Ab initio investigations of magnetic properties of ultrathin transition ...
Ab initio investigations of magnetic properties of ultrathin transition ...
Ab initio investigations of magnetic properties of ultrathin transition ...
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4.3 3d-Monolayers on Rh(111) Substrate: 69<br />
moments on square lattices. Additionally, the RW-AFM structure is not the only possible<br />
anti-ferro<strong>magnetic</strong> spin configuration on hexagonal substrates due to spin frustrations on<br />
triangular lattices as we will see later. Therefore, Rh(I) atoms will always have induced<br />
moments in case <strong>of</strong> any collinear AFM arrangement on hexagonal surfaces, although the<br />
are considerably small compared to those where induced ferro<strong>magnetic</strong>ally.<br />
Table 4.2: Results <strong>of</strong> optimized interlayer distance (in ˚A), obtained from FM (AFM) relaxations,<br />
between 3d monolayer and Rh(I) <strong>of</strong> Rh(001) and Rh(111) substrates.<br />
V Cr Mn Fe Co Ni<br />
Rh(001) 1.77 (1.77) 1.69 (1.81) 1.77 (1.73) 1.77 (1.67) 1.66 (1.65) 1.67 (1.65)<br />
Rh(111) 2.07 (-) - (2.09) 2.16 (2.08) 2.07 (2.02) 2.01 (2.01) 2.03 (2.03)<br />
The largest induced <strong>magnetic</strong> moments are caused by the Co and Ni monolayers on both<br />
Rh surfaces. This is due to their strong ferromagnetism and strongest inward relaxations<br />
with smallest interlayer distance from Rh(I) as shown in table 4.2. The induced moments<br />
from the FM calculations are larger for Rh(001) than for Rh(111) substrate due to the<br />
difference in the coordination number, as well as smaller 3d-Rh(I) interlayer distance. For<br />
the RW-AFM results, the Rh(I) atoms have almost zero <strong>magnetic</strong> moments induced by Cr<br />
or Mn, where they are noticeable for Fe, Co and Ni because <strong>of</strong> their large inward relaxations<br />
on Rh(111) (see fig. 4.15(right))<br />
4.3.2 Magnetic order:<br />
Collinear calculations were performed to calculate the total energy difference ΔE = EAFM−<br />
EFM between the RW-AFM and the FM relaxed configurations. The results are plotted<br />
in Fig.4.17 for the 3d TM monolayers on Rh(111)substrate, and compared to Rh(001)<br />
substrate results. For the Rh(111) substrate, we found that FM solution is more stable<br />
for Fe, Co and Ni, while it is c(2 × 2) AFM for Mn. As mentioned above, Cr (V) has<br />
no stable FM (RW-AFM) solution on Rh(111), therefore we are unable to calculate total<br />
energy difference. Except for Fe, the results <strong>of</strong> Rh(111) substrate show no difference in the<br />
3d <strong>magnetic</strong> order from what we obtained on the Rh(001) substrate.<br />
Using equation (3.11), a stronger tendency towards ferromagnetism is expected for large<br />
non<strong>magnetic</strong> LDOS at Fermi level, which means smaller band width (eq. 3.14) and then<br />
smaller coordination number (eq. 3.16), keeping the nearest neighbor distance constant.<br />
For different <strong>magnetic</strong> configurations <strong>of</strong> Fe on Rh substrate, we calculated the local density<br />
<strong>of</strong> states <strong>of</strong> the Fe monolayer on Rh(111) surface, and then compare the results to Fe density<br />
<strong>of</strong> states on Rh(001) as shown in figure 4.18. From the non<strong>magnetic</strong> calculations, we see<br />
that the Fe LDOS –at Fermi level– on Rh(001) is larger than Fe NM LDOS on Rh(111)<br />
substrate. These non<strong>magnetic</strong> results <strong>of</strong> LDOS agrees with the expectation that systems<br />
with large coordination number will have wider band width and then smaller non<strong>magnetic</strong><br />
density <strong>of</strong> states, which is the case for Fe/Rh(111) NM LDOS. But according to the Stoner<br />
model, Fe/Rh(001) should be more FM than on Rh(111).
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