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We use first-principles calculations based on density functional theory tostudy how the magnetic properties of an Fe monolayer on a W(001) surface --exhibiting a $c(2 \times 2)$ antiferromagnetic ground state -- can be modifiedby an additional 4d transition-metal overlayer. To obtain an overview of howthe 4d-band filling influences the exchange interactions in the Fe layer wehave calculated the energy dispersion of spin spirals for 4d/Fe/2W unsupportedquadlayers, in which the W(001)substrate is represented by only two atomiclayers. Hybridization with the overlayer leads to a reduced ferromagneticnearest-neighbor exchange interaction and the next-nearest neighbor exchangegains in strength. Surprisingly, we find that the $c(2 \times 2)$antiferromagnetic state is unfavorable for all systems with a 4d overlayer. For4d overlayers from the beginning (Nb) or end (Pd) of the series we find aferromagnetic ground state. As one moves to the center of the series there is atransition via a spin spiral (Mo, Rh) to a $p (2 \times 1)$ antiferromagneticground state (Tc, Ru). We have studied the Mo, Ru, and Pd overlayer onFe/W(001) representing the surface by a sufficiently large number of W layersto obtain bulk like properties in its center. The energy dispersion of spinspirals show qualitatively the same results as those from the 4\textit{d}/Fe/2Wquadlayers. The Dzyaloshinskii-Moriya interaction calculated upon includingspin-orbit coupling shows significant strength and considerable frustrationeffects. The calculated magnetocrystalline anisotropy energy is large as well.All 4d/Fe/W(001) films are potential candidates for complex non-collinear spinstructures.

Tuning exchange interactions in antiferromagnetic Fe/W(001) by 4d transition-metal overlayers