Magnetocrystalline anisotropy energy of Co and Fe adatoms on the (111) surfaces of Pd and Rh

Abstract

We performed a combined theoretical and experimental investigation of the orbital magnetism and magnetocrystalline anisotropy of isolated Co and Fe adatoms on Pd͑111͒ and Rh͑111͒. Theoretical calculations of the spin and orbital moments are based on ab initio spin-polarized density-functional theory ͑DFT͒ including a self-consistent treatment of spin-orbit coupling. The calculations use a slab model to represent the adsorbate/ substrate complex and allow for a complete structural relaxation leading to a strong inward displacement of the adatom and modest vertical and lateral relaxations in the substrate atoms. Compared to an idealized geometry where the atoms are kept on bulk lattice positions up to the surface, relaxation leads to a much stronger adatom/ligand hybridization. This is also reflected in the results for orbital moments and magnetocrystalline anisotropy energy ͑MAE͒. The enhanced hybridization leads to strong quenching of the adatom orbital moments but also to the formation of large induced spin and orbital moments in the substrate. As a consequence, we find that the substrate contribution to the MAE is much more important than estimated before on the basis of studies using an idealized geometry. We also find the surprising result that the MAE strongly depends on the adsorption site. The magnitude and even the sign of the MAE change for adatoms on face-centered cubic with respect to the ones on hexagonal close-packed hollow sites on the ͑111͒ surface. The dependence of the MAE on the combination of adatom and substrate has been analyzed in terms of the electronic structure, leading to a sound physical picture of the origin of the MAE. A fundamental problem, however, is the correct prediction of the size of the orbital moments of the adatoms. We suggest that this problem can be solved only via post-DFT corrections introducing an orbital dependence of the exchange potential. The theoretical results are compared to site-averaged, element-specific x-ray magnetic circular dichroism ͑XMCD͒ measurements. Lowtemperature XMCD spectra and magnetization curves reveal weak out-of-plane anisotropy for Fe adatoms on both substrates. Interestingly, Co adatoms on Rh͑111͒ present in-plane anisotropy with MAE of about −0.6 meV, contrary to the known out-of-plane anisotropy of Co on Pd͑111͒ and Pt͑111͒. The orbital to spin magnetic-moment ratio measured by XMCD shows that the Co adatoms present much stronger orbital magnetization components compared to Fe. The connection between orbital moments and MAE is discussed at the theoretical level including the contribution of the induced substrate magnetization.

Multiplet features and magnetic properties of Fe on Cu(111): From single atoms to small clusters

“…At normal incidence, the ratio μ L /μ S+7D is 0.30, more than twice the value of 0.12 obtained for Fe/Pd(111), and twice the one of Fe/Rh(111) (0.15) [12], confirming the reduced hybridization of the present system. The sum rule gives the spin moment together with the spin dipole moment.…”

“…Fe atoms on alkali-metal surfaces exhibit multiplet structures in photoemission spectra, with the degree of atomiclike behavior depending on the chosen substrate [9]. On the other hand, on the surfaces of 5d and 4d elements, such as Pt(111) [10,11], Rh(111), and Pd(111) [12], Fe atoms are known to be strongly hybridized. Cu(111) has an s-like density of states at the Fermi energy, bringing it close to alkali-metal surfaces, but at the same time is a 3d metal, thus it is not trivial to say whether a strong or a weak degree of hybridization is expected.…”

Magnetocrystalline anisotropy of FePt: A detailed view

“…For pure Fe monolayers the magnetic force theorem was shown to be valid to a high accuracy [65,66]. However, there are indications that this may no longer be true for systems with normally non-magnetic atoms with large induced moments and strong SOC [10,67] …”

4f occupancy and magnetism of rare-earth atoms adsorbed on metal substrates

“…Starting with the discovery of giant magnetic anisotropy energy (MAE) in single Co atoms on Pt(111) [1], the understanding of the magnetism of single adatoms has evolved rapidly. The most studied elements having been transition metals (TM) [2][3][4][5][6][7][8][9][10], the attention is now moving to rare-earth (RE) elements [11][12][13][14][15][16], culminating in the discovery of magnetic stability in single Ho atoms on MgO(100) thin films [17] and in single Dy atoms on graphene on Ir(111) [18].…”