Magnetic Anisotropy in Quantum Hall Ferromagnets

Abstract

We show that the sign of magnetic anisotropy energy in quantum Hall ferromagnets is determined by a competition between electrostatic and exchange energies. Easy-axis ferromagnets tend to occur when Landau levels whose states have similar spatial profiles cross. We report measurements of integer QHE evolution with magnetic-field tilt. Reentrant behavior observed for the ν = 4 QHE at high tilt angles is attributed to easy-axis anisotropy. This interpretation is supported by a detailed calculation of the magnetic anisotropy energy. 73.40Hm, 75.10Lp, 75.30Gw Typeset using REVT E X 1

Spin and Charge Ordering in the Quantum Hall Regime

“…These will be important in a later part of this chapter (section 3.3) and are discussed there in more detail. Also in the IQHE Ising-type spin transitions with broken symmetry can be realized as in the case of the FQHE by inducing a crossing of Landau levels with opposite spin orientation [173]. However, in the case of the IQHE, this is hampered by the fact that both the Zeeman and the cyclotron energy exhibit a linear -dependence.…”

“…However, in the case of the IQHE, this is hampered by the fact that both the Zeeman and the cyclotron energy exhibit a linear -dependence. Nevertheless, spin transitions have been achieved by using large tilt angles [173] or by resorting to wide quantum wells with an occupied second subband [162]. Special attention needs to be paid to the spin physics at filling factor = 1 ⁄2.…”

Effects of spin polarization in the HgTe quantum well

“…That's why we tentatively attribute the observed difference to the coupling of B || with the orbital degree of freedom in a QW of a finite width resulted in a different charge density profiles across the QW for the two approaching spin levels. 23 This coupling enhances a magnetic anisotropy energy for the ν = 3 coincidence as compared to that for ν = 2 since its B || is about a factor of 1.5 higher resulting in a shrinkage of the wave functions and thus the increased spatial difference between them. On the other hand, the coincidences at ν ≥ 4 are restored because they go outside of the QH range of B ⊥ .…”

“…This result looks counterintuitive since the overlapping of magnetic levels with decreased B ⊥ seems to monotonously destroy the causes for appearing of anticrossings, suppressing the spin polarization, as it has been observed so far on other materials. 22,23 A conventional explanation of the anticrossings is in terms of the magnetic anisotropy in the electronic system 1,23 : as the approaching spin levels of different spin orientations swop their order in energy relatively the Fermi level, the Hartree-Fock energy of the system may decrease due to changes in the many-body interaction concomitant to changes in the spin polarization. The decrease starts before the level crossing, due to a hybridization of the levels, and the crossing in fact does not occur, the stronger is the energy gain due to spin polarization the larger is the anticrossing gap.…”

“…On the other hand, the coincidences at ν ≥ 4 are restored because they go outside of the QH range of B ⊥ . 22,23 III. CONCLUSIONS…”