Spin-orbit coupling and magnetic interactions in Si(111):{C,Si,Sn,Pb}

TL;DR

This study investigates the magnetic properties of adatom systems on Si(111) surfaces, revealing strong spin-orbit interactions, complex magnetic orders, and potential skyrmion states, using advanced computational models and simulations.

Contribution

The paper introduces detailed low-energy models incorporating spin-orbit coupling and correlations for Si(111) adatom systems, highlighting strong Dzyaloshinskii-Moriya interactions and complex magnetic structures.

Findings

Surface adatom systems are insulators with non-collinear magnetic order.

Strong Dzyaloshinskii-Moriya interactions are present, especially with Sn and Pb adatoms.

Complex spin spiral and skyrmion lattice states are predicted at low temperatures and high magnetic fields.

Abstract

We study the magnetic properties of the adatom systems on a semiconductor surface Si(111):\{C,Si,Sn,Pb\} - ($\sqrt{3} \times \sqrt{3}$). On the basis of all-electron density functional theory calculations we construct effective low-energy models taking into account spin-orbit coupling and electronic correlations. In the ground state the surface nanostructures are found to be insulators with the non-collinear 120$^{\circ}$ N\'eel (for C, Si, Sn monolayer coverages) and 120$^{\circ}$ row-wise (for Pb adatom) antiferromagnetic orderings. The corresponding spin Hamiltonians with anisotropic exchange interactions are derived by means of the superexchange theory and the calculated Dzyaloshinskii-Moriya interactions are revealed to be very strong and compatible with the isotropic exchange couplings in the systems with Sn and Pb adatoms. To simulate the excited magnetic states we solve the constructed spin models by means of the Monte Carlo method. At low temperatures and zero magnetic field we observe complex spin spiral patterns in Sn/Si(111) and Pb/Si(111). On this basis the formation of antiferromagnetic skyrmion lattice states in adatom $sp$ electron systems in strong magnetic fields is discussed.