Spin Order in Paired Quantum Hall States

TL;DR

This paper investigates spin ordering in paired quantum Hall states at even-denominator filling fractions, especially $ u=5/2$, showing that spontaneous ferromagnetism can emerge in the ground state due to ferromagnetic fluctuations.

Contribution

It provides numerical and theoretical analysis demonstrating the emergence of ferromagnetism in paired quantum Hall states at $ u=5/2$, including a Ginzburg-Landau model and mean field calculations.

Findings

Incompressible ground state at $ u=5/2$ exhibits spontaneous ferromagnetism.

Ferromagnetic fluctuations can induce polarized superconducting states.

Ginzburg-Landau theory for spin degrees of freedom is a perturbed CP$^2$ model.

Abstract

We consider quantum Hall states at even-denominator filling fractions, especially $\nu=5/2$, in the limit of small Zeeman energy. Assuming that a paired quantum Hall state forms, we study spin ordering and its interplay with pairing. We give numerical evidence that at $\nu = 5/2$ an incompressible ground state will exhibit spontaneous ferromagnetism. The Ginzburg-Landau theory for the spin degrees of freedom of paired Hall states is a perturbed CP$^2$ model. We compute the coefficients in the Ginzburg-Landau theory by a BCS-Stoner mean field theory for coexisting order parameters, and show that even if repulsion is smaller than that required for a Stoner instability, ferromagnetic fluctuations can induce a partially or fully polarized superconducting state.