Out-of-plane nesting of spin spiral in ultrathin Fe/Cu(001) films revealed by SX-ARPES

We investigate the origin of the spin spiral (SS) state in epitaxial ultrathin Fe films on Cu(001) using soft x-ray (SX)-ARPES. Fe/Cu(001) films exhibit a SS, in contrast to the ferromagnetic 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. It was found that the SS is due to nested regions confined to out-of-plane FSs, which are drastically modified compared to in-plane FSs. From precise reciprocal space maps along $k_z$ in successive Brillouin zones, we identify the associated real space compressive strain of 1.5$\pm$0.5\% along {\it c}-axis. An autocorrelation analysis quantified the incommensurate ordering vector $\mathbf{q}$=(2$\pi/a$) (0,0,$\sim$0.86), favoring a SS. These results are consistent with magneto-optic Kerr effect [1] and surface x-ray diffraction experiments [2] on the Fe/Cu(001) films, and suggest the importance of in-plane and out-of-plane FS mapping for ultrathin films. [1] D.~Qian, {\it et al.}, Phys.~Rev.~Lett.~{\bf 87}, 227204 (2001). [2] H.~L.~Meyerheim, {\it et al.}, Phys.~Rev.~B {\bf 71}, 035409 (2005).