Materials Science and Engineering B84 (2001) 37 – 43 Two-dimensional electrons in spatially inhomogeneous magnetic field Akira Endo a , Mayumi Kato a , Minoru Kawamura a , Masato Ando a , Shingo Katsumoto a,b , Yasuhiro Iye a,b, * a Institute for Solid State Physics, Uniersity of Tokyo, 5 -1 -5 Kashiwanoha, Kashiwa, Chiba 277 -8581, Japan b CREST Project, Japan Science and Technology Corporation, 1 -4 -25 Mejiro, Toshima -ku, Tokyo 171 -0031, Japan Abstract Two-dimensional electron gas (2DEG) subjected to a spatially modulated magnetic field exhibits commensurability oscillation of magnetoresistance, analysis of which furnishes information on the modulation amplitude. Under a periodically modulated magnetic field with zero mean, the resistivity of the 2DEG gains an extra term expressed as  =AT 2 +C. The temperature quadratic term is attributed to electron – electron umklapp scattering, while the constant term arises from combined effect of the lateral magnetic superlattice and random impurities. In the composite Fermion (CF) regime near the half-filling of lowest Landau levels, spatial variation of the electron density is equivalent to magnetic field variation. Use of a short period lateral superlattice has enabled us to observe the commensurability oscillation of the magnetoresistance of CFs near the filling factor  =3/2. The positions of the resistance minima are consistent with those calculated by assuming magnetic modulation and fully spin-polarized CFs. © 2001 Elsevier Science B.V. All rights reserved. Keywords: GaAs/AlGaAs heterojunction; Magnetoresistance; Commensurability oscillation; Electron – electron umklapp scattering; Composite Fermion www.elsevier.com/locate/mseb 1. Introduction Two-dimensional electron gas (2DEG) in modulation doped GaAs/AlGaAs semiconductor heterostructures provides one of the cleanest electron systems in solids. The isotropic and parabolic conduction band of GaAs makes it a particularly simple system best suited for studies of fundamental physical processes on a well- characterized stage. One can create an artificial poten- tial landscape by fabricating a micro-patterned gate electrode on the surface of 2DEG sample. It is also possible to impose spatially varying magnetic field to the 2DEG by placing an array of micro-sized magnets [1]. Here, we present a few topics relevant to the electronic transport in such artificial landscape of po- tential and vector potential; commensurability oscilla- tion of magnetoresistance in spatially modulated magnetic field [2], electron – electron umklapp scattering in lateral magnetic superlattice [3], and commensurabil- ity oscillation in the composite Fermion regime [4]. We limit ourselves, in this paper, to the case of one-dimen- sional modulation. 2. Experimental The samples used in the present study were fabri- cated from an MBE grown GaAs/AlGaAs single het- erojunction wafer with the electron density and mobility n =3 ×10 15 m -2 and  =60 m 2 V -1 s -1 .A ferromagnetic grating was fabricated on surface of a Hall-bar sample as depicted in Fig. 1, by electron beam lithography, vacuum deposition of cobalt or nickel, and lift-off process. The periodicity of the grating was a = 500 nm and the thickness of the ferromagnetic wire was typically 60 nm. The depth of the 2DEG plane from the surface was 75 nm. The electron mean free path at helium temperatures was about 6 m, and was much greater than the period of the grating. The grating was fabricated with the direction of modulation parallel to * Corresponding author. Tel.: +81-471-363300; fax: +81-471- 363300. E-mail address: iye@issp.u-tokyo.ac.jp (Y. Iye). 0921-5107/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII:S0921-5107(01)00566-9