Itinerant ferromagnetism with finite-ranged interactions

Quantum fluctuations are of central importance in itinerant ferromagnets; when modeled by a homogeneous electron gas with contact interactions, fluctuations deliver a rich phase diagram featuring a first order ferromagnetic transition preempted by a spin spiral and a paired density wave. In this work we develop the formalism to analyze the effects of fluctuations with a realistic screened Coulomb potential. The finite-ranged interaction suppresses the tricritical point temperature of the first order ferromagnetic transition, bringing theory into line with experiment, while retaining the exotic spin spiral and paired density wave. In an ultracold atomic gas a finite-ranged interaction damps the competing molecular instability, permitting the observation of ferromagnetic correlations.

Figure 1

Phase boundaries at temperatures $T\in \{0,0.1,0.2,0.305\}{T}_{\text{F}}$ with a screened Coulomb interaction of strength $g\nu$ and range $k_{\text{F}}b$. The ferromagnetic transition is first order (solid blue curves) at low $k_{\text{F}}b$, separated from the second order at larger $k_{\text{F}}b$ (dotted blue curves) by the green dots. The dashed red line is the locus of tricritical temperatures. The black points with error bars show the DMC $T=0$ estimates for the phase boundary. The inset shows the tricritical (solid black line) and $p$-wave superconducting (dotted black) critical temperatures against $k_{\text{F}}b$, the red dots denote the CaRuO${}_3$ family and ZrZn${}_2$.

Figure 2

The phase diagram for a $T=0$ cold atom gas with pseudopotential interaction strength $k_{\text{F}}a$ and effective range $k_{\text{F}}{r}_{\text{e}}$. The two shaded regions denote zero loss, and a loss rate less than $0.5{\epsilon }_{\text{F}}$. The thick black line represents the transition to the ferromagnetic state for the separable pseudopotential (whose fluctuation correction rescaling is zero at the black dot), and the dotted line the reciprocal pseudopotential transition. The inset compares the phase diagram for the full fluctuation corrections with separable pseudopotential (solid black line) to one obtained using the $g(\mathbf{p},\mathbf{q})\mapsto g(\sqrt{2}{k}_{\text{F}},\sqrt{2}{k}_{\text{F}})$ approximation (dashed black line).