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

106 6 Co MCA from monolayers to atomic chains
MCA [meV/3d]
|| [ μΒ ]
Δm l = m l −m l
T
2
1.5
1
0.5
0
−0.5
−1
−1.5
0
−0.04
−0.08
1 ML Fe/4d
1 ML Co/4d
Ru Rh Pd
Rh Ru Pd
Fe UML Fe
Co UML Co
2.7 2.71 2.72 2.73 2.74 2.75 2.76
In-plane a 0 [Å]
Figure 6.3: Top: Magneto-crystalline anisotropy (MCA) presented by solid circles (squares)
for 1 ML Co (Fe) on Ru(0001), Rh(111) and Pd(111) (left) compared with UML results
with different lattice constants in (right). Bottom: orbital moments anisotropy (OMA)
presented by open circles (squares) (bottom). Positive MCA means an out of plane and
negative MCA means in-plane magneto-crystalline anisotropy. All calculations assuming
FM order.
meV/Co atom, which is similar to the self consistent increase, from 0.12 to 0.25 meV/Co.
This shows the importance of relaxations for MCA calculations. Using FT, we also calculated
the Co contribution, by switching of the spin-orbit coupling in the Rh atoms. This
gives us an indication about the hybridization and crystal field effect of the substrate.
Also, from figure 6.4, we see again the Co MCA increased with relaxing the structure.
We also notice that the crystal field leads the out-of-plane MCA already for the unrelaxed
structure, but with increasing relaxation, it becomes even more dominant. The decrease
of the absolute value of MCA as compared to the UML agrees with the fact that electron
delocalization and crystal field effects compete with the intra-atomic Coulomb interactions,
responsible for Hund’s rules, causing a substantial or total decrease of S and quenching of
L[42].
Because Ir has similar nature like Rh but with large spin orbit coupling parameter,
we also calculated the relaxations and the magnetic order and MCA for Co monolayer
on Ir(111). We found that Co/Ir(111) relaxations with respect to the Ir calculated GGA
bulk lattice constant 3.86˚A, are very similar to what was obtained for Co/Rh(111) (see
fig. 6.1). We also found that Co prefers FM ground state by +137 meV/Co on Ir(111)
substrate, with Δd12 = −9.6% and Δd23 =+1.7% relaxations . Also we found that a Co
monolayer has an out-of-plane magnetization on the Ir(111) with an anisotropy of +0.40
(0.44) meV/Co using force theorem (self consistent). From the self consistent results, we
see that the MCA of Co/Rh(111) is about 0.20 meV/Co atom less than for Co/Ir(111).
This difference reflects the strength of Ir spin-orbit coupling parameter. If we compare the