AuCo nanoparticles: ordering, magnetisation, and morphology trends predicted by DFT †

The rapid development of applications relying on magnetism at the nanoscale has put a spotlight on nanoparticles with novel morphologies that are associated with enhanced electronic and magnetic properties. In this quest, nanoalloys combining highly magnetic cobalt and weakly reactive gold could oﬀer many application-specific advantages, such as strong magnetic anisotropy. In the present study, we have employed density functional theory (DFT) calculations to provide a systematic overview of the size-and morphology-dependence of the energetic order and magnetic properties of AuCo nanoparticles up to 2.5 nm in diameter. The core–shell icosahedron was captured as the most favourable morphology, showing a small preference over the core–shell decahedron. However, the magnetic properties (total magnetic moments and magnetic anisotropy) were found to be significantly improved within the L1 0 ordered structures, even in comparison to monometallic Co nanoparticles. Atom-resolved charges and orbital moments accessed through the DFT analysis of the electronic level properties permitted insight into the close interrelation between the AuCo nanoparticle morphology and their magnetism. These results are expected to assist in the design of tailored magnetic AuCo nanoalloys for specific applications.


Introduction
6][7][8][9] However, synergistic effects captured within multimetallic alloys indicate that a vast new dimension of materials could emerge when two or more metals are combined at the nano-level.Furthermore, modern technology applications in the fields of biomedicine and catalysis have a limited tolerance in particle dimensions and surface chemistry, which makes it extremely challenging to access the desired material behaviour within a single component nanoscale system.To address the requirements of such applications, identifying the correlation between the physiochemical characteristics and geometrical relations of bi-and multi-metallic NPs is currently a hot topic, with modifications induced through the composition variations being especially intriguing.Bimetallic (and multimetallic) NPs, often referred to as nanoalloys, present properties with a very high degree of tunability owing to the variety of morphologies they can adopt.This morphology is specified not only by the geometric structure, as in the case of monometallic systems, but also by the composition and chemical ordering of its components, giving a complex landscape of possible combinations.Nanoalloys of noble and transition metals (TM) have gathered considerable interest for cost reduction and improvement of catalytic properties compared to rare metal NPs, as well as for their capacity to stabilise ferromagnetic TM NPs from oxidation for use in magnetic data storage or biomedical applications.Although phase diagrams of many noble-TM systems indicate their immiscibility over wide composition ranges, there are indications of significant deviations from bulk mixing trends at the nanoscale originating from a size-modified electronic structure.
When the components are weakly miscible, core-shell arrangements are expected with the more cohesive element (usually TM) situated within the NP core.This trend has already been observed for many noble-TM NPs, giving stable nanomaterials with novel properties.Most of the AgNi/Co NPs were found to be phase segregated core-shell systems, owing to the very fast reduction potential of silver.Through global optimisation studies, the icosahedral morphology was indicated to be among the most stable geometries for sizes up to 10 3 atoms.4][25][26][27] For AuFe systems, it was found that nanoscale alloys retain in their entirety the optical and magnetic properties of the individual components. 28Thus, AuFe NPs are particularly interesting in the context of MRI contrast agents, local heating, and drug delivery, [29][30][31] and they were found to adopt mostly icosahedral shapes with a homogeneous distribution of Fe and Au atoms, whereas annealing induces the formation of an Au-rich surface. 32,33][39] Core-shell AuCo NPs have also been proposed for biomedical applications, such as hyperthermia or MRI, as their Co core with large magnetic moment is highly responsive to an externally applied magnetic field, and the Au shell, which is inert and biocompatible, allows for easy functionalisation.2][43] A novel statistical-mechanics approach to determine the free energy cost of forming phase-separated aggregates developed by Ferrando et al. has shown that the decrease in cost is nonnegligible for AuCo NPs with diameters up to 10 nm, thus indicating the permanence of an equilibrium miscibility gap at the nanoscale and the nonexistence of a critical size below which phase separation is impossible. 44The global minimum geometries were corroborated by molecular dynamics studies, where rosette reconstructed icosahedra were found to be the most stable for systems with compact Co cores, whereas nanoparticles with larger Co core sizes adopted the shapes of regular Mackay icosahedra with central high-symmetry cores.6][47] In addition, reports have indicated that the optical and magnetic properties may both be tuned by tailoring the size of the Co core.
