Kinetic Magnetism From Doping A Frustrated Magnet

Abstract:  Strongly-correlated systems is a central topic of modern condensed matter physics. The interplay between strong correlation and geometric frustration could further lead to a plethora of novel magnetic phases, such as quantum spin liquids. The Hubbard model on an anisotropic triangular lattice offers a paradigm to study such systems, in which the phase diagram, especially upon doping, still remains an open question. I will report on our recent work using a quantum gas microscope to study the local spin order of the Hubbard model with ultracold fermions in anisotropic optical lattices continuously tunable from a square to a triangular geometry. In the Mott insulating regime, we observe how frustration reduces the range of magnetic correlations and drives a transition from a collinear Néel antiferromagnet to a short-range 120∘ spiral phase. Upon doping, magnetic correlations show a pronounced asymmetry between particle and hole doping and hint at a transition to ferromagnetic order at a particle doping around 50%. To understand the origin of the doping-dependent magnetism, we measure a three-point dopant-spin-spin correlation function enabled by our single-site resolved imaging and observed dopant induced magnetism polarons. Remarkably, we confirm the kinetic origin of these polarons, consistent with Nagaoka’s famous theorem. We reveal these polarons as extended ferromagnetic bubbles around particle dopants arising from the local interplay of coherent dopant motion and spin exchange. In contrast, kinetic frustration due to the triangular geometry promotes antiferromagnetic polarons around hole dopants, as proposed by Haerter and Shastry. Our work augurs the exploration of exotic quantum phases driven by charge motion in strongly correlated systems and over sizes that are challenging for numerical simulation.