Magnetic anisotropy and chirality of frustrated Cr nanostructures on Au(1 1 1)

By using a fully relativistic embedded cluster Green's function technique we investigated the magnetic anisotropy properties of four different compact Cr trimers (equilateral triangles) and Cr mono-layers deposited on the Au(1 1 1) surface in both fcc and hcp stackings. For all trimers the magnetic ground state was found to be a frustrated 120° Néel configuration. Applying global spin rotations to the magnetic ground state, predictions of an appropriate second order spin Hamiltonian were reproduced with high accuracy by first principles calculations. For the Cr trimers with adjacent Au atoms in similar geometry, we obtained similar values for the in-plane and out-of-plane anisotropy parameters, however, the Dzyaloshinskii-Moriya (DM) interactions appeared to differ remarkably. For two kinds of trimers we found an unconventional magnetic ground state showing 90° in-the-plane rotation with respect to the high symmetry directions. Due to higher symmetry, the in-plane anisotropy term was missing for the mono-layers and distinctly different DM interactions were obtained for the different stackings. The chiral degeneracy of the Néel configurations was lifted by an energy less than 2 meV for the trimers, while this value increased up to about 15 meV per 3 Cr atoms for the hcp packed mono-layer.