We study the hard-core Fermi-Hubbard model in the crossover between square and triangular lattices near half filling. As was recognized by Nagaoka in the 1960s, on the square lattice the presence of a single hole leads to ferromagnetic spin ordering. On the triangular lattice, geometric frustration instead leads to a spin-singlet ground state, which can be associated with a ${120}^{\circ }$ spiral order. On lattices which interpolate between square and triangular, there is a phase transition at which the ferromagnetic order becomes unstable to a spin spiral. We model this transition, finding the exact location of the spin-spiral instability.

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• Fermi gases
• Magnetic phase transitions
• Spin texture
• Strongly correlated systems
• Hubbard model
• Mean-field & cluster methods
• Perturbation theory