  Bulk specimens of the hetaerolite solid solution Zn$_x$Mn$_{3-x}$O$_4$, with
$x$ = 0, 0.25, 0.5, 0.75, and 1 have been prepared as homogeneous, phase-pure
polycrystalline samples as ascertained by neutron diffraction measurements.
Samples with $x$ = 0.25, 0.5, and 0.75 exhibit shifted magnetic hysteresis
loops at low temperature, characteristic of exchange bias typically seen in
magnetic composites. We propose that the unusual magnetic behavior arises as a
result of a nanoscale mixture of ferrimagnetic and antiferromagnetic regions
that are distinct but lack long-range order. While some glassy behavior is seen
in AC magnetic measurements, its magnitude is not sufficient to account for the
observed dramatic exchange bias. Furthermore, isothermal and thermoremanent
magnetization measurements distinguish this material from a pure spin glass.
The title system offers insights into the alloying of a ferrimagnet Mn$_3$O$_4$
with an antiferromagnet ZnMn$_2$O$_4$ wherein distinct magnetic clusters grow
and percolate to produce a smooth transition between competing orders.
