Ground-state magnetic properties ofCoNclusters on Pd(111): Spin moments, orbital moments, and magnetic anisotropy

Abstract

The ground-state spin moments $〈{S}_{z}〉,$ orbital moments $〈{L}_{z}〉,$ and magnetic anisotropy energy (MAE) of ${\mathrm{Co}}_{N}$ clusters deposited on the Pd(111) surface are determined in the framework of a self-consistent, real-space tight-binding method. Two-dimensional ${\mathrm{Co}}_{N}/\mathrm{Pd}(111)$ with $N<~13$ show remarkably large total magnetic moments per Co atom ${M}_{z}=(2〈{S}_{z}〉+〈{L}_{z}〉)/N=(2.4--2.7){\ensuremath{\mu}}_{B},$ which are the result of three physically distinct effects. The first and leading contribution comes, as expected, from the local spin moments $〈{S}_{\mathrm{iz}}〉$ at the Co atoms $i=1\ensuremath{-}N$ $[2〈{S}_{\mathrm{iz}}{〉}_{\mathrm{Co}}\ensuremath{\simeq}1.7{\ensuremath{\mu}}_{B}].$ Second, significant spin moments are induced at the Pd atoms $i>N$ close to the Co-Pd interface, which amount to about 20% of ${M}_{z}$ $[2〈{S}_{\mathrm{iz}}{〉}_{\mathrm{Pd}}=(0.2--0.3){\ensuremath{\mu}}_{B}].$ Finally, remarkably enhanced orbital magnetic moments $〈{L}_{\mathrm{iz}}〉$ are found that are responsible for approximately 20% of ${M}_{z}.$ In the case of Co atoms, $〈{L}_{\mathrm{iz}}{〉}_{\mathrm{Co}}\ensuremath{\simeq}(0.3--0.5){\ensuremath{\mu}}_{\mathrm{B}}$ is almost a factor of 3 larger than the Co-bulk orbital moment, while in Pd atoms $〈{L}_{\mathrm{iz}}{〉}_{\mathrm{Pd}}=(0.02--0.04){\ensuremath{\mu}}_{\mathrm{B}}$ represents about 10% of the total local moment ${\ensuremath{\mu}}_{\mathrm{iz}}=2〈{S}_{\mathrm{iz}}〉+〈{L}_{\mathrm{iz}}〉.$ The dependence of the orbital moments on the orientation of the magnetization with respect to the cluster structure is quantified. These results and the associated MAEs are analyzed from a local point of view. One- and two-dimensional (2D) ${\mathrm{Co}}_{N}$ are considered in order to investigate the structural dependence of the magnetic behavior. The role of the cluster-surface interactions is discussed by comparison with free cluster calculations. In particular, we observe that the lowest-energy magnetization direction (easy axis) changes from in-plane to off-plane upon deposition of 2D ${\mathrm{Co}}_{N}$ on Pd(111). Cluster-substrate hybridizations are therefore crucial for the magnetoanisotropic behavior of magnetic islands deposited on metallic substrates.