Abstract
We demonstrate that a two-dimensional (2D) optical lattice loaded with repulsive, contact-interacting fermions shows a rich and systematic magnetic phase diagram. Trapping a few (N ⩽ 12) fermions in each of the single-site minima of the optical lattice, we find that the shell structure in these quantum wells determines the magnetism. In a shallow lattice, the tunnelling between the single wells is strong, and the lattice is non-magnetic (NM). For deeper lattices, however, the shell filling of the single wells with fermionic atoms determines the magnetism. As a consequence of Hund's first rule, the interaction energy is lowered by maximizing the number of atoms of the same species. This leads to a systematic sequence of NM, ferromagnetic (F) and antiferromagnetic (AF) phases.
Highlights
Confined, small quantal systems exhibit a high potential for employing quantum physics in technology
The atom dynamics in an optical lattice is often described by the Hubbard or the Bose– Hubbard models [9, 16, 17]
We show that optical lattices with a few (N 12) fermionic atoms per lattice site with two hyperfine, or spin, species have an intriguing and rich magnetic structure
Summary
Confined, small quantal systems exhibit a high potential for employing quantum physics in technology. When the band is filled, each lattice site carries two fermions with opposite spins, and magnetism can not be observed. We show that optical lattices with a few (N 12) fermionic atoms per lattice site with two hyperfine, or spin, species have an intriguing and rich magnetic structure.
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