  Epitaxial ultrathin Fe films on fcc Cu(001) exhibit a spin spiral (SS), in
contrast to the ferromagnetism of bulk bcc Fe. We study the in-plane and
out-of-plane Fermi surfaces (FSs) of the SS in 8 monolayer Fe/Cu(001) films
using energy dependent soft x-ray momentum-resolved photoemission spectroscopy.
We show that the SS originates in nested regions confined to out-of-plane FSs,
which are drastically modified compared to in-plane FSs. From precise
reciprocal space maps in successive zones, we obtain the associated real space
compressive strain of 1.5+-0.5% along c-axis. An autocorrelation analysis
quantifies the incommensurate ordering vector q=(2pi/a)(0,0,~0.86), favoring a
SS and consistent with magneto-optic Kerr effect experiments. The results
reveal the importance of in-plane and out-of-plane FS mapping for ultrathin
films.
