Ferro- and Ferrimagnetic States of Ultracold Fermions in a Hubbard System

Ferromagnetism is one of most visible manifestations of quantum physics at the macroscopic scale. Understanding its emergence from first principles can however be challenging in strongly correlated systems. A prime example is the Fermi-Hubbard model, a simplified model that is central to describing a wide array of quantum materials but for which the existence of ferromagnetic phases has only been rigorously established in a handful of limiting cases. Ultracold fermions in optical lattices can shed light on itinerant electron magnetism by offering a pristine realization of the Hubbard model with access to single-particle resolved spin and charge observables.

Here, we report on two cold-atom realizations of intriguing magnetic states arising in Hubbard systems where interactions are large compared to kinetic energy scales. First, we demonstrate the existence of Nagaoka polarons in a particle-doped Mott insulator, imaged as extended ferromagnetic bubbles around single particle dopants that are stabilized by quantum path interference. Key to our observations is a triangular lattice, where kinetic magnetism is strongly enhanced due to frustration and the existence of short-length loops. Second, we report on the existence of a ferrimagnetic state realized in a Lieb lattice at half-filling, a paradigmatic example of a flat-band system whose large state degeneracy is lifted by weak interactions. This ferrimagnetic state is characterized by antialigned magnetic moments concomitant with a finite spin polarization. We demonstrate its robustness when increasing repulsive interactions to the Heisenberg regime, and study its emergence when continuously tuning the lattice unit cell from a square to a Lieb geometry. Future progress augurs the exploration of exotic low-temperature phases such as quantum spin liquids in kagome lattices and striped phases in cuprate compounds.