Small-Angle Shubnikov–de Haas Measurements in a 2D Electron System: The Effect of a Strong In-Plane Magnetic Field

Abstract

Measurements in magnetic fields applied at small angles relative to the electron plane in silicon MOSFETs indicate a factor of 2 increase of the frequency of Shubnikov -de Haas oscillations at H . H sat . This signals the onset of full spin polarization above H sat , the parallel field above which the resistivity saturates to a constant value. For H , H sat , the phase of the second harmonic of the oscillations relative to the first is consistent with scattering events that depend on the overlap instead of the sum of the spin-up and spin-down densities of states. This unusual behavior may reflect the importance of many-body interactions. PACS numbers: 71.30. + h, 72.20.My, 73.40.Hm, 73.40.Qv A great deal of interest has recently been focused on the anomalous behavior of two-dimensional (2D) systems of electrons [1,2] and holes [3][4][5] whose resistivities unexpectedly decrease with decreasing temperature, behavior that is generally associated with metals rather than insulators [6]. One of the most intriguing characteristics of these systems is their enormous response to magnetic fields applied in the plane of the electrons [7][8][9] or holes [5,10]: the resistivity increases sharply by more than an order of magnitude, saturating to a constant plateau value above a magnetic field H sat .In this paper we report studies of the resistivity of the 2D electron system in silicon metal-oxide-semiconductor field-effect transistors (MOSFETs) in magnetic fields applied at small angles f with respect to the plane. This allows a study of the Shubnikov-de Haas (SdH) oscillations in perpendicular fields sufficiently small that the orbital motion has a negligible effect on the response to the in-plane component of the magnetic field. At small tilt angles f, the SdH oscillations plotted versus filling factor have twice the period below H sat compared with the period above H sat . This implies that the electron system is fully spin polarized in high fields, H . H sat , where the resistivity has reached saturation. Detailed examination of the oscillations in fields below H sat indicates unusual behavior consistent with electron scattering that depends on the product rather than the sum of the spin-up and spin-down densities of states.Two silicon MOSFETs with mobilities m ഠ 20 000 V͞cm 2 s at T 4.2 K were used in these studies. Contact resistances were minimized by using samples with a split-gate geometry, which permit high densities in the vicinity of the contacts while allowing independent control of the density of the 2D system under investigation. Standard AC four-probe techniques were used at 3 Hz to measure the resistance in the linear regime using currents typically below 5 nA. Data were taken on samples mounted on a rotating platform in a 3 He Oxford Heliox system at temperatures down to 0.235 K in magnetic fields up to 12 T.

Spin-Independent Effective Mass in a Valley-Degenerate Electron System

“…On the experimental side, the main argument for the FL-nature of the metallic state is the observation of quite conventional Shubnikov-de Haas (ShdH) oscillations [3,4], which implies an existence of well-defined quasiparticles albeit with the renormalized effective mass m * and spin susceptibility χ * s . The ShdH and magnetoresistance experiments show that at low densities both m * and χ * s are significantly enhanced compared to their band values [4] and, according to some studies [9,10], even diverge at the resistive transition point.Although none drastically non-FL features of the metallic state have been found in ShdH measurements as of now, there is one very intriguing observation which does seem to present a challenge for the FL theory, at least in its conventional formulation. Namely, in all studies when the spin and orbital degrees of freedom were controlled independently by applying a tilted magnetic field, the effective masses, m * ↑ and m * ↓ , and Dingle temperatures (impurity scattering rates), T D↑ and T D↓ , of spin-up and -down electrons, were found to be almost the same.…”

“…On the experimental side, the main argument for the FL-nature of the metallic state is the observation of quite conventional Shubnikov-de Haas (ShdH) oscillations [3,4], which implies an existence of well-defined quasiparticles albeit with the renormalized effective mass m * and spin susceptibility χ * s . The ShdH and magnetoresistance experiments show that at low densities both m * and χ * s are significantly enhanced compared to their band values [4] and, according to some studies [9,10], even diverge at the resistive transition point.…”

Indication of the Ferromagnetic Instability in a Dilute Two-Dimensional Electron System

“…Indeed, the resistance of a 2D electron gas in silicon metaloxide-semiconductor field-effect transistors (MOSFETs) was found to be isotropic with respect to in-plane magnetic field, B, and rise steeply with the field saturating to a constant value above a critical magnetic field B c which depends on electron density [7]. Moreover, an analysis of Shubnikov -de Haas oscillations in tilted magnetic fields has established recently that the field B c corresponds to the onset of full spin polarization of the electron system [8,9].In this Letter, we study low-temperature parallel-field magnetotransport in a 2D electron system in silicon in a wide range of electron densities. We find that the saturation (or polarization) magnetic field, B c , is a strictly linear function of n s : B c~͑ n s 2 n c ͒ where n c is the critical electron density for the B 0 metal-insulator transition.…”

“…Indeed, the resistance of a 2D electron gas in silicon metaloxide-semiconductor field-effect transistors (MOSFETs) was found to be isotropic with respect to in-plane magnetic field, B, and rise steeply with the field saturating to a constant value above a critical magnetic field B c which depends on electron density [7]. Moreover, an analysis of Shubnikov -de Haas oscillations in tilted magnetic fields has established recently that the field B c corresponds to the onset of full spin polarization of the electron system [8,9].…”

Thermal correction to resistivity in dilute 2D Si-based systems

“…Another unusual property of dilute 2D systems is their enormous response to parallel magnetic field. At low temperatures the magnetic field found to suppress the metallic behavior of 2D electron(hole) gas and result in strong increasing of resistivity upon enhancement of spin polarization degree [6,7]. At high temperatures the parallel magnetoresistivity starts to be unaffected by magnetic field when the temperature exceeds a value being of the order of Zeeman energy.…”