The electronic and magnetic properties of quantum materials crucially depend on their crystalline structure. In contrast to their counterparts in cubic and square lattices, strongly correlated systems hosted by geometrically frustrated lattices can feature a plethora of novel ordered states and intriguing magnetic phases such as quantum spin liquids. Promising candidate materials for such phases can be described by the Hubbard model on an anisotropic triangular lattice, a paradigmatic model capturing the interplay between strong correlations and magnetic frustration. However, the fate of frustrated magnetism in the presence of itinerant dopants remains unclear, as well as its connection to the doped phases of the square Hubbard model.
In this talk, we show how recent experimental progress in Fermi gas microscopy can shed light on the magnetic states of a Hubbard model with controllable frustration and doping, by implementing anisotropic optical lattices continuously tunable from a square to a triangular geometry. At half-filling, we first probe signatures of a transition from a collinear Néel antiferromagnet to a short-range 120◦ spiral phase upon introducing frustration. Away from half-filling in triangular-like geometries, antiferromagnetic correlations tend to be stabilized by hole dopants but get further suppressed by particle dopants and even invert at a particle doping above 20%, hinting at a ferromagnetic instability. Measuring higher-order spin correlations can further shed light on the possible kinetic origin of magnetism in triangular lattices. This work paves the way towards exploring possible chiral ordered or superconducting phases in triangular lattices, and realizing t − t′ square lattice Hubbard models that may be essential to describe superconductivity in cuprate materials.