  We present a systematic study of the magnetic properties of semiconducting
ZnFe$_2$O$_4$ thin films fabricated by pulsed laser deposition at low and high
oxygen partial pressure and annealed in oxygen and argon atmosphere,
respectively. The magnetic response is enhanced by annealing the films at
250$^{\circ}$C and diminished at annealing temperatures above 300$^{\circ}$C.
The initial increase is attributed to the formation of oxygen vacancies after
argon treatment, evident by the increase in the low energy absorption at $\sim$
0.9 eV involving Fe$^{2+}$ cations. The weakened magnetic response is related
to a decline in disorder with a cation redistribution toward a normal spinel
configuration. The structural renormalization is consistent with the decrease
and increase in oscillator strength of respective electronic transitions
involving tetrahedrally (at $\sim$ 3.5 eV) and octahedrally (at $\sim$ 5.7 eV)
coordinated Fe$^{3+}$ cations.
