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

5.2 Results of Fe monolayer on different hexagonal substrates from non-collinear cal. 85
J (in units of J )
2 1
J /|J |
2 1
1
Néel FM
0
RW-AFM
-1
-2
1
(a)
(b) (c)
J < 0
SS �-M
0 2
J 1 (arb. units)
1
J > 0
1
Néel
FM
0
�-K-M
�-K-M
-1 �-M RW-AFM �-M
-1 0
J 3 /|J 1|
1 -1 0
J 3 /|J 1|
1
Figure 5.6: Phase diagrams of the classical Heisenberg model for a 2D hexagonal lattice
for states on the high symmetry lines. (a) J1-J2 plane for J3 =0. J2-J3 plane for (b)
J1 > 0 and (c) J1 < 0. White circles are the exchange interaction parameters obtained
from fitting the spin spiral curve using eq. (A-20) of free standing Mn/Fe monolayer within
the VCA. This plot was calculated by B. Hardrat at University of Hamburg.
of fictitious ”virtual” atoms that interpolate between the nuclear number Z of the atoms
in the parent compounds, which is possible if Z differs by ±1. This technique is widely
used in band-structure calculations. By using this approximation, one can calculate the
spin spiral curve for free standing monolayer of Mn, and then do a fractional increase
of Mn atomic number to reach Fe atomic number. This means that the energy spin
spiral curve is calculated as if we have an Fe1xMnx alloy, with x Mn concentration, we
can predict all possible magnetic ground states if we tune Mn concentration in the alloy.
I. e. we increase the 3d-band filling. This can also be applied if we have a pure magnetic
monolayer supported by a tunable substrate, like alloys of different substrates of different
atomic numbers like 4d- or5d-transition metals. From the energy spin spiral curve of free
standing Mn/Fe layer using the VCA, the exchange interaction parameters, J1, J2 and J3,
are calculated by fitting the energy dispersion curve to equation A-20. Using the values
of J, we see that pure Mn ML will have a RW-AFM ground state, while Fe ML prefers
FM ground state. We can see that Mn ML might have complex non-collinear magnetic