# Inducing and controlling magnetism in the honeycomb lattice through harmonic trapping potential

## TL;DR

This paper demonstrates how tuning a harmonic trap in a honeycomb lattice of ultracold fermions can induce and control various magnetic states, mimicking graphene nanostructures and revealing magnetic phenomena absent in extended sheets.

## Contribution

It introduces a method to induce and manipulate magnetic states in honeycomb lattices via harmonic trapping, creating artificial graphene nanoflakes with tunable magnetic properties.

## Key findings

- Harmonic trapping can confine fermions into nanostructures resembling graphene flakes.
- Different magnetic states, including antiferromagnetic and ferromagnetic, can be induced by adjusting trap strength.
- Magnetic patterns are influenced by the structure's termination, controlled by the trap.

## Abstract

We study strongly interacting ultracold spin-1/2 fermions in a honeycomb lattice in the presence of a harmonic trap. Tuning the strength of the harmonic trap we show that it is possible to confine the fermions in artificial structures reminiscent of graphene nanoflakes in solid state. The confinement on small structures induces magnetic effects which are absent in a large graphene sheet. Increasing the strength of the harmonic potential we are able to induce different magnetic states, such as a N\'eel-like antiferromagnetic or ferromagnetic states, as well as mixtures of these basic states. The realization of different magnetic patterns is associated with the terminations of the artificial structures, in turn controlled by the confining potential.