Multiply Twinned Morphologies of FePt and CoPt Nanoparticles

Based on large-scale density functional theory calculations we provide a systematic overview of the size dependence of the energetic order and magnetic properties of various morphologies of FePt and CoPt clusters with diameters of up to 2.5 nm. For FePt, ordered multiply twinned icosahedra and decahedra are more favorable than the $L{1}_0$ phase throughout the investigated size range. For CoPt, segregated morphologies predominate with considerably increased energy differences to the $L{1}_0$ structure. The compositional trends are traced back to differences between the morphologies in the partial electronic density of states associated with the $3d$ element.

Figure 1

Compositions of the investigated FePt and CoPt nanoclusters according to the compositions of cuboctahedra with perfect $L{1}_0$ order (marked by the circles).

Figure 2

Morphologies (a)–(i) of FePt nanoparticles and their corresponding energies as a function of the cluster size. The energy reference is defined by the $L{1}_0$ cuboctahedron (a). Only the structures with $N=561$ atoms (265 Fe and 296 Pt) are depicted. Dark blue spheres refer to Fe atoms, bright green spheres to Pt. Some of the icosahedral structures, (c),(g) and (i), are shown as cross sections, visualizing the inner arrangement of the atomic species. The broken (yellow) lines mark the interfaces of visible twins. In the diagram, cuboctahedra are represented by squares, icosahedra by circles and decahedra by pentagons. Shaded (green) symbols denote disordered isomers, hatched (blue) symbols ordered structures, thick and nested symbols core-shell icosahedra (red) as well as icosahedra with shellwise ordering tendencies (violet). The lines are guides to the eye.

Figure 3

Spin polarized DOS of selected ${\mathrm{Fe}}_{265}{\mathrm{Pt}}_{296}$ (${\mathrm{Co}}_{265}{\mathrm{Pt}}_{296}$) morphologies (a) and (c) according to Fig. 2. The thick lines denote to the total DOS, the thinner lines the element-specific contributions (full lines, dark blue for $\mathrm{Fe}/\mathrm{Co}$, bright green for Pt). Dashed lines describe the contributions of the 252 surface atoms.

Figure 4

Energies of CoPt clusters of various morphologies and sizes. The energy reference is again the $L{1}_0$ cuboctahedron. Symbols and lettering refer to the respective isomers in Fig. 2.

Figure 5

Magnetization of various FePt (upper panel) and CoPt (lower panel) morphologies as a function of the cluster size. Symbols as in Fig. 2, 4; the lines are guides to the eye.