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arXiv:cond-mat/0004334

Temperature dependence of the spin polarization in the fractional quantum Hall effects

Ganpathy N. Murthy

Published Apr 19, 2000• 0 citations
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Abstract

Using a Hamiltonian formulation of Composite Fermions that I recently developed with R. Shankar, I compute the dependence of the spin polarization on the temperature for the translationally invariant fractional quantum Hall states at $ν=1/3$ and $ν=2/5$. I compare my results to experiments at $ν=1/3$ and find reasonably good agreement.

DOI
10.48550/arxiv.cond-mat/0004334

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Using a Hamiltonian formulation of Composite Fermions that I recently developed with R. Shankar, I compute the dependence of the spin polarization on the temperature for the translationally invariant fractional quantum Hall states at ν=1/3ν=1/3ν=1/3 and ν=2/5ν=2/5ν=2/5. I compare my results to experiments at ν=1/3ν=1/3ν=1/3 and find reasonably good agreement.
Using the Hamiltonian formulation for composite fermions developed recently, the temperature dependence of the spin polarization is computed for the translationally invariant fractional quantum Hall states 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 is computed in a composite-fermion Hartree-Fock approximation. The computed magnetization for ν = 1/3 lies above the experimental results for intermediate temperatures indicating the importance of long-wavelength spin fluctuations which are not correctly treated in the Hartree-Fock approximation. In the second step, spin fluctuations beyond the Hartree-Fock approximation are included for ν = 1/3 by mapping the problem onto the coarse-grained continuum quantum ferromagnet. The parameters of the description in terms of the effective continuum quantum ferromagnet are extracted from the preceding Hartree-Fock analysis. After the inclusion of spin fluctuations in a large- N approach, the results for the finite-temperature spin polarization are in quite good agreement with the experiments.
The spin-wave excitation mode from the spin-polarized ground state in the fractional quantum Hall system at the Landau level filling of $\ensuremath{\nu}=\frac{1}{(2m+1)}$ is shown, by comparing with the exact numerical result for finite systems, to be accurately described, for wavelengths exceeding the magnetic length, in terms of the composite-fermion picture for the spin-wave (magnon) theory formulated in the spherical geometry. This indicates that the composite-fermion approach extends to excited states and also provides the spin stiffness in terms of exchange interaction with transformed interparticle interactions.
We compare quantum Hall systems at filling factors $\ensuremath{\nu}=2$ to $\ensuremath{\nu}=\frac{2}{3}$ and 25\frac{2}{5}52​, 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=1P=1P=1) and paramagnetic (P=0)(P=0)(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 $\ensuremath{\nu}=2$, we find spin domains at half-polarization (P=12)(P=\frac{1}{2})(P=21​), while antiferromagnetic order seems most favorable in the CF systems. The transition between P=0P=0P=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.
We apply Fermi hypernetted-chain theory to study the spin polarization of higher-order fractional quantum Hall (FQH) states at filling factors in between the primary FQH sequences, $\ensuremath{\nu}=p/({q}_{e}p\ifmmode\pm\else\textpm\fi{}1)$, where qe{q}_{e}qe​ is an even integer and ppp is a nonzero integer. The filling factors related to the higher-order FQH states include $\ensuremath{\nu}=3/8$, 4/114/114/11, 5/135/135/13, 5/175/175/17, 4/134/134/13, 6/176/176/17, 7/117/117/11, and so on. We use a model of strongly interacting fermions with different spin degrees of freedom to explain the states beyond primary FQH sequences. We calculate the correlation energy, the radial distribution function, as well as the static structure function associated with the Halperin wave function adopted for the mixture states of fermions with different spins. The results are comparable with those from the residual interaction between composite fermions.
The magnetic properties of a two-dimensional interacting electron system in a strong magnetic field are considered in the quantum Hall regime, where the motion of the electrons is restricted to the lowest Landau level. We apply an approach based on the many-particle quantum-field theory which we developed recently for the spin-polarized system in the fractional quantum Hall regime, and which treats the problem of the degeneracy of a partially filled Landau level properly. Via a gauge transformation of the fermion Green's function, we achieve a dressing of the propagator with multiple collective excitations. Our theory allows a calculation of the magnetic polarization M(T)M(T)M(T) for higher temperatures TTT, where $M(T)\ensuremath{\lesssim}0.4$ is not too large. For filling factor $\ensuremath{\nu}=1$ we obtain a magnetic polarization M(T)M(T)M(T) which agrees quite well with the data of a NMR experiment by Barrett [Phys. Rev. Lett. 74, 5112 (1995)].