Integral and fractional Quantum Hall Ising ferromagnets

TL;DR

This paper compares quantum Hall ferromagnets at different filling factors, revealing similarities and differences in their spin states, excitation spectra, and the role of composite fermion interactions, with implications for understanding fractional quantum Hall effects.

Contribution

It introduces a detailed comparison of integer and fractional quantum Hall systems, highlighting the role of composite fermion interactions and the nature of spin polarization transitions.

Findings

Spin domains at half-polarization in integer quantum Hall systems.

Antiferromagnetic order in fractional quantum Hall systems.

Observation of incommensurate half-polarized states in models.

Abstract

We compare quantum Hall systems at filling factor 2 to those at filling factors 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 filling factor 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 incompresible half-polarized state is found in some models.