Exotic magnetic orders for high spin ultracold fermions

TL;DR

This paper investigates exotic magnetic orders in high-spin ultracold fermionic atoms in optical lattices, deriving effective models and analyzing their phase diagrams, revealing stable plaquette and flux states influenced by interactions and magnetic fields.

Contribution

It introduces a method to derive low-energy effective models for high-spin fermions and identifies stable exotic magnetic phases in these systems.

Findings

Stable plaquette phase for F=3/2 fermions without fine tuning

SU(2) flux state is energetically favored over plaquette in certain regimes

Magnetic field stabilizes the SU(2) flux state in the phase diagram

Abstract

We study Hubbard models for ultracold bosonic or fermionic atoms loaded into an optical lattice. The atoms carry a high spin $F>1/2$, and interact on site via strong repulsive Van der Waals forces. Making convenient rearrangements of the interaction terms, and exploiting their symmetry properties, we derive low energy effective models with nearest-neighbor interactions, and their properties. We apply our method to $F=3/2$, and 5/2 fermions on two-dimensional square lattice at quarter, and 1/6 fillings, respectively, and investigate mean-field equations for repulsive couplings. We find for $F=3/2$ fermions that the plaquette state appearing in the highly symmetric SU(4) case does not require fine tuning, and is stable in an extended region of the phase diagram. This phase competes with an SU(2) flux state, that is always suppressed for repulsive interactions in absence of external magnetic field. The SU(2) flux state has, however, lower energy than the plaquette phase, and stabilizes in the presence of weak applied magnetic field. For $F=5/2$ fermions a similar SU(2) plaquette phase is found to be the ground state without external magnetic field.