# Itinerant ferromagnetism of two-dimensional repulsive fermions with Rabi coupling

## TL;DR

This paper investigates how two-dimensional repulsive fermions with Rabi coupling can undergo a quantum phase transition to a ferromagnetic state, analyzing the effects of interactions, Rabi coupling, and external confinement.

## Contribution

It provides an analytical study of itinerant ferromagnetism in 2D fermionic systems with Rabi coupling, including the effects of external harmonic traps.

## Key findings

- Quantum phase transition occurs when interaction energy exceeds kinetic and Rabi energies.
- Population imbalance depends on interaction strength, Rabi coupling, and density.
- External confinement leads to spatially varying spin polarization within the trap.

## Abstract

We study a two-dimensional fermionic cloud of repulsive alkali-metal atoms characterized by two hyperfine states which are Rabi coupled. Within a variational Hartree-Fock scheme, we calculate analytically the ground-state energy of the system. Then we determine the conditions under which there is a quantum phase transition with spontaneous symmetry breaking from a spin-balanced configuration to a spin-polarized one, an effect known as itinerant ferromagnetism. Interestingly, we find that the transition appears when the interaction energy per particle exceedes both the kinetic energy per particle and the Rabi coupling energy. The itinerant ferromagnetism of the polarized phase is analyzed, obtaining the population imbalance as a function of interaction strength, Rabi coupling, and number density. Finally, the inclusion of a external harmonic confinement is investigated by adopting the local density approximation. We predict that a single atomic cloud can display population imbalance near the center of the trap and a fully balanced configuration at the periphery.