  We study higher spin (pure and mixed spin) representations of the Yangian of
$\mathfrak{sl}_2$. We provide a geometric realization in terms of the critical
cohomology of representations of the quiver with potential of Bykov and
Zinn-Justin [BZJ20]. When the framing dimension is 1, it recovers the
evaluation pullback of the $\ell+1$-dimensional irreducible representation of
$\mathfrak{sl}_2$. We introduce the lattice model and prove that its partition
function coincides with the weight function constructed using the framed
shuffle formula. The latter follows the approach of Rim\'anyi, Tarasov and
Varchenko [RTV15].
