Lattice Monte Carlo simulations of FePt nanoparticles: Influence of size, composition, and surface segregation on order-disorder phenomena

Order-disorder phenomena in FePt nanoparticles are investigated by lattice Monte Carlo computer simulations. The Metropolis algorithm is applied based on particle exchange and configurational energies that are calculated by an Ising Hamiltonian including nearest- and next-nearest-neighbor interactions. The adjustable parameters were determined from the bulk phase diagram and experiments on surface segregation of FePt thin films. By monitoring the long-range order parameter we study the influence of size, composition and surface segregation on the order-disorder transition. Our results reveal a distinct segregation behavior for nonstoichiometric compositions. Platinum atoms in excess exhibit a clear tendency for complete surface segregation on edge positions and (100) facets. Excess iron atoms, in contrast, tend to preferentially alloy in the bulk and on (100) facets. For a given particle size and variations in composition of $\pm 4\%$ in maximum, the transition temperature is lowered by less than $50\mathrm{K}$, but more pronounced for excess Fe than Pt. For a fixed composition and varying size, in contrast, the transition temperature is lowered by $40\text{to}380\mathrm{K}$ compared to the bulk value for particle diameters ranging from $8.5\text{to}2.5\mathrm{nm}$. Nevertheless, for temperatures below $1100\mathrm{K}$, the ordered phase is the thermodynamically stable phase for all particle sizes. The most pronounced effect on the ordering behavior is observed, if surface segregation tendencies are systematically modified. If one element is fully occupying the outer surface layer, we observe the formation of internal disorder and the formation of $L{1}_2$ domains. By increasing the concentration of the segregating element and thus readjusting the stoichiometric composition in the bulk, the order in the particles can be restored.

Figure 1

Illustration of antiphase boundaries of the $L{1}_0$ ordered phase: (a) conservative antiphase boundary, (b) and (c) nonconservative antiphase boundary. Black stripes denote Fe layers, gray stripes denote Pt layers.

Figure 2

Comparison of the phase diagram of our model (full circles) with the experimentally determined FePt phase diagram (dashed lines). The experimental phase diagram is plotted using data from Ref. 10.

Figure 3

Influence of the model parameter $h$ on the segregation of Pt at the (111) surface of an ${\mathrm{Fe}}_{20}{\mathrm{Pt}}_{80}$ alloy at $1200\mathrm{K}$.

Figure 4

Depth profile of the Pt concentration at the (111) surface of an ${\mathrm{Fe}}_{20}{\mathrm{Pt}}_{80}$ alloy at $1200\mathrm{K}$. Comparison of experiments with the results of our model for $h=-0.15\mathrm{eV}$.

Figure 5

Illustration of a completely $L{1}_0$ ordered regular truncated octahedron with 9201 atoms $(d=6.3\mathrm{nm})$.

Figure 6

Structure of particles with $d=7.0\mathrm{nm}$ (12 934 atoms) after simulation at $300\mathrm{K}$. The particle concentration varies from $+4\mathrm{at.}\%$ Fe to $+4\mathrm{at.}\%$ Pt relative to the concentration of an ideally ordered TO. Pt atoms are displayed light gray, Fe atoms dark gray.

Figure 7

Analysis of the surface segregation behavior. The fraction of excess atoms segregating on the surface is plotted over the deviation of the particle composition from the respective ideal composition. Open symbols: particles with excess Pt, solid symbols: particles with excess Fe.

Figure 8

Dependence of ordering on temperature for particles with different composition. The size of the particles is $7\mathrm{nm}$. The inset shows a magnification of the region around the order-disorder transition.

Figure 9

Dependence of ordering temperature on particle size and composition.

Figure 10

Dependence of ordering on temperature for different sized particles. All particles possess the the respective ideal composition of an ordered regular TO. For comparison, the curve of the ${\mathrm{Fe}}_{50}{\mathrm{Pt}}_{50}$ bulk sample is also shown.

Figure 11

Dependence of the degree of surface segregation and $L{1}_0$ ordering on the parameter $h$ for a $4\mathrm{nm}$ particle with ideal composition $(T=300\mathrm{K})$.

Figure 12

Left column: Cross sections of completely Fe terminated particles with overall composition close to stoichiometry ($T=300\mathrm{K}$, $h=2.4\mathrm{eV}$). Right column: Dark gray patches indicate $L{1}_2$ ordered domains, light gray patches indicate $L{1}_0$ ordered domains.

Figure 13

Dependence of $L{1}_0$ ordering on particle size in completely Fe terminated particles with overall composition close to stoichiometry.

Figure 14

Dependence of $L{1}_0$ ordering on composition in completely Fe terminated particles with a diameter of $4\mathrm{nm}$. The insets show cross sections of particles at distinct compositions.