  Different regimes of entanglement growth under measurement have been
demonstrated for quantum many-body systems, with an entangling phase for low
measurement rates and a disentangling phase for high rates (quantum Zeno
effect). Here we study entanglement growth on a disordered Bose-Fermi mixture
with the bosons playing the role of the effective self-induced measurement for
the fermions. Due to the interplay between the disorder and a non-Abelian
symmetry, the model features an entanglement growth resonance when the
boson-fermion interaction strength is varied. With the addition of a magnetic
field, the model acquires a dynamical symmetry leading to experimentally
measurable long-time local oscillations. At the entanglement growth resonance,
we demonstrate the emergence of the cleanest oscillations. Furthermore, we show
that this resonance is distinct from both noise enhanced transport and a
standard stochastic resonance. Our work paves the way for experimental
realizations of self-induced correlated phases in multi-species systems.
