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

5.2 Results of Fe monolayer on different hexagonal substrates from non-collinear cal. 97
E Q −E FM [meV/Fe]
20
10
0
−10
−20
J 2 M 2
J 1 M 2
J 3 M 2
Tc Ru Rh Pd Ag
Hexagonal substrates
Figure 5.14: Heisenberg exchange interaction parameters J1M 2 (green squares), J2M 2 (red
circles) and J3M 2 (blue diamonds) obtained from spin spiral calculations for Fe monolayer
on 4d hexagonal substrates. Open symbols with (?) indicate that these are expected
values. Ru (Ag) results are taken from Ref.[57] ([30]).
which relies on localized magnetic moments, can provide a good description. We have seen
this in the uudd � MΓ/2 � double-Q structure, where the substrate magnetic moments were
not equally induced in Fe/Rh(111). On the other hand Fe moments on Tc(0001) were also
not equal. If we compare our the double-Q results to Fe/Ru(0001) (from ref [57]), then
we might have an idea how to modify the Heisenberg model Hamiltonian, to be able to
include interaction terms for highly polarized substrates, like Tc, Ru and Rh, which then
will increase the accuracy of predicting the magnetic ground state.
In figure 5.16, we compare the energy differences between the single-Q and the double-
Q uudd � MΓ/2 � and uudd � 3ΓK/4 � for Fe monolayer on 4d hexagonal substrates. From
the uudd � 3ΓK/4 � results, we see that adding the substrate to the Fe ML changes almost
nothing in the energy differences between single- and the double-Q. The Fe moments were,
as expected, increasing with the 4d band filling from Tc through Ag.
The situation is different in case of uudd � MΓ/2 � configuration, where we see the change
of moments in Fe film for the case of Tc and Ru, while on Rh, Pd and Ag, there is no
variation of Fe moments in the 4-atoms unit cell. On the other hand, the 4d(I) induced
moments are strongly polarized for Rh(I) and Ru(I) layer atoms. Also, there is small (large)
difference between the spin spiral single- and the uudd double-QMΓ/2 Fe (4d(I)) moments
while it is larger for the 4d(I) atoms, as shown in table 5.6. The effect of these changes in
Fe and 4d(I) magnetic moments can be seen in the energy differences, where there is large
(≈30) meV/Fe energy gain due to the substrate in the middle of the 4d-series.
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