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

2 INTRODUCTION
(ao =3.80 ˚A) is in between those of Cu and Ag and thus Rh serves as a potential substrate
to grow artificial phases of 3d transition-metal films such as fcc-Fe stabilized under tensile
strain or bcc-Co under compressive strain. The Rh(001) substrate provides favorable
growth conditions for transition-metal films despite a large lattice mismatch of fcc Fe or
Co and bcc Fe with Rh of about 6%, 8% and −7%, respectively. For example, no notable
intermixing has been encountered at the interface of Fe/Rh(001) during growth of Fe
films [19]. Epitaxial, pseudomorphic layer-by-layer growth of one and two layers of Co on
Rh(001) was reported by Begley et al. [20] and several groups [19, 21, 22, 23] have been able
to grow pseudopmorphically even thicker films of face-centered tetragonal Fe on Rh(001).
Hayashi et al. [22, 23] concluded on the basis of soft X-ray magnetic circular dichroism
(XMCD) experiments measured at room temperature that a monolayer and a bilayer of
Fe are not ferromagnetic and interpreted them as magnetically dead caused by the large
strain exerted in the interface of the thin film and the substrate. Hwang et al. [24] found
experimentally a suppression of the ferromagnetic order of Fe overlayers on the Rh(001)
surface, and he as well as Spisak et al. [25] predicted a c(2 × 2) AFM order for 1 ML Fe
on Rh(001) on the basis of DFT calculations.
Experimentally, the magnetic properties of FM monolayers can be investigated with
highly developed surface sensitive techniques, such as the spin-polarized scanning tunneling
microscope (SP-STM)[26]. A challenge is to study the ground state for complex magnetic
structures with atomic resolution such as Fe on W(001) [11] or even anti-ferromagnets
like Mn on hexagonal surfaces, due to the topological frustrations on triangular lattices.
A measure of the challenge can be estimated from the pioneering experimental study of
the magnetic state of a Fe monolayer on Ir(111) surface [27, 28], which revealed a very
complex ground state, and was approached theoretically to be described by a 15 atom unit
cell, a 7:8 mosaic structure with seven Fe atoms pointing in one quantization axis and eight
in the opposite one. The resolution of atomic-scale spin structures by the spin-polarized
scanning tunneling microscope was studied theoretically [29, 30] and followed by a new
theoretical prediction of a three-dimensional non-collinear ground state of a Mn monolayer
on the Cu(111) substrate, called 3Q-state [31]. Such non-collinear systems can be studied
by employing the classical Heisenberg model, where the atomic spins are considered to be
localized at the lattice sites and interact with each other by intersite exchange interaction
parameters obtained in part by density functional theory. These exchange interactions are
typically long-ranged as we deal here with metals and their Fermi surfaces. The general
solution of the classical Heisenberg model for a periodic system are spin-spirals, magnetic
moment of equal length on each site, rotating in spin-space by a constant angle from site
to site. Calculating the total energy of such spin-spiral states from first-principles can
be used to construct a model Hamiltonian with constant local spin moments, where the
exchange interaction parameters can be calculated by fitting the total energy dispersion
curve to this model Hamiltonian. Though, there are many possible applications for spinspiral
calculations, it was the discovery of a spiral ground state structure in fcc iron [32]
and 4f and 5f metals [33] that gave rise to many theoretical studies [34, 35].
Most likely the magnetic ground state can be found for spin-spiral wave vectors, which
lie at the high-symmetry lines of the two-dimensional Brillouin zone. High-symmetry