  Groundstate magnetism of the one-band Hubbard model on the frustrated square
lattice where both nearest-neighbour $t_1$ and next-nearest-neighbour $t_2$
hoppings are considered at half-filling are revisited within mean field
approximation. Two new magnetic phases are detected at intermediate strength of
Hubbard $U$ and relative strong frustration of $t_2/t_1$, named double-stripe
and plaquette antiferromagnetic states, both of which are metallic and stable
even at finite temperature and electron doping. The nature of the phase
transitions between different phases and the properties of the two new states
are analyzed in detail. Our results of various magnetic states emerging from
geometric frustration in the minimal model suggests that distinct
antiferromagnetism observed experimentally in the parent states of two
high-T$_c$ superconducting families, i.e., cuprates and iron-based
superconductors, may be understood from a unified microscopic origin,
irrespective of orbital degrees of freedom, or hoppings further than
next-nearest neighbour, etc.
