We have investigated correlation between spin polarization and magnetotransport in a high mobility silicon inversion layer which shows the metal-insulator transition. Increase in the resistivity in a parallel magnetic field reaches saturation at the critical field for the full polarization evaluated from an analysis of low-field Shubnikov-de Haas oscillations. By rotating the sample at various total strength of the magnetic field, we found that the normal component of the magnetic field at minima in the diagonal resistivity increases linearly with the concentration of "spin-up" electrons. 71.30.+h, 73.40.Qv, 73.40.Hm A metal-insulator transition (MIT) observed in Si metal-oxide-semiconductor field-effect transistors [1,2] (Si-MOSFET's) and other systems [3-6] attracts a great deal of attention since it seems to contradict an important result of the scaling theory by Abrahams et al. [7] that the conductance of a disordered two-dimensional (2D) system at zero magnetic field goes to zero for T → 0. In the metallic phase in Si-MOSFET's with high peak electron mobilities of µ peak > ∼ 2 m 2 /V s, the diagonal resistivity ρ xx shows a sharp drop with decreasing temperature from about 2 K [1]. Recent experiments [8,9] show that magnetic fields applied parallel to the 2D plane suppress the low temperature metallic conduction in Si-MOSFET's. Since the parallel magnetic field does not couple the orbital motion of electrons, this fact suggests an important role of the spin of electrons. However, the mechanism of the conduction in the anomalous metallic phase is not clear yet.The 2D systems that show the MIT [1-6] are characterized by strong Coulomb interaction between electrons. The mean Coulomb energy per electron U = (πN s ) 1/2 e 2 /4πε 0 κ is larger than the mean kinetic energy K = πh 2 N s /m * by an order of the magnitude around the critical point for the MIT. Here, N s is the electron concentration, κ is the relative dielectric constant at the interface, and m * is the effective mass of electron. It is estimated that U = 120 K, K = 14 K and the ratio r s = U/K = 8.3 for κ = 7.7 and m * = 0.19m e at N s = 1 × 10 15 m −2 in Si-MOSFET's. The ground state of the insulating phase of high mobility Si-MOSFET's is considered to be a pinned Wigner solid (WS) [10,11]. Magnetic field dependence of the thermal activation energy observed for various angles of the magnetic field was essentially explained by a model based on magnetic interactions in the pinned WS [12,13]. Although the quantum fluctuations change the 2D system into a liquid at higher-N s , electron-electron (e-e) interaction is expected to be still important.In the conduction band of silicon, the spin-orbit interaction is negligible and the spin polarization p = (N ↑ − N ↓ )/N s can always be given in the direction to the magnetic field. Here N ↑ and N ↓ are the concentrations of electrons having an up spin and a down spin, respectively (N s = N ↑ + N ↓ ). In the present work, we investigate the low temperature conduction in a high mobility Si-MOSFET for vario...

We have studied the magnetic and transport properties of an ultralow-resistivity two-dimensional electron system in a Si/SiGe quantum well. The spin polarization increases linearly with the in-plane magnetic field and the enhancement of the spin susceptibility is consistent with that in Si-MOS structures. Temperature dependence of resistivity remains metallic even in strong magnetic fields where the spin degree of freedom is frozen out. We also found a magnetoresistance anisotropy with respect to an angle between the current and the in-plane magnetic field.

