Ab initio investigations of magnetic properties of ultrathin transition ...

4.2 Results of 3d-Monolayers on Rh(001) Substrate 55
In our study, we determined the structural, electronic and magnetic properties of 3d
TM monolayers on Rh(001) by performing the first principles calculations using the full
potential linearized augmented plane wave (FLAPW) method in film geometry as implemented
in the (FLEUR) code (see chapter 2). The generalized-gradient approximation of
Perdew, Burke and Ernzerhof was applied (see section 1.5) leading to a Rh bulk lattice
constant of 3.819 ˚A which is only 0.4% larger than the experimental lattice constant of
3.804 ˚A[120]. The film was modeled by a symmetric seven layer Rh(001) slab covered by
a single 3d monolayer (see figure 2.2), using the calculated in-plane Rh lattice constant.
Relaxations were considered for the topmost two layers, i.e., the 3d ML and the interface
ML Rh(I). Both, the FM and the c(2×2) AFM configuration were relaxed. We used about
120 LAPW basis functions per atom with a muffin-tin radius of 1.22 ˚A for the 3d monolayer
atoms and 1.28 ˚A for the Rh atoms. The irreducible part of the two-dimensional
Brillouin zone (I2DBZ) was sampled with 78 k� points for the FM (AFM) configuration.
4.2.1 Relaxations and magnetic moments:
Here we present relaxations results of 1 ML 3d/Rh(001). The formula we used to calculate
the relaxation, Δdxy, between the layer i and j is:
Δdij = dij − do
do
(4.1)
where, dij is the interlayer distance and do is the ideal bulk interlayer distance of the
substrate. First we relaxed the top most monolayers of the clean Rh(001) surface. The
nonmagnetic relaxations of the interlayer spacing between the topmost monolayer and the
second layer, Δd12, and the second Rh interlayer spacing, Δd23, were −0.3% and +0.2%
respectively. Our prediction of top most two monolayers’ Rh(001) relaxations are in a very
good agreement compared to the experimental relaxations:Δd12 = +0.5±1.0 (−1.6±1.6)%
and Δd23 =0±1.5% (0±1.6)%[121]([122]).
The relaxations of the interlayer spacing between the 3d monolayer and the topmost
substrate layer, Δd12, and the first Rh interlayer spacing, Δd23, are presented in Figure 4.4
for both FM and AFM configurations.
For the FM configuration, we notice that the smallest inward relaxation of the 3d
monolayer occurs for Mn and Fe on Rh(001), where the magneto-volume effect (the atomic
volume dependence of the magnetic susceptibility) is strongest, i.e. the large magnetic
moments (see Fig. 4.5) of these TM compensate the strong inward relaxation – caused by
the larger Rh lattice constant – most efficiently. Of course there are also other factors
controlling the Δd12 that is, e.g., for V smaller than for Cr although the magnetic moment
of the latter is much larger that of vanadium. Here, also the fact that the bulk lattice
constant of V is 5% larger than that of Cr has to be considered. With the exception
of Ni, in all cases the equilibrium distance between the interface Rh layer and the bulk
Rh underneath increases with respect to the substrates bulk interlayer spacing. Moving
from left to right through the periodic table, we find that Δd23 decreases, supporting the
interpretation that the d-band filling controls these relaxations[123, 124]. This highlights