Article pubs.acs.org/JPCC
Magnetic Phase Transition in 2 nm NixCu1−x (0 ≤ x ≤ 1) Clusters Junais Habeeb Mokkath and Udo Schwingenschlögl* Physical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia ABSTRACT: NixCu1−x (0 ≤ x ≤ 1) clusters with a diameter of 2 nm (459 atoms) are modeled by a combination of basin hopping global sampling and reoptimization within spin-polarized density functional theory. The favorable structures for different Ni/Cu ratios are obtained by probing the energy landscape of face-centered cubic clusters. A sharp phase transition from nonmagnetic to ferromagnetic behavior is discovered above x = 0.4 and explained in terms of the distribution of the Ni atoms in the clusters. Small Cu magnetic moments are induced by proximity.
I. INTRODUCTION In the past decade, intensive research has dealt with nanoalloys from theoretical and experimental studies to materials engineering for specific technological applications.1−4 The size of the particles typically ranges from 1 to 100 nm. Nanoalloys show unique magnetic, catalytic, and optical properties due to their large surface-to-volume ratio, reduced local coordination, and special symmetry. Rapid progress in synthesis and characterization has facilitated the fabrication of controlled sizes and compositions.5 However, an in-depth understanding of the materials properties is hindered by the huge structural and physicochemical complexity. On the one hand, the particles can appear in a variety of geometries with or without crystalline ordering.6 On the other hand, variations in the composition can result in qualitatively different chemical patterns, including core−shell and multishell structures.7−9 The combination of both these degrees of freedom turns the sampling of the energy landscape into a formidable task, provoking an active field of research. Besides general interest from the perspective of energy landscape complexity, NiCu alloys are particularly appealing systems because of their remarkable phase diagram of facecentered cubic structures with randomly diffused Ni and Cu atoms and a miscibility gap below 630 K.10 The origin of this behavior is the small lattice mismatch between Cu (a = 3.62 Å) and Ni (a = 3.54 Å) and modest (positive) enthalpies of solution.11 Regarding the magnetic properties, the investigation of nanoalloys is demanding because of finite size and surface effects, which depend on the distribution of the elements involved.12 In addition, there is the possibility of inducing spinpolarization of nonmagnetic elements by proximity to magnetic neighbors.13 Understanding the magnetic properties as a function of the composition therefore is essential, but also a huge challenge. Nanoclusters have various medical applications, for instance, in magnetic hyperthermia.14 In this technique, the diseased © 2014 American Chemical Society
tissue with embedded magnetic nanoparticles is heated to 41− 46 °C for a period of time by applying an alternating magnetic field, enabling a localized deposition of energy. Nanoparticles with the right Curie temperature protect the healthy tissue from overheating, because the magnetic coupling is reduced in the paramagnetic regime. NiCu nanoclusters have magnetic phase transitions in the desired temperature range and therefore are ideal candidates for this purpose.15 Furthermore, they show interesting catalytic properties16 due to atomic ordering in the surface and subsurface, such as Cu enrichment in the surface of Ni rich particles.17 In order to lay the ground for predicting and engineering the magnetic and catalytic features, this work investigates the structures and electronic properties of NixCu1−x (0 ≤ x ≤ 1) clusters with 459 atoms as a function of the Ni:Cu ratio. To this aim we employ a combination of basin hopping global sampling and spin-polarized density functional theory. Details of the methodology are given in Section II and the obtained results are presented Section III. We will address the favorable structures, the composition dependence of the spin-polarization, and the electronic structure. Finally, we conclude in Section IV.