However, the fact that the surface of the nanoalloy is expected to contain mostly noble metal atoms due to the atomic radius or surface energy, does not invariably determine the chemical ordering of such systems.The size, structure, and chemical arrangement of bimetallic NPs can be experimentally controlled throughout the synthesis protocol, allowing for metal species to intermix and maximise the synergistic benefits available through their alloying and interfaces.For example, physical methods were reported for the synthesis of AgNi ordered NPs, which exhibited substantial enhancement of their optical limiting efficiency. 48Core-shell AuNi NPs with inverted segregation (Au cores covered by Ni) showed huge magnetisation, which was maintained even after the formation of NiO on the surface. 49Furthermore, intermixed nanoalloys of magnetic 3d TM with Pt are potential materials to overcome the superparamagnetic limit due to their exceptional values of magnetic anisotropy, which can thus fulfil demanding requirements for high density information storage.Compared to the intermixed state of CoPt NPs, surface-segregated cuboidal counterparts have shown their magnetic moment reduced by 0.52 m B with a 19% reduction in magnetic anisotropy and, more pronouncedly, when adopting cuboctahedral morphology, reductions were of the order of 4.96 m B and 45%, respectively. 50Distinct L1 0 orderings in CoPt systems have already shown how improved magnetic anisotropy can translate into superior catalytic performance in fuel cells, 51 while a similar arrangement in FePt NPs indicated high anisotropy and promising integration in magnetic recording applications at room temperature. 52he hybrid systems based on Au and Co nanoalloys are consequently also expected to offer unique properties in different chemical orderings because of the possible magnetoresistance effect and optical-magnetic bifunctionalities. 53Although the limited literature on AuCo systems is almost exclusively focused on the core-shell structures, Marbella et al. have demonstrated the synthesis of discrete, composition-tuneable alloyed AuCo NPs with random ordering of Au and Co atoms, whose magnetic susceptibility can be tailored while maintaining almost identical particle size and surface chemistry. 54Finally, a recent theoretical study has shown that magnetic effects can destabilise core-shell arrangements of AgCo and AuCo systems; their icosahedral structures remain preferential, but peculiar quantum effects reverse the energetics in favour of intermediate compositions, presenting a much more thorough intermixing of noble metal phases with the cobalt atoms. 55espite these previous efforts, the knowledge of AuCo binary nano-systems is still rather limited, since only a few confined sizes, compositions, and morphologies have been studied both theoretically and experimentally, with no systematic studies available.Since the physiochemical characteristics of bimetallic NPs depend distinctly on their structure, diameter, and chemical composition, the knowledge of magnetic and electronic properties, as well as the structural evolution with increasing size, is of crucial importance for further improvement of propertytuning strategies.This dependency is in no way trivial, and theoretical approaches can provide a useful contribution in this respect by narrowing down the structural candidates with application-specific properties.
To improve the comprehension of size and shape property alternations of AuCo NPs, the stabilities and structures of selected magic-numbered NPs with varying morphologies were probed with accurate DFT calculations.The electronic and magnetic properties of distinct orderings (core-shell, L1 0 ordered, and disordered NPs) were also predicted, including the atomresolved magnetic orbital moments and magnetic anisotropy energies (MAE), thereby providing a detailed overview of morphology-specific AuCo NP features.

Computational details
The central difficulty in studying the morphological dependence of the properties of bimetallic NPs lies in the complexity of possible composition, geometry, and chemical ordering combinations.7][58][59] This simplification is governed by two assumptions: (i) that the NP surface chemistry is dominated by the first two or three atomic layers, and (ii) that the chemistry of appearing NP crystal facets can be approximated by their respective single crystal surfaces.While periodic models can approximately resemble large particles with an appreciable share of facet areas, in most cases they cannot represent a realistic picture of NP systems, especially when it comes to NPs of a few nanometres in diameter.In such cases, the nonnegligible portion of chemically under-saturated sites (steps, edges, vertices) significantly changes the NP reactivity and magnetic behaviour.][68][69] For this reason, the calculations carried out here were performed using particle models.
