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

92 5 Fe monolayers on hexagonal nonmagnetic substrates
Fe LDOS [state/eV]
Rh(I) LDOS [state/eV]
4
2
0
−2
−4
2
1
0
−1
(a)
RW-AFM
FM
uudd(M/2)
-6 -4 -2 0 2
(b)
−2
−6 −4 −2 0 2
E-E [eV]
F
Figure 5.10: LDOS of the RW-AFM (gray shaded), FM (black line) and uudd � MΓ/2 � (red
line) state of (a) Fe monolayer and (b) Rh(I) layer.
the observed magnetic unit cell seems to be large and contains more than 4-atoms per
unit cell we constructed by superposition of two Q spiral points (see Fig. 5.5). Simple
trial is, if we make a super position of another two spiral points at QM/2 , we will have
16-atoms per unit cell, each group of four atoms have the same atomic spin and rotate
by π
2
with respect to each other as illustrated in figure 5.11, with coplanar vortex-like
magnetic structure. Using this large unit cell, we performed total energy calculations for
Fe UML, and found that the vortex-like structures has +66 meV/Fe atom energy above
the FM solution, where the Fe UML 4-atoms uudd � MΓ/2 � configuration has −7 meV/Fe
atom energy less than the the FM solution. This two dimensional possibility is not the
only one, but there are another two complex three dimensional possible spin structures can
be constructed from the same vortex-like Q-points. This was tested for only one Fe UML
due to the large computational effort, which makes it very difficult to perform calculations
of realistic systems. On the other hand, there are many possible AFM configurations that
might be constructed in real space on hexagonal lattices along [112], but not from a linear
combination of two Q-points on the high symmetry line as the uudd-states we studied. We
checked one possibility by calculating the total energy of an uuud-state along [112] and
found that it has lower energy than the collinear FM state of Fe/Rh(111) by −17 meV/Fe
atom, but remains higher than the uudd � MΓ/2 � ground state we found by +13 meV/Fe