Magnetic structure of an imbalanced Fermi gas in an optical lattice

TL;DR

This paper investigates the magnetic phases of an imbalanced Fermi gas in optical lattices, revealing ferromagnetic edges and canted antiferromagnetic centers, with insights into the effects of interaction strength and dimensionality.

Contribution

It provides a detailed analysis of magnetic structures in imbalanced Fermi gases using Hartree-Fock calculations and discusses the influence of interactions and dimensionality on magnetic order.

Findings

Edge ferromagnetism emerges above a critical interaction Uc.

Canted antiferromagnetic order appears in the Mott region below Uc.

Spin conservation induces complex magnetic textures.

Abstract

We analyze the repulsive fermionic Hubbard model on square and cubic lattices with spin imbalance and in the presence of a parabolic confinement. We analyze the magnetic structure as a function of the repulsive interaction strength and polarization. In the first part of the paper we perform unrestricted Hartree-Fock calculations for the 2D case and find that above a critical interaction strength $U_c$ the system turns ferromagnetic at the edge of the trap, in agreement with the ferromagnetic Stoner instability of a homogeneous system away from half-filling. For $U<U_c$ we find a canted antiferromagnetic structure in the Mott region in the center and a partially polarized compressible edge. The antiferromagnetic order in the Mott plateau is perpendicular to the direction of the imbalance. In this regime the same qualitative behavior is expected for 2D and 3D systems. In the second part of the paper we give a general discussion of magnetic structures above $U_c$. We argue that spin conservation leads to nontrivial textures, both in the ferromagnetic polarization at the edge and for the Neel order in the Mott plateau. We discuss differences in magnetic structures for 2D and 3D cases.