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.
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