Out-of-Plane Nesting Driven Spin Spiral in Ultrathin $\mathrm{Fe}/\mathrm{Cu}(001)$ Films

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

Figure 1

Characterization of the sample and determination of $k_z$. (a) Typical RHEED oscillations for $\mathrm{Fe}/\mathrm{Cu}(001)$ grown at RT. (b) and (c) LEED patterns for clean Cu(001) substrate and 8 ML EU $\mathrm{Fe}/\mathrm{Cu}(001)$ films. (d) The volume BZ of fcc Fe. The IP and OP regions probed in the present study are marked by blue and red lines, respectively. (e) EDCs along IP $\Gamma \mathrm{\text{−}}X$ ($k_x$) measured at $h\nu =430\mathrm{eV}$. (f) and (g) EDCs along OP $\Gamma \mathrm{\text{−}}X$ ($k_z$) measured using $h\nu =415–580$ and 740–940 eV. (h) The calculated $k_z$ positions from the photon energy dependence of EDCs. We used an inner potential and work function of 6 and 5 eV, respectively. The colors of the arcs corresponds to EDCs in (f) and (g). The EDCs plotted as thick lines correspond to momenta associated with the SS, as marked by arrows in Fig. 3e.

Figure 2

ARPES results of $\mathrm{Fe}(8\mathrm{ML})/\mathrm{Cu}(001)$ at 50 K. (a) and (d) IP band maps measured at $h\nu =430$ and 580 eV. The gray lines and points are the band calculation of fcc Fe for ${\mathit{q}}_2=(2\pi /a)(0.5,0,1.0)$ [4]. (b) and (e) Corresponding EDCs; numbers labeled on EDCs indicate the probed $k_x$ positions shown in (a) and (d). (c) and (f) MDCs at $E_F$.

Figure 3

In-plane and out-of-plane FSs of $\mathrm{Fe}(8\mathrm{ML})/\mathrm{Cu}(001)$ and autocorrelation analysis. (a) and (b) IP and OP FSs measured over $1/4$ of the BZ. (c) and (d) IP and OP FS crossings extracted from MDCs. FSs for full BZ were obtained by symmetrizing data from $1/4$ of BZ. The regions indicated by the red dashed lines are the nesting parts and were used for the ACA. (e) MDCs for $\Gamma \mathrm{\text{−}}X$ along $k_x$, $k_y$, and $k_z$. The $k$-cut positions are marked by black, red, and green lines in (c) and (d). $a=3.61$ and $3.55\AA$ are used for the IP and OP lattice parameters. The peaks observed only in the MDC along $k_z$ are indicated by the arrows and the corresponding EDCs are emphasized as thick lines in Figs. 1f, 1g. (f) AC map for the restricted regions in OP FS. (g) Line profile of AC map at $q_z=(2\pi /a)\times \pm 0.86$, indicated by red dashed lines in (f). (h) The comparison of the present result and early MOKE measurements: SS period ${\varphi }_{\mathrm{SS}}=2.3d$ (present result), ${\varphi }_{\mathrm{SS}}=2.6d$ [16] and ${\varphi }_{\mathrm{SS}}=2.7d$ [18].