Integral and fractional quantum Hall Ising ferromagnets

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2007

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We compare quantum Hall systems at filling factors ν=2 to ν= 2 3 and 2 5, corresponding to the exact filling of two lowest electron or composite fermion (CF) Landau levels. The two fractional states are examples of CF liquids with spin dynamics. There is a close analogy between the ferromagnetic (spin polarization P=1) and paramagnetic (P=0) incompressible ground states that occur in all three systems in the limits of large and small Zeeman spin splitting. However, the excitation spectra are different. At ν=2, we find spin domains at half-polarization (P= 1 2), while antiferromagnetic order seems most favorable in the CF systems. The transition between P=0 and 1, as seen when, e.g., the magnetic field is tilted, is also studied by exact diagonalization in toroidal and spherical geometries. The essential role of an effective CF-CF interaction is discussed, and the experimentally observed incompressible half-polarized state is found in some models. © 2007 The American Physical Society.

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