulator-metal transition. ii) external magnetic field along
the sublattice magnetization with higher amplitude.
