Magnetic Phases of the 2D Hubbard Model at Low Doping

TL;DR

This paper investigates the magnetic phases of the 2D Hubbard model at low doping, revealing that mean-field predicted spiral states are unstable and that the true ground state is noncoplanar, indicating a novel spin reorientation scenario.

Contribution

It demonstrates that mean-field spiral states in the 2D Hubbard model are unstable and identifies a noncoplanar ground state at low doping.

Findings

Spiral states have negative bosonic modes, indicating instability.

The true ground state is noncoplanar, not a spiral.

A new spin reorientation scenario is proposed.

Abstract

We study the equilibrium spin configuration of the 2D Hubbard model at low doping, when a long-range magnetic order is still present. We use the spin-density-wave formalism and examine the two suggested candidates for a ground state: the planar spiral $(\pi,Q)$ and $(Q,Q)$ states. In a mean-field theory, each of these two states is a ground state in a certain range of parameters. We however show that both states have negative bosonic modes in a transverse channel which implies that the spiral states are in fact unstable (the $(Q,Q)$ state, in addition, has a negative longitudinal stiffness). We searched for a ground state in a parameter range which on a mean-field level favored the $(\pi,Q)$ phase, and found that the equilibrium spin configuration is noncoplanar. These findings lead to a novel scenario of spin reorientation upon doping in Hubbard antiferromagnets.