  The search for elusive Nagaoka-type ferromagnetism in the Hubbard model has
recently enjoyed renewed attention with the advent of a variety of experimental
platforms enabling its realization, including moir\'e materials, quantum dots,
and ultracold atoms in optical lattices. Here, we demonstrate a universal
mechanism for Nagaoka ferromagnetism (that applies to both bipartite and
nonbipartite lattices) based on the formation of ferromagnetic polarons
consisting of a dopant dressed with polarized spins. Using large-scale
density-matrix renormalization group calculations, we present a comprehensive
study of the ferromagnetic polaron in an electron-doped Hubbard model,
establishing various polaronic properties such as its size and energetics.
Moreover, we systematically probe the internal structure of the magnetic
state$\unicode{x2014}$through the use of pinning fields and three-point
spin-charge-spin correlation functions$\unicode{x2014}$for both the
single-polaron limit and the high-density regime of interacting polarons. Our
results highlight the crucial role of mobile polarons in the birth of global
ferromagnetic order from local ferromagnetism and provide a unified framework
to understand the development and demise of the Nagaoka-type ferromagnetic
state across dopings.
