  Extragalactic peaked-spectrum radio sources are thought to be the progenitors
of larger, radio-loud active galactic nuclei (AGN). Synchrotron self-absorption
(SSA) has often been identified as the cause of their spectral peak. The
identification of new megahertz-peaked spectrum sources from the GaLactic and
Extragalactic All-sky Murchison Widefield Array (GLEAM) survey provides an
opportunity to test how radio sources with spectral peaks below 1 GHz fit
within this evolutionary picture. We observed six peaked-spectrum sources
selected from the GLEAM survey, three that have spectral characteristics which
violate SSA and three that have spectral peaks below 230 MHz, with the Very
Long Baseline Array at 1.55 and 4.96 GHz. We present milliarcsecond resolution
images of each source and constrain their morphology, linear size, luminosity,
and magnetic field strength. Of the sources that are resolved by our study, the
sources that violate SSA appear to be compact doubles, while the sources with
peak frequencies below 230 MHz have core-jet features. We find that all of our
sources are smaller than expected from SSA by factors of >20. We also find that
component magnetic field strengths calculated from SSA are likely inaccurate,
differing by factors of >5 from equipartition estimates. The calculated
equipartition magnetic field strengths more closely resemble estimates from
previously studied gigahertz-peaked spectrum sources. Exploring a model of the
interaction between jets and the interstellar medium, we demonstrate that
free-free absorption (FFA) can accurately describe the linear sizes and peak
frequencies of our sources. Our findings support the theory that there is a
fraction of peaked-spectrum sources whose spectral peaks are best modelled by
FFA, implying our understanding of the early stages of radio AGN is incomplete.
