Abstract
We have measured the magnetic field dependence of thermal activation energy in an insulating phase of a two-dimensional electron system formed in a Si inversion layer to investigate magnetic interactions among electrons. Experimental results are summarized as follows. (1) In a magnetic field parallel to the two-dimensional plane, increases linearly with the total strength of the magnetic field for while it takes a saturation value in the complementary high- region. (2) The normal component of the magnetic field causes a peculiar change in where two minima appear at and for . All the results are quantitatively explained by a model based on exchange interactions in a Wigner solid (WS) formed at . We assume that a three-particle ring exchange among localized electrons in the WS and a standard two-particle exchange between a thermally created mobile electron and a localized electron in the WS play dominant roles in determining the magnetic behavior of the system. At , the three-particle ring exchange interaction leads to the ferromagnetically ordered ground state of the WS. The antiferromagnetic two-particle exchange interaction favors magnetic states of a mobile electron different from the lowest spin-valley state of the localized electrons. Thermal activation, which involves a spin flip at low or a transition between the valley states which we call a “pseudo-spin-flip” at high explains the experimental result (1). Magnetic flux through the exchange path can change the nature of the ring exchange interaction due to the Aharonov-Bohm effect. A simple calculation using an exchange constant of , which is consistent with the WKB calculation of Roger [Phys. Rev. B 30, 6432 (1984)], for the three-electron ring exchange interaction reproduces the experimental result (2). Theoretical values of at magnetic-flux-induced antiferromagnetic phase transitions, which occur in the pseudospin system for large values of agree with the observed minima in .
- Received 27 August 1997
DOI:https://doi.org/10.1103/PhysRevB.57.9097
©1998 American Physical Society