Non-collinear Effects and Substrate-mediated Magnetic Interactions in Mn trimers on the GaN (000-1) Surface

As a pre-cursor to the formation of 2D MnGaN[1], Mn deposition on GaN(000-1) at 300 K can at first lead to a 3x3 trimer structure[2]. Collinear and non-collinear calculations based on density functional theory are carried out to elucidate the magnetic ordering of monomers, dimers and trimers of Mn on GaN(000-1) surface. We estimate the magnetic anisotropy energy (MAE), and we find that in the case of Mn dimers, the exchange magnetic coupling is the dominant interaction, and that the ground state has the Mn spins in-plane with the GaN(000-1) substrate. In the Mn trimer case, the magnetic ground state also has the Mn spins in-plane with the GaN surface, but the relative spin orientation within each trimer is non-collinear. By exploring the nature of the magnetic interaction among the Mn trimers, we find that the surface states of the substrate play a key role, involving a Ruderman-Kittel-Kasuya-Yosida (RKKY)-type interaction. To the best of our knowledge, this is the first report of an electron-mediated long-distance exchange coupling between localized magnetic moments on a GaN(000-1) surface.

[1] Y. Ma et al., Nano Letters, 18, 158 (2018)
[2] A. Chinchore, Phys Rev B 87, 165426 (2013)