Magnetism in a Wigner solid and the Aharonov-Bohm effect: Experiment and theory

We have measured the magnetic field dependence of thermal activation energy E-A 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, E-A increases linearly with the total strength B-tot of the magnetic field for B(tot)less than or similar to 3 T, while it takes a saturation value in the complementary high-B-tot region. (2) The normal component B-perpendicular to of the magnetic field causes a peculiar change in E-A, where two minima appear at B(perpendicular to)approximate to 0.6N(s) phi(0) and B(perpendicular to)approximate to 1.1N(s) phi(0) for phi(0)=h/e. All the results are quantitatively explained by a model based on exchange interactions in a Wigner solid (WS) formed at r(s) approximate to 8. 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 B-perpendicular to=0, 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 hip at low B-tot or a transition between the valley states which we call a "pseudo-spin-flip" at high B-tot, 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 0.3 K, 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 Bperpendicular toNs-1/phi(0) at magnetic-flux-induced antiferromagnetic phase transitions, which occur in the pseudospin system for large values of B-tot, agree with the observed minima in E-A(B-perpendicular to). [S0163-1829(98)04315-X].