CONTROL OF MAGNETIC FIELD MODULATION ON TWO-DIMENSIONAL ELECTRON GAS AT THE GaAs/AlGaAs HETEROINTERFACE BY PARALLEL MAGNETIC FIELD MAYUMI KATO, AKIRA ENDO, SHINGO KATSUMOTO* and YASUHIRO IYE* Institute for Solid State Physics, University of Tokyo, Roppongi, Tokyo, 106, Japan AbstractÐWe have studied the magnetoresistance oscillation (Weiss oscillation) in a two-dimensional electron gas (2DEG) subjected to a one-dimensional periodic modulation of magnetic ®eld. Magnetic ®eld modulation was produced by placing nickel grating on the surface of 2DEG wafer and applying a magnetic ®eld B 6 parallel to the 2DEG plane. We show that the amplitude of the magnetic modulation can be varied by rotating B 6 with respect to the grating, independent of the perpendicular ®eld B _ used for the measurement of magnetoresistance. With decreasing magnetic modulation amplitude, the mag- netoresistance oscillation loses its amplitude without shifting the phase, until peak-to-valley inversion takes place. This demonstrates that the magnetic modulation thus produced is spatially out-of-phase with the small residual electrostatic potential modulation inevitably brought about by the grating. # 1998 Elsevier Science Ltd. All rights reserved 1. INTRODUCTION Two-dimensional electron gas (2DEG) with weak one-dimensional periodic modulation of electro- static potential and/or magnetic ®eld shows oscil- latory magnetoresistance periodic in 1/B (Weiss oscillation). The oscillation originates from the commensurability between the spatial modulation period a and the cyclotron radius R c = hk F /eB, where k F =  2pn e p represents the Fermi wavenumber with n e the electron density. For magnetic ®eld modulation, minima in resistivity occur at 2R c a  n  1 4 n  1, 2, 3, ...: 1 while for potential modulation, peaks and valleys interchange their roles and Equation (1) represents the positions of maxima. Experimentally, magnetic ®eld modulation has been realized by placing a micro-patterned grating of ferromagnet[1±3] or superconductor[4] on the surface of 2DEG wafer. However, the attachment of the grating is inevitably accompanied by electro- static potential modulation, mainly through the dierential thermal contraction between the metal and the semiconductor[5,6]. Therefore the devices fabricated for periodic magnetic modulation usually also contain periodic potential modulation. Recently, Skuras et al.[7] have shown that the strain-induced potential mainly arises from piezo- electric coupling and that the eect depends on the orientation of the stripe pattern with respect of the crystal axes of GaAs/AlGaAs. It has been shown that the strain-induced potential can be made mini- mal by orienting the stripe pattern to the [100] direction. The direction is applied to the study of 2DEG with a spatially varying magnetic ®eld by Nogaret et al.[8]. In the present paper, we study 2DEG with a fer- romagnetic metal (nickel) grating on top. Magnetic ®eld B 6 parallel to the 2DEG plane is employed to generate magnetic ®eld modulation. This allows us to manipulate the magnetic modulation indepen- dently from the cyclotron motion of 2DEG elec- trons which is aected only by the ®eld B _ perpendicular to the 2DEG plane; a distinct advan- tage over more conventional experimental con®gur- ation using only B _ [1±4]. We will show that the modulation amplitude can be controlled by the direction of B 6 with respect to the grating. In con- trast to the conventional con®guration, the mag- netic ®eld modulation and the remnant potential modulation are out-of-phase with each other, as will be shown. We also use [100] direction to mini- mize the potential modulation. 2. EXPERIMENTAL The device used in the present study was fabri- cated from a molecular beam epitaxy (MBE)-grown GaAs/AlGaAs single heterostructure with electron density n e =2.7  10 15 m 2 and mobility m = 60 m 2 V 1 s 1 at 1.5 K. The 2DEG plane resides at a depth 90 nm from the surface. A stan- Solid-State Electronics Vol. 42, No. 7±8, pp. 1121±1124, 1998 # 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0038-1101/98 $19.00 + 0.00 PII: S0038-1101(97)00313-4 *Also at CREST, Japan Science and Technology Corporation (JST). 1121