Exchange energy of the ferromagnetic electronic ground-state in a monolayer semiconductor

Abstract

Mobile electrons in the semiconductor monolayer-MoS${}_2$ form a ferromagnetic state at low temperature. The Fermi sea consists of two circles, one at the $K$-point, the other at the $\tilde{K}$-point, both with the same spin. Here, we present an optical experiment on gated MoS${}_2$ at low electron-density in which excitons are injected with known spin and valley quantum numbers. The resulting trions are identified using a model which accounts for the injection process, the formation of antisymmetrized trion states, electron-hole scattering from one valley to the other, and recombination. The results are consistent with a complete spin polarization. From the splittings between different trion states, we measure the exchange energy, $\Sigma$, the energy required to flip a single spin within the ferromagnetic state, as well as the intervalley Coulomb exchange energy, $J$. We determine $\Sigma =11.2$meV and $J=5$meV at $n=1.5\times 10^{12}$cm${}^{-2}$, and find that $J$ depends strongly on the electron density, $n$.

13 pages, 11 figures