  Near zero temperature, quantum magnetism can non-trivially arise from
short-range interactions, but the occurrence of magnetic order depends
crucially on the interplay of interactions, lattice geometry, dimensionality
and doping. Even though the consequences of this interplay are not yet fully
understood, quantum magnetism is believed to be connected to a range of complex
phenomena in the solid state, for example, in the context of high-$T_c$
superconductivity and spin liquids in frustrated lattices. Ultracold atomic
Fermi gases in optical lattices constitute an experimental system with
unrivalled tunability and detection capabilities to explore quantum magnetism
by analog quantum simulation. In this work, we study the emergence of
antiferromagnetic correlations between ultracold fermionic atoms in two
dimensions with decreasing temperature. We determine the magnetic
susceptibility of the Hubbard model from simultaneous measurements of the
in-situ density of both spin components. At half-filling and strong
interactions our data approach the Heisenberg model of localized spins with
antiferromagnetic correlations. Moreover, we observe the disappearance of
magnetic correlations when the system is doped away from half-filling. Our
observation of the dependence of quantum magnetism on doping paves the way for
future studies on the emergence of pseudogap and pairing phenomena away from
half-filling.