II. COMPUTATIONAL ASPECTS Our computational methodology consists of two steps. First, we perform basin hopping global sampling18 within a semiempirical Gupta potential using the symmetry-orbit shell optimization technique.19 This technique exploits the full point group symmetry of a cluster to partition the atoms into shells. Thus, for a given structure the number of inequivalent homotops is reduced from 2T, where T is the total number of atoms, to 2S, where S is the number of atomic shells. We Received: December 26, 2013 Revised: March 21, 2014 Published: April 2, 2014 8169
dx.doi.org/10.1021/jp412635m | J. Phys. Chem. C 2014, 118, 8169−8173
The Journal of Physical Chemistry C
Article
summarized in Table 2. A prominent multishell arrangement, for example, appears for m = 228 Ni atoms (x = 49%), compare Figure 1. Shells 1−4, 6−7, 9, 15, and 17−18 are occupied by Cu atoms, whereas shells 5, 8, 10−12, 14, and 16 are occupied by Ni atoms. Moreover, we observe that the Cu atoms favor to occupy surface sites even for high Ni concentration, see the case of m = 358 Ni atoms (x = 77%), for instance. Preferential Cu segregation on the surface previously has been found for Ni101Cu100 clusters by bond order simulations.24 The atomic distribution in bimetallic nanoalloys depends on various factors, which partially are common with bulk alloys.2 The most important factor is the relative strength of the different bonds, because a stronger (weaker) bonding within the same species as compared to that between the species will favor segregation (mixing). On the other hand, the surface energies of the two species play a key role for the surface segregation in nanoalloys. In addition, larger atoms tend to favor surface sites where they are less confined. The specific atomic distribution in a cluster is determined by a balance between the aforementioned ingredients. Our calculations within density functional theory show that the Ni−Ni bond has the highest cohesive energy of 1.49 eV/atom, followed by the Ni−Cu bond (1.16 eV/atom), and the Cu−Cu bond (1.13 eV/atom). While Ni−Ni bonds thus are clearly advantageous, the similarity of the Ni−Cu and Cu−Cu bond strengths can cause complex structural features. Because the bulk cohesive energy of Ni (4.44 eV) is larger than that of Cu (3.49 eV)25 and Cu (1.96 Jm−2) has a lower surface energy than Ni (2.63 Jm−2),26 surface segregation of Cu atoms is energetically favorable. In addition, the slightly larger atomic radius of Cu (1.28 Å) as compared to Ni (1.25 Å) favors Cu atoms at the surface. The multishell atomic arrangements of the Ni and Cu atoms in NixCu1−x (0 ≤ x ≤ 1) clusters have interesting consequences for the physical and chemical properties. For example, the catalytic activity is enhanced by a variety of active surface and subsurface sites. In the following, we address in more detail the magnetic properties. One naively may speculate about a crossover from nonmagnetic to ferromagnetic behavior for increasing Ni concentration. Being already close to the bulk, the pure Ni459 and Cu459 clusters are ferromagnetic and nonmagnetic, respectively, so that the magnetic nature must change between these extreme cases in NixCu1−x (0 ≤ x ≤ 1) at an intermediate Ni concentration. In the following, we will demonstrate that this change occurs in form of a sharp phase transition and we will explain the origin of the transition. We plot in Figure 2a the average magnetic moments as a function of the Ni concentration, separately for the group of Ni atoms and the group of Cu atoms. For 0 ≤ x ≤ 40%, all cluster atoms show vanishing moments. At x = 46%, a distinct magnetic phase transition is encountered, which comes along with the creation of Ni moments averaging to 0.44 μB. While the Ni atoms in the inner shell 6, for instance, show small moments of 0.2 μB (shell average but with very small variations), the moments increase toward the outer shells. For x > 46%, the average Ni moment increases almost linearly and reaches 0.7 μB for the pure Ni cluster. While all the Ni moments are aligned ferromagnetically, the Cu atoms exhibit small (typically 0.01 μB) induced moments with different orientations, so that the average is close to zero, see Figure 2a. The origin of the sudden onset of spin-polarization can be related to qualitative differences in the distribution of Ni in the atomic shells from x = 40% to x = 46%, see Table 2. Whereas
consider the highly symmetric face centered cubic structure of 459 atoms described in ref 20, which has 18 shells. In order of increasing distance from the center of the cluster, these shells comprise 1, 12, 6, 24, 12, 24, 8, 48, 6, 36, 24, 24, 24, 72, 48, 12, 48, and 30 atoms, resulting in 218 = 262 144 structures. In the basin hopping search, atomic and shell exchange moves are taken into account, while constraining the symmetry. For each geometry and composition, ∼3000 basin hopping sampling runs are carried out with a low thermal energy of 0.02 eV. We use the empirical Gupta potential as introduced by Cleri and Rosato21 to represent the Ni−Ni, Ni−Cu, and Cu−Cu interatomic interactions. The cluster potential energy is the sum of all atomic bonding Eib
1/2 ⎧ ⎡ ⎛ rij ⎞⎤⎫ ⎪ ⎪ 2 = −⎨ ∑ ξ exp⎢ −2q⎜ − 1⎟⎥⎬ ⎢⎣ ⎪ j≠i,r
