Hall coefficient of a dilute two-dimensional electron system in a parallel magnetic field

Abstract

Recent experiments in the two-dimensional electron systems in silicon metal-oxide-semiconductor field effect transistors have shown that the in-plane magnetic field H sat required to saturate the conductivity to its high-field value, and the magnetic field H s needed to completely align the spins of the electrons, are comparable. By small-angle Shubnikov-de Haas oscillation measurements that allow separate determinations of the spin-up and spin-down subband populations, we show to an accuracy 5% that H sat ϭH s . DOI: 10.1103/PhysRevB.64.073101 PACS number͑s͒: 72.15.Gd, 73.25.ϩi, 73.40.Qv, 73.50.Jt Dilute two-dimensional electron ͑or hole͒ systems, which display unexpected metallic behavior, are currently the subject of great interest. 1 These strongly interacting systems also exhibit enormous magnetoresistances in response to a magnetic field applied parallel to the electron plane: 2-6 with increasing field, the resistivity rises sharply and saturates to a constant value for HϾH sat ; the saturation field H sat is of the order of several tesla and varies with temperature and electron density.Two experiments have recently shown that the behavior of the resistance is related to the spin polarization of the electrons. On the assumption that the product gm* of the interaction-enhanced g factor g and effective mass m* measured in a small field does not change in a strong in-plane magnetic field, Okamoto et al. 7 found that the saturation field H sat is close to the field at which the two-dimensional ͑2D͒ electron system in silicon metal-oxide-semiconductor field effect transistors ͑MOSFET's͒ becomes fully spin-polarized. Similar conclusions were drawn by Vitkalov et al.,8 who demonstrated that the frequency of small-angle Shubnikov-de Haas ͑SdH͒ oscillations versus filling factor in high fields HϾH sat , is double the frequency at low fields HϽH sat . This signals a decrease of the density of states by a factor of 2 and the complete depopulation of one of the spin subbands when HϾH sat . The equivalence between the field H sat at which the resistance saturates and the field H s required to obtain complete alignment of the electron spins, was established in these experiments to an accuracy of Ϸ10% to 15%. By using a modification of the small-angle Shubnikov-de Haas method of measurement, 8 which allows a determination of the population of each spin subband separately, we show in the present paper that H sat ϭH s with an accuracy of Ϸ5%. 9 The method is based on the following considerations. The populations of the spin-up and spin-down subbands are governed by the Zeeman energy, which is determined by the total magnetic field. The splitting of the Landau levels is controlled by the normal component of the magnetic field H Ќ : ប c ϭeH Ќ /mc. By rotating the 2D electron plane relative to the direction of the magnetic field, we change the normal component of the magnetic field and, therefore, the Landau-level spitting in each band. For a fixed total magnetic field H, the sizes of the Fermi circles k F ↑,↓ , formed by...

Hall coefficient and electron-electron interaction of two-dimensional electrons in Si MOSFETs

“…This is in apparent contradiction with expectations based on straightforward arguments [11] that predict different mobilities of the spin-up and spin-down electrons and, therefore, a substantial variation of the Hall coefficient with in-plane magnetic field [10]. The purpose of the present paper is to provide a possible explanation of the behavior of the Hall coefficient.…”

“…The Hall coefficient was measured at higher magnetic fields up to 18T at the National High Magnetic Field Laboratory in Tallahassee, Florida. The details of the experiment are presented in the paper [10,12]. The Hall coefficient R H , corresponding to different electron densities from n s = 1.22 × 10 11 cm −2 to n s = 4.42 × 10 11 cm −2 , is shown in Fig.1.…”

Hall coefficient and magnetoresistance of two-dimensional spin-polarized electron systems

“…Remarkably, recent measurements of the 2D Hall resistance [5] in a parallel magnetic field have shown unexpected physical behavior which is in sharp contrast with the strong in-plane field dependence of the 2D magnetoresistivity. The measured Hall coefficient seems to contradict qualitatively the results based on the screening theory [6] even though the longitudinal magnetoresistance can be explained by the change of the screening as the spin-polarization of the system varies.…”

Quantum electron transport in magnetically entangled subbands

“…33 The experiments show sizable contributions of the product of spin-up and spin-down density of states to quantum resistance oscillations. Furthermore investigations of the resistivity tensor in tilted magnetic fields have revealed an independence of the Hall coefficient on the spin subband populations while the electron mobility in each spin subband was substantially affected by the in-plane magnetic field 34 . This behavior has been interpreted by a mixing between spin subbands due to electron-electron interaction.…”