Canted antiferromagnetic and spin-singlet quantum Hall states in double-layer systems

We present details of earlier studies [Zheng et al., Phys. Rev. Lett. 78, 310 (1997) and Das Sarma et al., 79, 917 (1997)] and additional results on double-layer quantum Hall systems at a total filling $\nu =2\mathrm{}{\nu }_1$, where a single layer at filling ${\nu }_1$ forms a ferromagnetic, fully spin-polarized, gapped incompressible quantum Hall state. For the case ${\nu }_1=1\mathrm{}$, a detailed Hartree-Fock analysis is carried out on a realistic, microscopic Hamiltonian. Apart from the state continuously connected to the ground state of two well-separated layers, we find two double-layer quantum Hall phases: one with a finite interlayer antiferromagnetic spin ordering in the plane orthogonal to the applied field (the “canted” state), and the other a spin singlet. The quantum transitions between the various quantum Hall states are continuous, and are signaled by the softening of collective intersubband spin-density excitations. For the case of general ${\nu }_1$, closely related results are obtained by a semi-phenomenological continuum quantum field theory description of the low-lying spin excitations using a nonlinear $\sigma$ model. Because of its broken symmetry, the canted phase supports a linearly dispersing Goldstone mode and has a finite-temperature Kosterlitz-Thouless transition. We present results on the form of the phase diagram, the magnitude of the canted order parameter, the collective excitation dispersions, the specific heat, the form of the dynamic light-scattering spectrum at finite temperature, and the Kosterlitz-Thouless critical temperature. Our findings are consistent with recent experimental results.