Magnetic phase stability of monolayers: Fe on aTaxW1−x(001)random alloy as a case study

We present an approach to study the magnetic phase stability of magnetic overlayers on nonmagnetic substrates. The exchange integrals among magnetic atoms in the overlayer are estimated in the framework of the adiabatic approximation and used to construct the effective classical two-dimensional Heisenberg Hamiltonian. Its stability is then studied with respect to a large number of collinear and noncollinear magnetic arrangements which include, as special cases, not only ferromagnetic and various antiferromagnetic configurations but also possible incommensurate spin-spiral structures. This allows us to investigate a broader class of systems than a conventional total energy search based on few, subjectively chosen configurations. As a case study we consider the Fe monolayer on the random nonmagnetic bcc-${\text{Ta}}_{x}{\text{W}}_{1\ensuremath{-}x}(001)$ surface which was studied recently by a conventional approach. We have found a crossover of the ground state of the Fe monolayer from the ferromagnet on the Ta surface to the $c(2\ifmmode\times\else\texttimes\fi{}2)$ antiferromagnet on the W surface and that at the composition with about 20% of Ta an incommensurate magnetic configuration might exist.