The structural, magnetic and optical properties of TMn@(ZnO)42 (TM = Fe, Co and Ni) hetero-nanostructure

The magnetic transition-metal (TM) @ oxide nanoparticles have been of great interest due to their wide range of applications, from medical sensors in magnetic resonance imaging to photo-catalysis. Although several studies on small clusters of TM@oxide have been reported, the understanding of the physical electronic properties of TMn@(ZnO)42 is far from sufficient. In this work, the electronic, magnetic and optical properties of TMn@(ZnO)42 (TM = Fe, Co and Ni) hetero-nanostructure are investigated using the density functional theory (DFT). It has been found that the core-shell nanostructure Fe13@(ZnO)42, Co15@(ZnO)42 and Ni15@(ZnO)42 are the most stable structures. Moreover, it is also predicted that the variation of the magnetic moment and magnetism of Fe, Co and Ni in TMn@ZnO42 hetero-nanostructure mainly stems from effective hybridization between core TM-3d orbitals and shell O-2p orbitals, and a magnetic moment inversion for Fe15@(ZnO)42 is investigated. Finally, optical properties studied by calculations show a red shift phenomenon in the absorption spectrum compared with the case of (ZnO)48.


Introduction
Semiconducting hybrid materials with improved functionalities such as optical, electric and magnetic properties have been considered as potential candidates for a wide range of applications. For example, Rh, Pd and Pt particles supported on oxides, such as CeO2 and Al2O3, are widely used in catalysis [1,2]; magnetic iron-oxide nanoparticles have been investigated as contrast agents for magnetic resonance imaging [3], which is of important use in cancer therapy. In particular, the physical properties of ZnO doped with ions of transition metal elements have been one of the most intriguing research topics in current materials science [4][5][6][7][8][9]. The characteristics of ZnO with Zn being a transition metal enables it to easily dope magnetic transition metal (TM) ions such as Mn 2+ , Fe 3+ , Co 2+ and Ni 2+ in place of Zn 2+ in the crystal of ZnO. Dietl et al. discovered room temperature ferromagnetism in Mn-doped ZnO thin film, receiving tremendous attention to ZnO based materials [10]. Since then several studies have been carried out in ZnO based materials with different combinations of TM ions [4,11,12].
Some reports revealed the importance of point defects such as oxygen and zinc vacancies and interstitials in magnetic ordering [13,14]. Mishra and Das [15] studied the optical characteristics of Fe-doped ZnO nanoparticles using FTIR. Sawalha et al. [16] investigated the electrical conductivity of pure and doped ZnO ceramic systems.
Their experiment indicated that donor concentration, point defects, and adsorption-desertion of oxygen were affected by the Fe doping for ZnO. Moreover, Shi and Duan [17] studied the magnetic properties of TM (Cr, Fe and Ni) doped in ZnO nanowires by first-principles theory. Xiao et al. [18] calculated the structural and electronic properties of Fe-doped ZnO nanoparticles, and the results showed that Fe doped ZnO nanoparticles were structurally more stable than the isolated FeO and ZnO phases.
In recent years, core-shell structures in which metals form the core and ZnO constitutes the shell have attracted intense interest due to their significantly high effectiveness in improving the photo-catalytic activity and the synergistic effect among components [19][20][21][22]. The core-shell architecture avoids exposing the inner core to the environment and thus maximizes the interaction between the building blocks. Moreover, the composition, size and morphology of the inner core and outer shell are important aspects of structural property and would most probably affect its stability. So far, to the best of our knowledge, investigations on the physical mechanism for the effect of composition, size and morphology of magnetic TM-core/ZnO-shell heterogeneous nanoparticles are very rare. Here, we report the theoretical studies on a series of TMn@(ZnO)42 (TM = Fe, Co and Ni) heterostructures by using the density functional theory (DFT). The structural, magnetic and optical properties of such core-shell heterostructures have been investigated. Stable structures are founded among different models and variation of magnetic moment are studied, especially for the moment inversion of Fe15@(ZnO)42. Furthermore, a red shift phenomenon is also obtained for the absorption spectrum of Fe15@(ZnO)42 compared with the case of (ZnO)48. We expect that our results for TMn@(ZnO)42 can help to understand the effects of the encapsulation on the structure, stability, and magnetic properties of TM clusters.

