Pseudospin Ferromagnetic Order in Bilayer Electron Systems

Koji Muraki, Tadashi Saku, and Yoshiro Hirayama
Physical Science Laboratory

@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).
@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 = 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.

[1] K. Muraki, N. Kumada, T. Saku, and Y. Hirayama, Jpn. J. Appl. Phys. 39 (2000) 2444.
[2] 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 = 3 and 4. (c) Activation energy as a function of B.