  High-temperature (high-$T_{\rm c}$) superconductivity appears as a
consequence of the carrier-doping of an undoped parent compound exhibiting
antiferromagnetic order; thereby, ground-state properties of the parent
compound are closely relevant to the superconducting state. On the basis of the
concept, a spin-fluctuation has been addressed as an origin of pairing of the
superconducting electrons in cuprates. Whereas, there is growing interest in
the pairing mechanism such as an unconventional spin-fluctuation or an advanced
orbital-fluctuation due to the characteristic multi-orbital system in
iron-pnictides. Here, we report the discovery of an antiferromagnetic order as
well as a unique structural transition in electron-overdoped
LaFeAsO$_{1-x}$H$_x$ ($x$ ~ 0.5), whereby another parent phase was uncovered,
albeit heavily doped. The unprecedented two-dome superconducting phases
observed in this material can be interpreted as a consequence of the
carrier-doping starting from the original at $x\sim0$ and advanced at
$x\sim0.5$ parent phases toward the intermediate region. The bipartite parent
phases with distinct physical properties in the second magnetic phase provide
us with an interesting example to illustrate the intimate interplay among the
magnetic interaction, structural change and orbital degree of freedom in
iron-pnictides.
