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

96 5 Fe monolayers on hexagonal nonmagnetic substrates
E Q −E FM [meV/Fe]
200
100
0
−100
Fe/Ag(111)
Fe/Rh111)
Fe/Tc(0001)
Fe/Ru(0001)
2Q 3Q 2Q
−200
⎯Γ ⎯Κ
Q (2π/a)
⎯Μ ⎯Γ
Figure 5.13: (a) Total energy of spin spirals for 1 ML Fe/4d relative to Γ-point. Green
(Blue) solid squares (circles) connected by solid lines are our GGA results for Fe on Rh
(Tc) hexagonal substrates. Red (Black) solid diamonds (up-triangles) connected by solid
line are the GGA results of Fe on Ru (Ag) hexagonal substrates taken from ref. [57] ([30]).
Our calculated double- and multi-Q states GGA total energies for Fe on Ag, Rh and Tc
results are presented by stars. Ru double- and multi-Q states GGA results are taken from
ref. [57].
substrates. We can see from this comparison how the Fe magnetic ground state changes
by increasing the 4d-band filling, i. e. tuning the substrate from Tc through Ag. The
strength of the exchange interactions can also bee seen, with the negative nearest neighbors
interactions dominate for the early 4d-TMs substrates to stabilize the Néel ground state
on Tc and Ru, while at the positive neighbor interactions dominate and stabilize the FM
ground state for the Ag or Pd substrate. In between, i. e. only for the Rh substrate,
complex magnetism appears, due to the higher interactions, especially when J3 ≈−J1 as
illustrated in figure 5.14.
After inserting the Js into the phase diagram of the 2D Heisenberg model, shown in
figure 5.15, we can provide a complete picture of the substrates’ impact on the Fe exchange
coupling by including spin spiral calculations for an Fe ML on Tc(0001), Ru(0001),
Rh(111), and Ag(111). In the J1-J2 plane of the diagram, we see that the d-band filling
of the substrate drives the system along the line J2 ≈ 0fromaNéel configuration on Tc
and Ru to the FM solution on Rh and Ag. For small J1, we need to consider also the
phase diagrams in the J2-J3 plane showing the spin spiral minimum of Fe on Rh(111) in
the ΓKM-direction, Fig. 5.15(c), and the 120◦ Néel state of Tc(0001), Fig. 5.15(b).
For itinerant magnets such as iron, it is not a priori clear that the Heisenberg model,