Stabilizing spin systems via symmetrically tailored RKKY interactions.

Spins of single atoms adsorbed on substrates are promising building blocks for spintronics and quantum computation schemes. To process spin information and for increased magnetic stability, these spins have to be coupled to arrays. For a single atom, a high symmetry of the environment increases its spin stability. However, little is known about the role of the symmetry of the magnetic couplings in the arrays. Here, we study arrays of atomic spins coupled via Ruderman-Kittel-Kasuya-Yosida interaction, focusing on Dzyaloshinskii-Moriya and symmetric anisotropic exchange. We show that the high spin stability of a trimer can be remotely detected by a nearby atom, and how the Dzyaloshinskii-Moriya interaction leads to its destabilization. Adding more nearby atoms further destabilizes the trimer, due to a non-local effective transverse anisotropy originating in the symmetric anisotropic exchange. This transverse anisotropy can be quenched for highly symmetric structures, where the spin lifetime of the array increases drastically.