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

5.1 Results of Fe monolayer on different hexagonal substrates from non-collinear cal. 79
with the filling of the substrate’s d-band. The antiferromagnetic exchange interaction is
strong and important for Fe on most of these substrates except for Pd and Pt on which Fe
is clearly ferromagnetic. The antiferromagnetic interaction on a triangular lattice leads to
the frustration of magnetic interactions and is the origin of complex magnetic states. Fe on
Re or Tc exhibits strong antiferromagnetic interactions as shown by the large energy gain
when assuming a RW-AFM state and the true ground state could be a 120 ◦ -Néel state.
Due to the small energy difference between the FM and RW-AFM order for Fe on Os, Ru,
Rh and Ir many magnetic states have to be considered as possible ground states. Since Fe
MLs were studied on Ru(0001)[57], we focus our study on Rh(111) as model systems of
complex magnetism on a triangular lattice [27, 28]. For completeness we will also analyze
Fe monolayer on Tc(0001) substrate.
5.2 Results of Fe monolayer on different hexagonal
substrates from non-collinear calculations:
We concluded in the previous section (5.1.2), that the nearest-neighbor exchange interaction,
J1, in the Fe ML changes continuously from antiferro- to ferromagnetic with filling of
the substrate d-band. For an Fe ML on substrates such as Rh, Ru, Re or Ir, J1 is small, as
we will see in this section, and interactions beyond nearest-neighbors or higher-order spin
interactions can be relevant.
We also Study the so-called multi-Q states, which are a superposition of symmetry
equivalent spin spirals, that are degenerate in the Heisenberg model but can gain energy,
e.g., due to the presence of biquadratic or four-spin interactions [31]. The theory behind
that can be explained and understood by constructing a model Hamiltonian using the well
known classical Heisenberg model of atomic spins on local lattices sites (eq. 3.22). In this
section we will show the model Hamiltonian in case of triangular lattices, and then find out
the relationship between single and multi-Q states in terms of the higher order terms of
the biquadratic and 4-spin interactions. After wards we present our computational results
for spin spirals of Fe monolayer on Rh(111) and Tc(0001), and then compare them to
what have been done in case of Fe monolayer on different 4d-transition metals hexagonal
substrates.
5.2.1 Model Hamiltonian & Heisenberg model for 2D hexagonal
lattices:
For an antiferromagnetic material, the spin structures are frustrated if they are put on
a triangular lattice. In this case, the nearest neighbor spin interactions predict a 120 ◦
Néel ground state if one goes beyond that to see how the long range exchange interaction
influences the magnetic ground state, and more complex structures (spin-spirals) can be
found. The best way is to describe these systems in terms of exchange parameters using a
model Hamiltonian such as the classical Heisenberg model (eq. 3.22), where the quantum