Finite-temperature magnetism in fractional quantum Hallsystems: the composite-fermion Hartree-Fock approximation and beyond

Abstract

Using the Hamiltonian formulation for composite fermions developedrecently, the temperature dependence of the spin polarization iscomputed for the translationally invariant fractional quantum Hallstates at ν = 1/3 and ν = 2/5 in two steps. In the first step,the effect of particle-hole excitations on the spin polarization iscomputed in a composite-fermion Hartree-Fock approximation. Thecomputed magnetization for ν = 1/3 lies above the experimentalresults for intermediate temperatures indicating the importance oflong-wavelength spin fluctuations which are not correctly treated inthe Hartree-Fock approximation. In the second step, spinfluctuations beyond the Hartree-Fock approximation are included forν = 1/3 by mapping the problem onto the coarse-grained continuumquantum ferromagnet. The parameters of the description in terms ofthe effective continuum quantum ferromagnet are extractedfrom the preceding Hartree-Fock analysis. After the inclusion ofspin fluctuations in a large-N approach, the results for thefinite-temperature spin polarization are in quite good agreementwith the experiments.