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Physical Review B

Magnetic phase diagram of ν=2 quantum Hall systems

Kanako Yoshizawa, Kazuo Takayanagi

Published Mar 24, 2009• 2 citations
Publisher

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.

DOI
10.1103/physrevb.79.125321

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We present the magnetic phase diagram of the \ensuremathν=2\ensuremath{\nu}=2\ensuremathν=2 quantum Hall system on the whole (rs,EZ)({r}_{s},{E}_{Z})(rs​,EZ​) 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 rs\ensuremath∼2{r}_{s}\ensuremath{\sim}2rs​\ensuremath∼2 and EZ\ensuremath≲0.06\ensuremathℏ\ensuremathωc{E}_{Z}\ensuremath{\lesssim}0.06\ensuremath{\hbar}{\ensuremath{\omega}}_{c}EZ​\ensuremath≲0.06\ensuremathℏ\ensuremathωc​, 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.
We present the magnetic phase diagram of the ν = 2 quantum Hall system on the whole (rs, EZ ) plane.We fix the phase boundaries of the paramagnetic and ferromagnetic states by looking for a softening of spin density excitations (SDE) in the time-dependent Hartree-Fock theory.A new phase is obtained in the self-consistent Hartree-Fock theory for rs ∼ 2 and EZ 0.06 ωc, where both the paramagnetic and ferromagnetic states show spin instability.We show that the new phase is the spin density wave (SDW) state, and explain the mechanism how the SDW stabilizes.
We investigate possible spin instabilities of integer quantum Hall systems as a function of the density within the framework of the self-consistent Hartree-Fock theory. We have found a spin density wave (SDW) state that is lower in energy than the paramagnetic and ferromagnetic states for the filling factor $\ensuremath{\nu}=2$ in the density region 2.01<rs<2.152.01<{r}_{s}<2.152.01<rs​<2.15. The new SDW phase is the very one that has been expected by the softening of excitation spectra of the spin density excitation. We have examined the SDW phase in detail using the density matrix.
We consider the effect of interaction on electrons confined to two dimensions at Landau level filling = 2, with the specific aim of determining the range of parameters where the fully polarized state is stable. We calculate the charge- and the spin-density collective modes in the random-phase approximation (RPA) including vertex corrections (also known as the time-dependent Hartree-Fock approximation), and treating the Landau level mixing accurately within the subspace of a single particle-hole pair. It is found that the spin-wave excitation mode of the fully polarized state has a roton minimum which deepens as a result of the interaction-induced Landau level mixing, and the energy of the roton vanishes at a critical Zeeman energy, signalling an instability of the fully polarized state at still lower Zeeman energies. The feasibility of the experimental observation of the roton minimum in the spin-wave mode and its softening will be discussed. The spin- and charge-density collective modes of the unpolarized state are also considered, and a phase diagram for the = 2 state as a function of r S and the Zeeman energy is obtained.
We study intersubband spin density collective modes in double-layer quantum Hall systems at $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ within the time-dependent Hartree-Fock approximation. We find that these intersubband spin density excitations may soften under experimentally accessible conditions, signaling a phase transition to a new quantum Hall state with interlayer inplane antiferromagnetic spin correlations. We show that this novel canted antiferromagnetic phase is energetically stable and that the phase transition is continuous.
Ground-state properties of the two-dimensional Hubbard model with point-defect disorder are investigated numerically in the Hartree-Fock approximation. The phase diagram in the p(point defect concentration)--\ensuremath{\delta}(deviation from half filling) plane exhibits antiferromagnetic, spin-density-wave, paramagnetic, and spin-glass-like phases. The disorder stabilizes the antiferromagnetic phase relative to the spin-density-wave phase. The presence of U strongly enhances the localization in the antiferromagnetic phase. The spin-density-wave and spin-glass-like phases are weakly localized.