  Altermagnetism represents a new type of collinear magnetism distinct from
ferromagnetism and conventional antiferromagnetism. In contrast to the latter,
sublattices of opposite spin are related by spatial rotations and not only by
translations and inversions. As a result, altermagnets have spin split bands
leading to unique experimental signatures. Here, we show theoretically how a
d-wave altermagnetic phase can be realized with ultracold fermionic atoms in
optical lattices. We propose an altermagnetic Hubbard model with anisotropic
next-nearest neighbor hopping and obtain the Hartree-Fock phase diagram. The
altermagnetic phase separates in a metallic and an insulating phase and is
robust over a large parameter regime. We show that one of the defining
characteristics of altermagnetism, the anisotropic spin transport, can be
probed with trap-expansion experiments.
