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

5.1 Results of Fe monolayer on different hexagonal substrates from collinear cal. 75
on Rh(111). In this section we present a theoretical comparison of magnetic properties of
Fe monolayer on different 4d hexagonal substrates. Since we have Fe results on Pd, Rh
and Tc, we will add to our comparison the Ru results obtained in reference [57].
The electronic and magnetic properties were determined based on density-functional
theory. Calculations have been carried out in the generalized gradient approximation
(GGA) to the exchange-correlation functional [138] using the full-potential linearized augmented
plane wave (FLAPW) method, as implemented in the fleur code [50, 56]. All
calculations have been performed in the scalar-relativistic approximation, i.e. neglecting
the effect of spin-orbit coupling. The collinear magnetic states were investigated in systems
modeled by 7 layers of 4d-TM substrate with hcp or fcc stacking covered by a pseudomorphic
Fe monolayer on each side of the films. We have used the theoretical lattice constants
obtained by GGA calculations (see table5.1), which are in good agreement to the the experimental
values. Both, the FM and the RW-AFM configurations were relaxed. We used
about 120 LAPW basis functions per atom with a muffin-tin radius of 1.22 ˚Afor the Fe
monolayer atoms and 1.28 ˚A for the 4d substrate atoms. we used 2.17˚A value for the cutoff
of the plane wave expansion of wavefunctions. The irreducible part of the two-dimensional
Brillouin zone (I2DBZ) was sampled with 36 k�-points to determine the relaxations and
the energy differences between the different magnetic configurations with the same two
atomic unit cell.
5.1.1 Structural optimization & relaxations:
The relaxations and magnetic moments of Fe monolayers on 4d-TM substrate are shown
in Table 5.1. All relaxations are calculated using equation (4.1). We relaxed the topmost,
3d and 4d(I) layers. The Fe stacking on the 4d substrate was checked. Fe prefers to be
fcc on Pd and hcp stacking on Rh(111) and Tc(111). It also prefers hcp stacking with
Ru(0001) [57]. It is important to mention that relaxing only the top most monolayer is not
enough to have good understanding of what affects the interlayer 3d-4d relaxed distance.
For example, in reference [57], relaxations were done only for the Fe monolayer, while the
substrates interface layer Ru(I) was not relaxed. Having the same relaxations conditions,
we tested Fe on Ru(0001) FM relaxations including the Ru(I) layer. We found that the
optimized Fe-Ru(I) interlayer distance, d12, is 2.08 ˚A instead of 2.18 ˚A in ref. [57]. This
means that, we cannot have quantitatively predict of what affects the 3d-4d interlayer
optimized distance, which is very helpful to trace the magnetic interactions between the
3d and 4d monolayer. The FM relaxations of Fe monolayer on 4d hexagonal substrate
obtained from collinear calculations are shown in table 5.1. We don’t show here the AFM
relaxations, because of frustrations on triangular lattices which makes it difficult to predict
which the optimum collinear AFM arrangement for our comparison.
From table (5.1), we see that the relaxations of the 3d monolayer were all directed
inwards to the substrate. This is due to the large lattice mismatch between the 3d and
4d bulk lattice constants. From the interlayer distance, d12, between the 3d monolayer
and the 4d interface layer, one can explain the origin of the relaxations of 3d on different
substrates. Mainly, three major factors that affect Fe interlayer distance on the substrate