  We present a new 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 non-collinear 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-Ta(x)W(1-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(2x2) antiferromagnet on the W surface and that at the
composition with about 20 % of Ta an incommensurate magnetic configuration
might exist.
