J.P. Eisenstein, Caltech, DMR If it were not for the Coulomb repulsion between electrons, iron would not be ferromagnetic. It would instead be a paramagnet with a small magnetic susceptibility. In contrast, a two dimensional electron gas in a large magnetic field would be ferromagnetic even in the total absence of Coulomb interactions. This fundamental difference is a direct result of the quantizaion of the kinetic energy of 2D electrons into a sequence of discrete Landau levels. However, interactions can in fact never be ignored in this circumstance. Sharp Landau levels are qualitatively affected by even the weakest of interactions. As a result, the ground state spin polarization ranges from 0 to 1 depending on the precise filling fraction of the Landau level. In this work we have studied a new kind of ferromagnetic transition. By choosing the right magnetic field the total number of 2D electrons in a GaAs/AlGaAs heterostructure can be made to fill exactly one-half of the states within the lowest Landau level. In the absence of interactions this would be a ferromagnetic situation. Instead, we find that at low electron density the system is only partially polarized. At higher density (and thus magnetic fields) a transition to full polarization occurs. This phenomenon must be due to Coulomb interactions within the 2D system. Our results, gleaned from a novel NMR technique, suggest that this transition may be accompanied by phase separation within the 2D gas. Ferromagnetism in the Half-Filled Landau Level Observation of the ferromagnetic transition in a half-filled Landau level at 45 and 100 mK. Upper plot shows the observed changes in resistance R xx of the 2D gas resulting from small, NMR induced, changes of the Zeeman energy E Z. The vanishing of this parameter at high fields is due to the onset of complete spin polarization. Lower plot shows the nuclear spin lattice relaxation time, T 1. As the electron gas becomes fully polarized T 1 rises rapidly.

Graduate Students: Lisa Tracy Collaborators: Loren Pfeiffer and Ken West, Bell Labs J.P. Eisenstein, Caltech, DMR Related Publications: “Resistively-Detected NMR in a Two-Dimensional Electron System near = 1: Clues to the Origin of the Dispersive Lineshape”, L.A. Tracy, et al., Phys. Rev. B 73, (R) (2006). “Spin Transition in a Strongly Correlated Bilayer Two-Dimensional Electron System”, I.B. Spielman, et al., Physical Review Letters 94, (2005). “Spin Transition in the Half-Filled Landau Level”, L.A. Tracy, et al., in preparation. Selected Invited Presentations: “Spin Physics in 2DES's Probed by NMR Techniques ”, Gordon Conference on Correlated Electron Systems, June 2006 (Tracy). “Correlated 2D Electrons at High Magnetic Field: Spin and Pseudo- Spin”, 17th Int'l Conf. on High Magnetic Fields in Semiconductor Physics, Würzburg, Germany; August 2006 (Eisenstein). Ferromagnetism in the Half-Filled Landau Level B ~ 7 T H 1 ~ 1  T Schematic illustration of GaAs/AlGaAs Hall bar containing a 2D electron gas and surrounded by a NMR coil. Radio frequency magnetic fields H 1 created by this coil are tuned to the nuclear Larmor frequency of 75 As. Via the hyperfine interaction, the RF-induced nuclear polarization changes alter the electronic Zeeman energy. This in turn alters the resistivity of the 2D electron gas and is readily detected.