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Magnetic phase diagram of nu=2 quantum Hall systems

Kanako Yoshizawa, Kazuo Takayanagi

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

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.

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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 present the magnetic phase diagram of the $\ensuremath{\nu}=2$ 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 ${r}_{s}\ensuremath{\sim}2$ 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.
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 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.
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.
A detailed investigation has been made of the application of the Hartree-Fock approximation to the stability and thermodynamic behaviour of spin-density waves in a model with a single electronic energy band and a delta-function-type interaction between electrons. It is shown that for a half-filled band the ground state at zero temperature is always a spin-density wave, provided only that the width of the band is sufficiently small. For other bands the conditions for the relative stability of the spin-density wave, ferromagnetic and paramagnetic states are more complicated, and are studied in detail for a special band form. For a half-filled band the energy per atom and specific heat have been calculated as functions of temperature for the spin-density wave, ferromagnetic and paramagnetic states. The temperature dependence of the amplitude for the spin-density wave and ferromagnetic states, and of the entropy for the spin-density wave and paramagnetic states have also been calculated. The formulation of the problem has been made using a Green function method in order to allow the development in a later paper of a higher-order approximation to the correlation problem.