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

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