The possibility of noncollinear magnetism of Fe along the Bain ͑body-centered to face-centered cubic structure͒ transformation is investigated through first-principles density-functional calculations. We find that a sizable portion of the tetragonal deformation phase space exhibits spin-spiral alignment of spins. Such complex magnetic behavior is predicted for overlayers of Fe on a number of substrates, for example, Cu 84 Al 16 , Cu, and possibly Ni. We also point out special cases with enhanced sensitivity of the theoretical predictions to the computational details, in particular on the use of different exchange-correlation functionals.The study of continuous transformations between highsymmetry states of solids can be used to characterize fundamental properties such as tensile strength or structure of overlayer thin films. 1 A special case is the so-called Bain transformation that connects body-centered ͑bcc͒ and facecentered ͑fcc͒ cubic lattices through a sequence of bodycentered tetragonal ͑bct͒ structures. The Bain transformation for Fe has attracted particular interest since it is associated with many different magnetic behaviors.The complex magnetic behavior of Fe upon structural deformations has been the subject of numerous firstprinciples density-functional calculations. Bagno, Jepsen, and Gunnarsson 2 showed that the inclusion of generalizedgradient corrections ͑GGA͒ in the exchange-correlation ͑XC͒ functional remedies the shortcomings of the local-density approximation ͑LDA͒ and renders bcc as the true ground state for Fe. This finding was subsequently confirmed in numerous other studies. [3][4][5][6][7] showed that the higherenergy fcc structure exhibits noncollinear magnetism, and Antropov et al. 9 studied its complex spin dynamics for different volumes. More recently, a number of works have unveiled an even richer magnetic behavior with enhanced magnetoanisotropy 10 and strong dependence of the spin alignment on the tetragonal deformation of bulk Fe and overlayers. 6,7,11,12 In the present Brief Report, we extend the scope of the previous theoretical studies on the Fe Bain transformation to include noncollinearity explicitly in the form of spin-spiral states. Our investigations reveal several points both on the merits of the methodology and also on the possible magnetic state of Fe thin films. We find that the energy profile for the Fe bcc-fcc transformation is highly sensitive not only to the use of LDA versus GGA, but even among different GGA functionals. We also find, that for the same XC functionals, our method gives results in good agreement with more computationally intensive methods. We are thus able to correlate our predictions for the structural and magnetic states of Fe overlayers with experimental observations and point out the possibility of spin-spiral structures for Fe grown on a number of substrates.The results of this work were obtained with a scalarrelativistic linear muffin-tin orbital ͑LMTO͒ code 13 in the tight-binding representation. The method utilizes the atomicsphere approxim...