Electronic and lattice instability and its relaxation mechanism in Pt-Co interfaces

Lattice instabilities of bimetallic Pt-Co interfaces have been examined within density functional theory. We discovered that the lattice instability and electron instability in momentum space were strongly correlated on bimetallic interfaces. The lattice instability of the Pt-Co interface was illustrated by Fermi surface nesting in two dimensions, and the nesting vector along the (110) direction in electron momentum space has been identified. The predicted reconstruction-induced Pt diffusion trend was in excellent agreement with previously obtained experimental findings.

Figure 1

(a) Phonon density of states of 1–4-ML Co(111) on 6-ML Pt(111) substrates. The negative (imaginary) frequency parts are marked in blue. (b) Phonon dispersion relation of 2-ML Co/6-ML Pt(111). The first Brillouin zone of a hexagonal lattice is shown. (c) Phonon dispersion relation of 3-ML Co(111)/6-ML Pt(111). (d) Phonon dispersion relation of 4-ML Co(111)/6-ML Pt(111). (e) Projected PDOS of 4-ML Co(111)/6-ML Pt(111). The outermost cobalt layer was labeled as Co${}_1$. (f) Contour of the vibrational frequency of the softest mode along the q${}_x$-q${}_y$ plane in 4-ML Co(111)/6-ML Pt(111). b${}_x$ and b${}_y$ were the basis vectors of the reciprocal lattice.

Figure 2

(a) Fermi contour of 4-ML Co(111)/6-ML Pt(111) in a (1$\times$1) supercell. (b) Schematic diagram of the Fermi contour after shifting the origin. The Fermi surface nesting vectors are labeled q${}_1$ and q${}_2$. In (a) and (b), Fermi contours of $\alpha$ spin are shown. (c) Electronic band structure along P${}_1$ and P${}_2$ as labeled in (b). Both $\alpha$ spin (blue) and $\beta$ spin (red) are shown. (d) The soft mode corresponding to $\mathbf{q}=(0.5,0.5)$ is shown. The arrows illustrate the atomic displacement of the topmost Co layer. (e) Profile of structural transformation of 4-ML Co(111)/6-ML Pt(111) from (111) to (100) faces at 300 K. Pt and Co atoms are shown by blue and yellow, respectively. (f) Electronic density of states of $\alpha$ electrons for Co(111) and Co(100) overlayers. (g) Electronic density of states of $\beta$ electrons for Co(111) and Co(100) overlayers. In (f) and (g), the unit of EDOS is in states/eV/cell, and the energy is relative to the Fermi energy.

Figure 3

Projected electronic density of states (EDOS) of the first (or topmost, blue), second (red), third (orange), and fourth (cyan) layer of the 4-ML Co/6-ML Pt(111) sample. (a) $\alpha$ spin of Co(111). (b) $\beta$ spin of Co(111). (c) $\alpha$ spin of Co(100). (d) $\beta$ spin of Co(100). In (a)–(d), the Fermi energies are represented by dotted lines.

Figure 4

(a) Intralayer radial distribution function of Pt-Pt (topmost, red) and Co-Co (blue) in 1-ML Co(111)/6-ML Pt(111) in a (2$\times$2) supercell. (b) Snapshot of the 1-ML Co(111)/6-ML Pt(111) at the 1000th time step. (c) Snapshot of the 1-ML Co(111)/6-ML Pt(111) at the 2000th time step. The periodic unit cell was labeled in a parallelogram in (b) and (c).

Figure 5

Potential energy profiles of Pt segregation. (a) 1-ML Co(111)/6-ML Pt(111); (b) 2-ML Co(111)/6-ML Pt(111) and 2-ML Co(100)/6-ML Pt(111); (c) 3-ML Co(100)/6-ML Pt(111).