Local and chemical environment dependence of the magnetic properties of CoRh core-shell nanoparticles

The ground-state magnetic properties of Co${}_x$Rh${}_{1-x}$ nanoparticles having sizes in the range of 0.8–2 nm ($N=43$ and 273 atoms) and Co concentrations $x\approx 0$, $0.25$, $0.5$, $0.75$, and 1 are investigated in the framework of density-functional theory by using a fixed-moment method. Electron correlation effects are explored by comparing the results of the local spin-density and generalized-gradient approximations to the exchange and correlation functional. The role of chemical order on the magnetic behavior is investigated by considering a variety of core-shell atomic arrangements with nearly spherical CoRh interfaces. A local relaxation of the cluster geometry is performed by taking face-centered cubic structures as starting configurations. All considered Co${}_x$Rh${}_{1-x}$ clusters are found to be magnetic with an average spin moment per CoRh unit that is larger than in macroscopic alloys having similar concentrations. This is a consequence of both, the enhancement of the Co moments and the occurrence of important induced Rh moments, which couple parallel to the Co moments. The distribution of the local magnetic moments within the clusters is found to depend strongly on the local and chemical environment of the atoms. In particular, the Rh moments show a nontrivial dependence as a function of the distance to the CoRh interface. The results for the local magnetic moments are correlated to the electronic densities of states, which reflect the concentration and chemical-order dependence of the cluster electronic structure. Finally, the effects of coating and of the 3$d$-4$d$ interface are analyzed by comparing the magnetic behaviors of core-shell particles with those of the corresponding pure Co and Rh cores.

Figure 1

Illustration of the relaxed core-shell fcc-like structures of CoRh clusters having $N=43$ atoms and different relative core sizes ${\eta }_c=N_c/N$, where $N_c$ is the number of atoms in the core. Light (blue) balls represent Co atoms and dark (red) balls represent Rh atoms. The notation Co${}_n$Rh${}_m$ (Rh${}_n$Co${}_m$) designates a cluster having $n$ Co atoms (Rh atoms) in the core and $m$ Rh atoms (Co atoms) in the outer shell.

Figure 2

Local spin magnetic moments ${\mu }_l$ within the Wigner-Seitz spheres of the Co atoms (circles) and Rh atoms (triangles) in core-shell CoRh clusters having $N=43$ atoms. Results are given for the average ${\mu }_l$ at each NN shell $l$ surrounding the central atom $l=1$. Co${}_n$Rh${}_m$ (Rh${}_n$Co${}_m$) designates a cluster having $n$ Co atoms (Rh atoms) in the core and $m$ Rh atoms (Co atoms) in the outer shell. The relative core sizes ${\eta }_c$ are indicated in the insets. The lines connecting the points are a guide to the eye, where full (dashed) lines refer to the generalized-gradient (local-density) approximation. The corresponding relaxed cluster structures are illustrated in Fig. 1.

Figure 3

Spin-polarized average density of states (DOS) of core-shell Co${}_n$Rh${}_m$ clusters having $N=n+m=43$ atoms as a function of the Kohn-Sham energy $\varepsilon$ relative to the Fermi energy ${\varepsilon }_F$. Positive (negative) values refer to results for majority (minority) spin as obtained in the GGA. The corresponding average magnetic moments per atom $\overline{\mu }=({\nu }_{\uparrow }^T-{\nu }_{\downarrow }^T)/N$ are indicated, together with the average magnetic moment per Co atom ${\overline{\mu }}_{\mathrm{Co}}^{\mathrm{WS}}=\left({\sum }_{i=1}^{m+n}{\mu }_i\right)/n$ in brackets. The left-side (right-side) plots refer to clusters having a Co (Rh) core surrounded by a Rh (Co) outer shell. The underlying relaxed geometries are illustrated in Fig. 1.

Figure 4

Illustration of the relaxed core-shell fcc-like structures of CoRh clusters having $N=273$ atoms and different relative core sizes ${\eta }_c=N_c/N$, where $N_c$ is the number of atoms in the core. Light (blue) balls represent Co atoms and dark (red) balls represent Rh atoms. Co${}_n$Rh${}_m$ (Rh${}_n$Co${}_m$) designates a cluster having $n$ Co atoms (Rh atoms) in the core and $m$ Rh atoms (Co atoms) in the outer shell.

Figure 5

Local spin magnetic moments ${\mu }_l$ within the Wigner-Seitz spheres of the Co atoms (circles) and Rh atoms (triangles) in core-shell CoRh clusters having $N=273$ atoms. Results are given for the average ${\mu }_l$ at each NN shell $l$ surrounding the central atom $l=1$. Co${}_n$Rh${}_m$ (Rh${}_n$Co${}_m$) designates a cluster having $n$ Co atoms (Rh atoms) in the core and $m$ Rh atoms (Co atoms) in the outer shell. The relative core sizes ${\eta }_c$ are indicated in the insets. The lines connecting the points are a guide to the eye, where full (dashed) lines refer to the generalized-gradient (local-density) approximation. The corresponding relaxed cluster structures are illustrated in Fig. 4.

Figure 6

Spin-polarized average density of states (DOS) of core-shell Co${}_n$Rh${}_m$ clusters having $N=n+m=273$ atoms as a function of the Kohn-Sham energy $\varepsilon$ relative to the Fermi energy ${\varepsilon }_F$. Positive (negative) values refer to majority (minority) spin. The corresponding average spin moments per atom $\overline{\mu }=({\nu }_{\uparrow }^T-{\nu }_{\downarrow }^T)/N$ are indicated together with the average local moment per Co atom ${\overline{\mu }}_{\mathrm{Co}}^{\mathrm{WS}}=\left({\sum }_{i=1}^{m+n}{\mu }_i\right)/n$ in brackets. The left-side (right-side) plots correspond to clusters having a Co (Rh) core surrounded by a Rh (Co) shell. The underlying relaxed geometries are illustrated in Fig. 4.

Figure 7

Comparison between the magnetization profiles of pure (full symbols) and coated (open symbols) clusters: (a) Pure Co${}_{13}$, Rh-coated Co${}_{13}$Rh${}_{30}$, pure Rh${}_{13}$, and Co-coated Rh${}_{13}$Co${}_{30}$, and (b) pure Co${}_{79}$, Rh-coated Co${}_{79}$Rh${}_{194}$, pure Rh${}_{79}$, and Co-coated Rh${}_{79}$Co${}_{194}$. Results are given for the local spin moments ${\mu }_l$ within the WS spheres of the atoms at the NN shells $l$ surrounding the central atom $l=1$. Full (dashed) lines refer to the GGA (LDA).