Interstitial-Induced Ferromagnetism in a Two-Dimensional Wigner Crystal

The two-dimensional Wigner crystal (WC) occurs in the strongly interacting regime (rs >> 1) of the two-dimensional electron gas (2DEG). The magnetism of a pure WC is determined by tunneling processes that induce multispin ring-exchange interactions, resulting in fully polarized ferromagnetism for large enough rs. Recently, Hossain et al. [Proc. Natl. Acad. Sci. U.S.A. 117, 32244 (2020)] reported the occurrence of a fully polarized ferromagnetic insulator at rs greater than or similar to 35 in an AlAs quantum well, but at temperatures orders of magnitude larger than the predicted exchange energies for the pure WC. Here, we analyze the large rs dynamics of an interstitial defect in the WC, and show that it produces local ferromagnetism with much higher energy scales. Three hopping processes are dominant, which favor a large, fully polarized ferromagnetic polaron. Based on the above results, we speculate concerning the phenomenology of the magnetism near the metal-insulator transition of the 2DEG.