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Groundstate magnetism of the one-band Hubbard model on the frustrated squarelattice where both nearest-neighbour $t_1$ and next-nearest-neighbour $t_2$hoppings are considered at half-filling are revisited within mean fieldapproximation. Two new magnetic phases are detected at intermediate strength ofHubbard $U$ and relative strong frustration of $t_2/t_1$, named double-stripeand plaquette antiferromagnetic states, both of which are metallic and stableeven at finite temperature and electron doping. The nature of the phasetransitions between different phases and the properties of the two new statesare analyzed in detail. Our results of various magnetic states emerging fromgeometric frustration in the minimal model suggests that distinctantiferromagnetism observed experimentally in the parent states of twohigh-T$_c$ superconducting families, i.e., cuprates and iron-basedsuperconductors, may be understood from a unified microscopic origin,irrespective of orbital degrees of freedom, or hoppings further thannext-nearest neighbour, etc.

Uncovering double-stripe and plaquette antiferromagnetic states in the one-band Hubbard model on a frustrated square lattice