First-principles modeling of magnetic misfit interfaces

We investigate the structural and magnetic properties of interfaces with large lattice mismatch, choosing Pt/Co and Au/Co as prototypes. For our first-principles calculations, we reduce the lattice mismatch to 0.2% by constructing Moiré supercells. Our results show that the roughness and atomic density, and thus the magnetic properties, depend strongly on the substrate and thickness of the Co slab. An increasing thickness leads to the formation of a Co transition layer at the interface, especially for Pt/Co due to strong Pt-Co interaction. A Moiré supercell with a transition layer is found to reproduce the main experimental findings and thus turns out to be the appropriate model for simulating magnetic misfit interfaces.

Figure 1

Relationship between lattice mismatch and Moiré pattern. Red and blue circles indicate the lattice mismatch of the Au/Co and Pt/Co interfaces, respectively. Application of ($5\times 5$)Au/($6\times 6$)Co and ($7\times 7$)Pt/($8\times 8$)Co supercells reduces the lattice mismatch to 0.2%.

Figure 2

Dependence of the Co atomic density on the size of the $X$/Co supercell ($X=\mathrm{Au}$, Pt). The atomic density of $X$ is fixed. A horizontal line indicates the atomic density in bulk Co.

Figure 3

$X$/Co interfaces ($X$ $=$ Pt, Au): (a) Coherent model. The atomic densities of $X$ and Co are the same (atoms of the Co1 layer occupy hollow sites of the $X$1 layer). (b) Supercell containing $5\times 5$ $X$ and $6\times 6$ Co unit cells per layer; top views are shown in (c) and (d). (c) The interface Co1 layer has the same structure as the bulk (atoms of the Co1 layer occupy hollow sites of the Co2 layer). (d) The interface Co1 layer constitutes a transition layer between the substrate $X$1 layer and next Co2 layer (atoms of the Co1 layer occupy partially hollow sites of the $X$1 layer and partially hollow sites of the Co2 layer).

Figure 4

Dependence of the average binding energy of the Co atoms on the size of the supercell. For more details about the models, see Fig. 2. Big shaded triangles (diamonds) indicate the most stable models with one (four) Co layer(s).

Figure 5

Roughness of the Co surface for one and four Co layers on Au or Pt. The numbers in brackets are the maximal deviations of Co atoms from the average $z$ value. An asterisk indicates the presence of a transition layer.

Figure 6

Average magnetic moment per layer for the (a) Au/Co interface and (b) Pt/Co interface. Vertical black lines indicate the magnetization in the bulk compounds. An asterisk indicates the presence of a transition layer. Au1, Pt1, and Co1 are the interface layers.