Origin of Structural Modulations in Ultrathin Fe Films on Cu(001)

Employing ab initio calculations we demonstrate that the complex structural modulations experimentally observed in ultrathin Fe films on Cu(001) originate from Fe bulk phases that arise under extreme deformations. Specifically, we show that the structural modulations correspond to the motifs observed when transforming fcc Fe to bcc Fe in the Pitsch orientation relationship [$(001{)}_{\mathrm{fcc}}||(1\overline{1}0{)}_{\mathrm{bcc}}$]. The observed structural equivalence between surface and unstable bulk structures naturally explains the experimentally reported magnetic and structural transitions when going from low (two to four MLs) to intermediate (four to ten MLs) film coverages.

Figure 1

(a) Schematic illustration of the $(1\times n),[n=n_1+n_2]$ modulations in ultrathin Fe films on Cu(001). In the current example, $n=3$ with $n_1=2$ and $n_2=1$. $\phi$ and $-\phi \prime$ are defined as shear angles relative to the primitive cell of fcc(001) Fe. The gold spheres refer to the Fe atoms on the surface and the open circles indicate the original positions of the Fe atoms on fcc(001) Fe. (b) Structural and magnetic features of three distinct regions observed in experiments. The green layer denotes the Cu substrate and the orange layers represent the Fe layers. The AFM Fe layers are shaded by light orange.

Figure 2

Minimum energy paths of the FM $\mathrm{fcc}\to \mathrm{bcc}$ Fe transition in the Pitsch OR. The reaction coordinate is normalized to 1 with images equally distributed along the path. The orthorhombic unit cells (12 atoms) for fcc, bcc, and MS1 are shown as insets. The atoms are visualized by gold spheres and shaded based on the depth of the atoms in the $c$ direction. The light blue arrows show the displacements of Fe atoms to transform from fcc Fe to MS1. The resulting modulation is sketched by the light blue dashed line.

Figure 3

Top view of the various surface structures: (a) fcc, (b) MS1, (c) MS2, and (d) bcc. The yellow shaded boxes with labels $F$ and $B_{\phi }$ (or $B_{-\phi \prime }$) indicate the fcc-like or bcc-like structural motifs in the modulated structures, respectively. The black dashed lines show the ($2\times 3$) unit cell as the reference.

Figure 4

(a1) Energy of ultrathin Fe films on Cu(001) as a function of coverage considering different structures and magnetic states (the layer magnetization is indicated by uparrow and downarrow). The energy is defined as the difference from the FM fcc film with an identical thickness normalized by the number of Fe atoms [57]. (a2) Experimental thickness dependence of the Kerr ellipticities (reproduced from Ref. [9]), clearly indicating three regions. The vertical dashed lines denote the critical thicknesses for transitions between two regions. The lower boundary of region III is reduced to eight MLs after ion bombardment [58, 59, 60]. (b1),(b2) Surface structures (top view) of the four-ML films in the FM state with MS1 and MS2, respectively. (b3),(b4) Side views of the FM films. (c1),(c2) The film structures in the AFM state. The gold spheres refer to Fe atoms, while the green ones represent Cu atoms. (d) Minimum energy path of the FM $\mathrm{MS}1\to \mathrm{FM}$ bcc Fe (representatively, five MLs) transition on Cu(001).