  During nuclear fission, a heavy nucleus splits into two rotating fragments.
The associated angular momentum is large, yet the mechanism of its generation
and its dependence on the mass of fragments remain poorly understood. In this
Letter, we provide the first microscopic calculations of angular momentum
distributions in fission fragments for a wide range of fragment masses. For the
benchmark case of $^{239}$Pu($n_{\text{th}}$,f), we find that the angular
momentum of the fragments is largely determined by the nuclear shell structure
and deformation, and that the heavy fragments therefore typically carry less
angular momentum than their light partners. We use the fission model
$\tt{FREYA}$ to simulate the emission of neutrons and photons from the
fragments. The dependence of the angular momenta on fragment mass after the
emission of neutrons and statistical photons is linear for the heavy fragments
and either constant or weakly linear for the light fragments, consistent with
the universal sawtooth pattern suggested by recent experimental data. Finally,
we observe that using microscopic angular momentum distributions modifies the
number of emitted photons significantly.
