  We use coupled-channel statistical calculations to explore the effects of
external magnetic fields and hyperfine interactions on the ultracold chemical
reactions {of triplet alkali-metal dimers with alkali-metal atoms. Using the Na
+ NaLi$(a^3\Sigma^+)$ $\to$ Na$_2(^1\Sigma_g^+)$ + Li reaction as a
representative example}, we find that the reaction rates are sensitive to the
initial hyperfine states of the reactants, and that the chemical reaction of
fully spin-polarized NaLi($a^3\Sigma^+,v=0,N=0$) molecules with Na atoms is
suppressed by a factor of $\simeq$10-100 compared to that of unpolarized
reactants. We interpret these findings within the adiabatic state model, which
treats the chemical reaction {as a sequence of nonadiabatic transitions between
the initial high-spin (non-reactive) and final low-spin (reactive) diabatic
states of the reaction complex.} Our results demonstrate that it is possible to
efficiently control the chemical reactions of open-shell alkali-metal dimers
with alkali-metal atoms by tuning the internal hyperfine states of the
reactants and by applying an external magnetic field.
