Pseudospin Ferromagnetic Order in Bilayer Electron Systems
Koji Muraki, Tadashi Saku, and Yoshiro Hirayama
Physical Science Laboratory
Ā@With advanced semiconductor growth techniques, it is possible to prepare two layers of two-dimensional electron gases separated by a thin tunnel barrier of a few nanometer thickness. Such systems, referred to as bilayer electron systems, allow one to tune the strengths of electron-electron interactions and tunneling between two layers, and exhibit novel physical properties that can not be achieved in a single layer. In particular, perpendicular magnetic fields enhance the electron-electron interactions by quenching the kinetic energy of electrons into discrete Landau levels. In this study, we reveal that the electron system exhibits a ferromagnetic order in particular situations when two Landau levels coincident at the Fermi energy (EF) are regarded as up and down states of virtual spin (pseudospin).
Ā@We have fabricated a novel GaAs/AlGaAs quantum-well (QW) structure having both front gate and n+-GaAs Back gate to control the total electron density, ns, and the potential symmetry independently [1, 2]. We employ a 40-nm wide single QW, which involves two occupied subbands with symmetric (S) and antisymmetric (A) wave functions and therefore behaves effectively like a bilayer [Fig. 1(a)]. When a perpendicular magnetic field, B, is applied, two sets of Landau levels originate from the two subbands, giving rise to various level crossings [Fig. 1(b)]. The energy diagram and the level crossings can be confirmed by measuring the magnetoresistance as a function of B and ns while keeping the QW potential symmetric [Fig. 1(c)]. Activation measurements reveal that, at Landau level filling factor É“ = 3 and 4, there is a finite energy gap even when two levels cross at EF [Fig. 2(a),(b),(c)]. This energy gap shows the existence of a ferromagnetic order in the electron system, which suppresses the pseudospin flip and hence a dissipative current. This is a new class of integer quantized Hall effect which relies solely on interactions.
 K. Muraki, N. Kumada, T. Saku, and Y. Hirayama, Jpn. J. Appl. Phys. 39 (2000) 2444.
 K. Muraki, T. Saku, and Y. Hirayama, Phys. Rev. Lett. 87 (2001) 196801.
Fig. 1. (a) calculated wave functions for the single QW. (b) Landau level energy diagram in a bilayer system. (c) Gray-scale plot of magnetoresistance Rxx at 50 mK. Dark regions represent small values of Rxx.
Fig. 2. (a) Rxx vs 1/T. (b) energy level diagram near the crossings for É“ = 3 and 4. (c) Activation energy as a function of B.