Effect of exchange interaction on the spin-polarized bound states on metal surfaces: Ab initio study

The exchange interaction between magnetic adatoms on a metal surface is known to significantly influence the magnetic characteristics of the system. In present study we analyze the effect of the exchange interaction on the spin-dependent localization of the surface state. Our ab initio study of spin-polarized bound states arising at pairs of magnetic adatoms shows that both the position and the shape of the bound-state peak are strongly affected by the spin coupling in the system. Moreover we demonstrate that the spin splitting of the bound-state peak can serve as a suitable tool for probing the exchange coupling in the system. By the example of Co pairs on a Cu(111) surface at different interatomic separations, we demonstrate that the presence of the spin splitting of the bound-state peak is a signature of a ferromagnetic coupling while its absence signifies an antiferromagnetic configuration of the system spins. Also, the amount of splitting can be regarded as a measure of the interaction’s strength.

Figure 1

(Color online) The geometry considered in calculations: (a) an adatom and (b) a dimer of Co adsorbed on a Cu(111) surface. The majority (red solid) and minority (blue dashed) LDOSs above (c) a single Co adatom. The gray-filled curve represents a surface state of a clean Cu(111) surface.

Figure 2

(Color online) The majority (red solid) and minority (blue dashed) LDOSs at a single Co adatom. The peaks in both spin channels are mainly of a $d$ character.

Figure 3

(Color online) The majority (red solid) and minority (blue dashed) LDOSs above the middle of a compact Co dimer $\left(d=2.55\text{Å}\right)$, aligned along the $\left[\overline{1}10\right]$ direction of a Cu(111) surface, in (a) ferromagnetic and (b) antiferromagnetic configurations. The gray curve shows the surface state above a clean Cu(111) surface. It has been scaled by a factor of 2 for clarity.

Figure 4

(Color online) The majority (red solid) and minority (blue dashed) LDOSs at one of the atoms in a compact Co dimer $\left(d=2.55\text{Å}\right)$, aligned along the $\left[\overline{1}10\right]$ direction of a Cu(111) surface, in (a) ferromagnetic and (b) antiferromagnetic configurations. The peaks in the LDOS are mainly of the $d$ character.

Figure 5

(Color online) The majority (red solid) and minority (blue dashed) LDOSs above the middle of Co dimers at different separations (right panel), and the corresponding configurations, interatomic separations, and exchange coupling energies (left panel). LDOSs have been scaled for clarity. The scaling factors are given near each curve.

Figure 6

(Color online) (a) The position of the bound state of Co dimers as a function of the interatomic separation for antiferromagnetic (dashed line, squares) and ferromagnetic (spin-up–solid red curve with triangles pointing up, spin-down–solid blue, triangles pointing down) configurations. (b) The amount of spin splitting of the bound state above a ferromagnetically coupled dimer (solid curve, squares) and a dimer in the GS configuration (dashed, circles) versus the interatomic distance.

Figure 7

(Color online) The majority (red solid) and minority (blue dashed) LDOSs above the middle of compact [(a) and (b)] Fe and [(c) and (d)] Mn dimers $\left(d=2.55\text{Å}\right)$, aligned along the $\left[\overline{1}10\right]$ direction of a Cu(111) surface, in [(a) and (c)] ferromagnetic and [(b) and (d)] antiferromagnetic configurations.