Magnetic phase diagram ofν=2quantum Hall systems

Abstract

We present the magnetic phase diagram of the $\ensuremath{\nu}=2$ quantum Hall system on the whole $({r}_{s},{E}_{Z})$ plane. We fix the phase boundaries of the paramagnetic and ferromagnetic states by looking for a softening of spin-density excitations in the time-dependent Hartree-Fock theory. A nontrivial phase is obtained in the self-consistent Hartree-Fock theory for ${r}_{s}\ensuremath{\sim}2$ and ${E}_{Z}\ensuremath{\lesssim}0.06\ensuremath{\hbar}{\ensuremath{\omega}}_{c}$, where both the paramagnetic and ferromagnetic states show spin instability. We show that the obtained phase is the spin-density wave (SDW) state, and explain the mechanism how the SDW stabilizes.