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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Chapter 5<br />
Fe monolayers on hexagonal<br />
non<strong>magnetic</strong> substrates<br />
Describing the <strong>magnetic</strong> order <strong>of</strong> the square lattices (001) monolayers, using Heisenberg<br />
model equation (3.22) up to the second nearest neighbor interaction (J1, J2), is relatively<br />
simple. As long as the nearest neighbor interaction is the dominating one, there are only two<br />
phases to be considered: the ferro<strong>magnetic</strong> p(1×1) structure (J1 > 0) the antiferro<strong>magnetic</strong><br />
c(2×2) superstructure (J1 < 0). If we describe the solution <strong>of</strong> the Heisenberg model as<br />
spin-spirals with a q�-vector from the first Brillouin zone, the c(2×2) structure corresponds<br />
to the M-point in the 2DBZ <strong>of</strong> the square lattice. If the next-nearest neighbor interaction<br />
is antiferro<strong>magnetic</strong>, J2 < 0, and sufficiently strong, |J1| < 2|J2|, then the ground state<br />
changes to be <strong>magnetic</strong> structure with a 2Dq� vector at the X-point in the 2DBZ. This<br />
means that an anti-ferro<strong>magnetic</strong> p(2×1) or p(1×2) structure (ferro<strong>magnetic</strong> rows <strong>of</strong> atoms<br />
along the [001] or [010] direction coupling antiferro<strong>magnetic</strong>ally from row to row) becomes<br />
the <strong>magnetic</strong> ground state.<br />
A recent theoretical study was preformed to predict the <strong>magnetic</strong> ground state <strong>of</strong> Fe<br />
monolayers on a TaxW1−x alloy if the substrate is tuned by changing the Ta concentration<br />
x[14]. Non-collinear <strong>magnetic</strong> structures at critical Ta concentration were predicted. This<br />
means that complex <strong>magnetic</strong> order can be obtained even in single monolayer (ML) <strong>magnetic</strong><br />
films on non-<strong>magnetic</strong> (001) substrates. Furthermore, recently a spin-spiral state was<br />
discovered for a Mn ML on W(110) [132] and for a Mn ML on W(001) [12], although the<br />
driving force in this case is not a Heisenberg-type interaction but rather Dzyaloshinskii-<br />
Moriya type exchange. As a result, one can control the <strong>magnetic</strong> order <strong>of</strong> 3d monolayer by<br />
tuning the substrate.<br />
By that, the investigation <strong>of</strong> the <strong>magnetic</strong> order on square lattices started from late<br />
(Ag, Pd) and ended with early (W) <strong>transition</strong> metals substrates as illustrated in figure<br />
(5.1). For the hcp elements there is no square lattices which could help to have a complete<br />
understanding <strong>of</strong> the <strong>magnetic</strong> order trend <strong>of</strong> 3d monolayers on non<strong>magnetic</strong> substrates.<br />
Our case <strong>of</strong> study focuses on Fe because it has intensively been studied theoretically and<br />
experimentally.<br />
This leads us to continue investigating the Fe <strong>magnetic</strong> ground state on hexagonal sub-<br />
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