Interstitial-Induced Ferromagnetism in a Two-Dimensional Wigner Crystal

Kyung-Su Kim (김경수), Chaitanya Murthy, Akshat Pandey, and Steven A. Kivelson

Phys. Rev. Lett. 129, 227202 – Published 22 November 2022

Abstract

The two-dimensional Wigner crystal (WC) occurs in the strongly interacting regime ( $r_{s} ≫ 1$ ) 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 $r_{s}$ . Recently, Hossain et al. [Proc. Natl. Acad. Sci. U.S.A. 117, 32244 (2020)] reported the occurrence of a fully polarized ferromagnetic insulator at $r_{s} ≳ 35$ 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 $r_{s}$ 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.