The structural properties of TMn@(ZnO)42 hetero-nanostructure
In simulation, due to the multiplicity and indeterminacy of core-shell heterostructure, it is always a challenge to optimize the stable structure of metal-oxide heterogeneous with increasing number of atoms. In the following calculations, the TMn@(ZnO)42 core-shell model is built to investigate stable structure of TMn@(ZnO)42 with different n (n=6-18). Considering the rationality of the structure, the magic number nanostructure of (ZnO)48 with D3d symmetry is firstly chosen to be the initial configurations due to the fact that the (ZnO)48 models has the highest binding energy [29]. Therefore, six ZnO in the center of relaxed (ZnO)48 are removed, and magnetic TM-core TMn clusters are constructed. The central empty position to put the magnetic TM-core relies on some physical and chemical intuition based on the symmetry of bond-length and structure. Then, these atomic geometries are fully optimized until the convergence criteria are reached. According to our scheme, the stable configurations of and Ni) are nearly located at the center of the cages due to the inner core TMn cluster and outer shell cage sizes. The shells of n from 6 to 12 are a cage-like structure while the shells of n≥13 has a tendency to change into a sphere, which may imply that with the increase of n, the shell is increasingly inclined to become a spherical structure. The exact symmetry for each TM cluster is C1 except that Ni12 is C2. Furthermore, it is intriguing that, in the TMn clusters, the TM atom located at the prominent position and the center of TMn (yellow balls in Fig. 1) have relatively small local magnetic moments.
Therefore, there is a strong tendency of the magnetic TMn clusters for lower symmetry structures, which helps to increase their energy stability due to the splitting of the highest occupied states. From the results of bond lengths (see Fig. 1), the Fen clusters are much more non-compact than the Con and Nin structures, indicating that the core is more close to shell for Fen@(ZnO)42. This trend may affect the magnetic moments (see  Table 1 together with other calculated work [29], from which it can be seen that our results of (ZnO)48 reach an agreement with the other studies [29]. It is also obvious that there is a contraction behavior for the outer-shell of M@ZnO compared with (ZnO)48, indicating that doping at the center with a magnetic TM atom could provide strong bonding among surface atoms, that is, the Zn-O bonding of M@ZnO is stronger than the (ZnO)48 cluster due to the interaction of M-O.

The magnetic and electronic structure properties of TMn@(ZnO)42 heteronanostructure
The magnetic properties of encapsulated TMn (TM = Fe, Co and Ni) clusters inside (ZnO)42 are calculated based on the stable geometries discussed above. All of the transition metal atom magnetic moments of the TMn@(ZnO)42 core-shell nanostructure are shown in Table 2 and 3. More details of magnetic moments are described in the Supporting Information II. The following trends can be observed: (i) Except for a few cases, the magnetic moments decrease from outside to inside for core transition metal atoms. For example, for relatively stable structure Fe15@(ZnO)42, Co15@(ZnO)42, and Ni13@(ZnO)42, the center Fe, Co, Ni atoms have the magnetic moments 1.996, 1.167, and 0.226μB/atom, which are significantly smaller than the other magnetic moments such as 2.64, 1.78, and 0.68μB/atom, the average value for Fe, Co and Ni, respectively.
(ii) As is presented in Table 4, a general feature is that local magnetic moments tend to have some relationship with the TM-O distance and the small distance corresponds to a small magnetic moment. Especially for several Fen@(ZnO)42 systems, e.g., Fe15@(ZnO)42, it is found that some Fe local magnetic solutions change from ferromagnetic to antiferromagnetic phases (e.g. -2.176μB /atom) with the Fe-O distance decreased. A similar phenomenon can also be found in the TM@Mg12O12 [30] and TMm@Cn [31].

The optical properties of M@ZnO and (ZnO)48
In order to investigate the influence of magnetic TM inner-core on the optical  Fig. 4(d)), we found that this smaller peak originates from the stronger interaction between Ni-O atoms and more abundant charge transfer of O -Zn atom (see Supporting Information II). We contrast the DOS of M@ZnO (Fig. 4(d)) and conclude that the influence on Zn-O interaction for the case of introducing Ni atoms is weaker than the case of Co, Fe atoms, particularly at < 3 eV. Moreover, it is noted that,   Fig. 4(d), M@ZnO shows a typical half-metallic behavior from spin majority and minority components, which is in keeping with the result of the real part of dielectric function. In addition, the spin polarization of Fe, Co and Ni is the major contribution for DOS around the Femi level.
Furthermore, the imaginary part of dielectric function shows that the curve of (ZnO)48 has no distinct peak while M@ZnO appears to have a larger peak at around 0.85-1.47 eV, which is mainly due to the contribution of Co, Fe, Ni atoms in the core.
It indicates that there is an evident absorptive action in the infrared region and the margin of visible light, especially in the case of Fe15@(ZnO)42, whose peak of absorption is closer to the visible light region. Finally, due to the interaction between O atom in shell and metal atom in core, the peak at 9.68 eV of (ZnO)48 vanishes and the curve decreases to zero rapidly. Compared with the absorption spectrum of the (ZnO)48, we find that an obvious red shift has occurred, and it is in accordance with the behavior of the calculated electronic structure.

Methods
All calculations in this paper are performed in the VASP codes [23,24] based on density functional theory (DFT) [25,26] within the projector augmented wave (PAW) [27]. The exchange and correlation potential is treated with the generalized gradient approximation (GGA) methods as described by Perdew-Burke-Ernzerhof (PBE) [28].
The electron wave functions are expanded in plane wave with a cutoff energy of 480 eV. All atoms are fully relaxed and the convergence tolerance for energy and maximum force are set to 1.0 × 10 -5 eV and -5× 10 -3 eV/Å. For k-point sampling, we use a single Γ point for the geometry optimizations in the first Brillouin zone. Spin-polarization is taken into account in this work. In the calculations, the free TMn@(ZnO)42 is located in a rectangular supercell with a size of 30×30×30 Å 3 . The interaction between periodic images could be neglected on this size.     Co 1 5 @(ZnO) 4 2 Fe 1 3 @(ZnO) 4 2 Ni 1 5 @(ZnO) 4 2 (ZnO) 4