Itinerant ferromagnetism in a two-dimensional atomic gas

Motivated by the first experimental evidence of ferromagnetic behavior in a three-dimensional ultracold atomic gas, we explore the possibility of itinerant ferromagnetism in a trapped two-dimensional atomic gas. Firstly, we develop a formalism that demonstrates how quantum fluctuations drive the ferromagnetic reconstruction first order, and consider the consequences of an imposed population imbalance. Secondly, we adapt this formalism to elucidate the key experimental signatures of ferromagnetism in a realistic trapped geometry.

Figure 1

(a) The growth of magnetization $m$ with scattering length for different temperatures. The inset figures show the energy landscape with magnetization for $T=0$ either side of the first order transition. (b) the phase diagram of temperature with scattering length shows the first order (dashed red line) and second order (solid red line) (quasi)ferromagnetic ordering from the paramagnetic phase.

Figure 2

(a) The growth of magnetization $m$ with scattering length at $T=0$. (b) the $T=0$ phase diagram for imposed population imbalance $p$ with scattering length $a/b$ shows the first order (dashed red line) and second order (solid red line) ferromagnetic ordering from the unmagnetized (UnM) to the partially magnetized (PM) and fully magnetized (FM) regions, here unmagnetized refers to having no in-plane magnetization.

Figure 3

The variation of (a) cloud size, (b) kinetic energy, and (c) atom loss rate on ferromagnetic ordering with increasing scattering length $a/b$ for the orthodox Stoner mean-field theory case. The thin blue dashed line highlights the small $a/b$ behavior. The solid lines are at zero population imbalance whereas the dotted line is with an imposed population imbalance of $0.5$.

Figure 4

The variation of (a) cloud size, (b) kinetic energy, and (c) atom loss rate on ferromagnetic ordering with increasing scattering length $a/b$ when fluctuation corrections are taken into account. The thin blue dashed line highlights the small $a/b$ behavior. The solid lines are at zero population imbalance whereas the dotted line is with an imposed population imbalance of $0.5$.

Figure 5

The reparametrization of the momenta ${\mathbf{k}}_{1,2,3,4}$. ${\theta }_{12}$ represents the angle between ${\mathbf{k}}_1$ and ${\mathbf{k}}_2$. The two momenta ${\mathbf{p}}_{12}={\mathbf{k}}_1+{\mathbf{k}}_2$ and ${\mathbf{p}}_{34}={\mathbf{k}}_3+{\mathbf{k}}_4$ are constrained to be equal, ${\mathbf{p}}_{12}={\mathbf{p}}_{34}$, by the Dirac delta function in Eq. (A1).