  The search for ferromagnetism in the Hubbard model has been a problem of
outstanding interest since Nagaoka's original proposal in 1966. Recent advances
in quantum simulation have today enabled the study of tunable doped Hubbard
models in ultracold atomic systems. Here, we examine a realistic variant of
such a model wherein any second electron on a single lattice site is weakly
bound compared to the first one. Employing large-scale density-matrix
renormalization group calculations, we establish the existence of high-spin
ground states on square and triangular lattices, analyze the microscopic
mechanisms behind their origin, and investigate the interplay between
ferromagnetism and other competing orders, such as stripes. Our results also
explain$\unicode{x2014}$and shed new light on$\unicode{x2014}$the intriguing
observations of ferromagnetic correlations in recent optical-lattice
experiments.
