Dimensional Control of Nagaoka Ferromagnetism via Manipulating Kinetic Frustration

The kinetic mechanism of dopants in frustrated triangular lattices has garnered renewed interest due to its applications in moiré materials. On the other hand, a typical macroscopic quantum effect of itinerate magnetism – the Nagaoka Ferromagnetism (NFM) – has been realized in quantum simulators. Motivated by this, we investigate the instability of the NFM by controlling the kinetic frustration of the hole dopant. We show that the reduced dimensionality of the 1D (trestle) lattice facilitates spin polaron formation, destabilizing the ferromagnet for any infinitesimal kinetic frustration. In contrast, NFM instability in the 2D triangular lattice happens at significantly higher critical frustration. By tuning the kinetic frustration, we further observe the first-order ground state phase transition from NFM to Haerter and Shastry antiferromagnet, separated by spin density wave. In addition, we predict ferromagnetic instability arising from the interplay between hole density and kinetic frustration and find that increasing hole doping reduces critical frustration due to renormalized effective band curvatures. Our findings are suitable for predicting future cold atom experiments and have some implications in moiré lattice with extreme interaction.

*Funded by NSF PREP Grant No. PHY-2216774 and DOE award number DE-SC0024524