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We have measured the magnetic field dependence of thermal activation energy E A in an insulating phase of a two-dimensional electron system formed in a Si inversion layer to investigate magnetic interactions among electrons. Experimental results are summarized as follows. ͑1͒ In a magnetic field parallel to the twodimensional plane, E A increases linearly with the total strength B tot of the magnetic field for B tot Շ3 T, while it takes a saturation value in the complementary high-B tot region. ͑2͒ The normal component B Ќ of the magnetic field causes a peculiar change in E A , where two minima appear at B Ќ Ϸ0.6N s 0 and B Ќ Ϸ1.1N s 0 for 0 ϭh/e. All the results are quantitatively explained by a model based on exchange interactions in a Wigner solid ͑WS͒ formed at r s Ϸ8. We assume that a three-particle ring exchange among localized electrons in the WS and a standard two-particle exchange between a thermally created mobile electron and a localized electron in the WS play dominant roles in determining the magnetic behavior of the system. At B Ќ ϭ0, the three-particle ring exchange interaction leads to the ferromagnetically ordered ground state of the WS. The antiferromagnetic two-particle exchange interaction favors magnetic states of a mobile electron different from the lowest spin-valley state of the localized electrons. Thermal activation, which involves a spin flip at low B tot or a transition between the valley states which we call a ''pseudo-spin-flip'' at high B tot , explains the experimental result ͑1͒. Magnetic flux through the exchange path can change the nature of the ring exchange interaction due to the Aharonov-Bohm effect. A simple calculation using an exchange constant of 0.3 K, which is consistent with the WKB calculation of Roger ͓Phys. Rev. B 30, 6432 ͑1984͔͒, for the three-electron ring exchange interaction reproduces the experimental result ͑2͒. Theoretical values of B Ќ N s Ϫ1 / 0 at magnetic-flux-induced antiferromagnetic phase transitions, which occur in the pseudospin system for large values of B tot , agree with the observed minima in E A (B Ќ ). ͓S0163-1829͑98͒04315-X͔ PHYSICAL REVIEW B 15 APRIL 1998-I VOLUME 57, NUMBER 15 57 0163-1829/98/57͑15͒/9097͑11͒/$15.00 9097

Magnetotransport in 2DES's formed in Si-MOSFET's and Si/SiGe quantum wells at low temperatures is reported. Metallic temperature dependence of resistivity is observed for the n-Si/SiGe sample even in a parallel magnetic field of 9 T, where the spins of electrons are expected to be polarized completely. Correlation between the spin polarization and minima in the diagonal resistivity observed by rotating the samples for various total strength of the magnetic field is also investigated. 71.30.+h, 73.40.Qv, 73.20.Dx Metallic temperature dependence of resistivity at a zero magnetic field has been observed in two-dimensional electron systems (2DES's) in Si-MOSFET's [1,2] and other 2D systems [3][4][5][6][7][8] characterized by strong Coulomb interaction between electrons (or holes) [7]. In experiments on Si-MOSFET's, it was found that a magnetic field applied parallel to the 2D plane can suppress the metallic behavior [9][10][11]. This result indicates that the spins of electrons play an important role in the metallic region as well as in the insulating region [12,13].The parallel magnetic field B does not couple the orbital motion of electrons within the 2D plane, but it changes the spin polarization of the 2DES. The spin polarization can be defined as p = (N ↑ − N ↓ )/N s , where N ↑ and N ↓ are the concentrations of electrons having an up spin and a down spin, respectively, and N s is the total electron concentration (N s = N ↑ + N ↓ ). p is expected to increase linearly with the total strength B tot (= B ) of the magnetic field. We have p = B tot /B c for p < 1 and B c = 2πh 2 N s /µ B g v g FL m FL if the system can be considered as Fermi liquid. Here, µ B (=he/2m e ) is the Bohr magneton and the valley degeneracy g v is 2 on the (001) surface of silicon. The strong e-e interaction is expected to change the effective g-factor g FL and the effective mass m FL from g * = 2.0 and m * = 0.19m e in the non-interacting 2DES in a (001) silicon surface.In the present work, we use two n-type silicon samples. A Si-MOSFET sample denoted Si-M has a peak electron mobility of µ peak = 2.4 m 2 /V s at N s = 4 × 10 15 m −2 and T = 0.3 K. The estimated SiO 2 layer thickness is 98 nm. A Si/SiGe sample denoted Si-G was grown by combining gas-source MBE and solid-source MBE. Details of the growth and characterization have been reported elsewhere [14,15] and T = 0.36 K. The samples were mounted on a rotatory thermal stage in a pumped 3 He refrigerator or in a 3 He-4 He dilution refrigerator together with a GaAs Hall generator and resistance thermometers calibrated in magnetic fields.In Ref.[11], some of the present authors have determined the product of g FL and m FL in Si-M from the low-temperature Shubnikov-de Haas oscillations in tilted magnetic field based on work of Fang and Styles [16]. The obtained enhancement factor α = g FL m FL /0.38m e is shown in Fig. 1(a) as a function of r s = π 1/2 (e/h) 2 (m * /κε 0 )N s −1/2 . r s is a dimensionless 1