The computational search for the low-energy geometric structures of a given NP size comprises an additional problemthe number of NP isomers (same size, different shape) increases drastically with the increase in the number of atoms.The addition of a secondary metal introduces further parameters of composition and ordering, and the number of NP homotops (same size and shape, different atom arrangement) quickly grows beyond the ability to consider each homotop separately.In addition, the term composomers has been introduced by Johnston and Belchior, 70 referring to compositional isomers (same size and geometry, but different composition).Hence, the systematic study of structurally and energetically favourable bimetallic NPs is, even within the single size or composition, extremely challenging.Several theoretical tools are available to at least partially reveal morphology preferences of certain nanoalloy systems.A thorough exploration of the potential energy surface was performed by molecular dynamics (MD) calculations for NPs of some metal pairs.However, the accuracy of available interatomic potentials is strictly systemdependent.3][74][75] The challenge of developing efficient and accurate interatomic potentials for metal intermixing hence constitutes a rapidly progressing research field. 76,77Although atomistic models can treat NPs of tens of thousands of atoms, far out of the reach of DFT calculations, ab initio methods still have an important role in the assessment of their properties.
However, open-shell magnetic compounds pose a challenge also for DFT methods, where the often employed generalized gradient approximation (GGA) exchange-correlation functional suffers from the over-delocalisation of the electrons in metal d orbitals, resulting in deficient descriptions of magnetic and electronic structures.This can be partially solved by introducing the Hubbard parameter (U), which localises the electrons on the d-metal atoms. 78However, the localised formulation of DFT+U is constructed to impose a finite discontinuity to the exchange-correlation potential which is important in the description of semiconductors and insulators, but is in general not well suited to treat weakly correlated transition metals.Arguably the most important correlation effects in metals, namely fluctuation-induced mass renormalisation and itinerant exchange interactions, are hence missing, and excessive stabilisation of occupied states due to the +U corrective potential remains questionable in cases where the prediction of properties related to electronic localisation (such as magnetisation) cannot be accomplished without compromising the description of delocalised metal electrons. 79,80Hybrid density functionals correct these errors by partially incorporating the exact exchange.Nevertheless, the main improvement of hybrid functionals is in the correct treatment of the valence bands near the Fermi level, again leading to improved localisation of the electrons mostly in semiconducting and insulating materials.2][83][84][85] Specifically for Co clusters, it has been shown that the lowest energy structures and magnetic properties are not as sensitive to the level of the exchangecorrelation functional, and results indicate that the differences between GGA, GGA+U, and hybrid methods are purely an electronic effect. 86he DFT systems of choice are usually driven by the wellknown often occurring NPs with a complete, regular outer geometry designated as full-shell NPs.These sizes, known as magic numbers, 87,88 were the criteria implemented in this study on various fcc-based NP shapes, namely cuboctahedron, icosahedron, and Ino decahedron.The compositions were fixed to L1 0 ordered cuboctahedra with terminating Au layers, Fig. S1 of the ESI, † which are energetically more favourable than Co-terminated NPs.Such compositions deviate from perfectly ordered Ino decahedra, which were accordingly adapted with an excess of Co atoms distributed randomly over the Au antisites to allow direct comparison of their energetic and magnetic properties with icosahedra and cuboctahedra of the same sizes.With the central aim of identifying morphology trends, four magic sizes (N = 55, 147, 309, and 561 atoms) were considered.
The structural, energetic, and magnetic properties of AuCo NPs were determined by employing spin-polarised DFT calculations as implemented in the Vienna Ab initio Simulation Package (VASP). 892][93][94][95] The spatially confined core electrons were treated through the projector augmented wave (PAW) approach, 96 with the wave functions of the valence electrons expanded to an energy cut-off of 400 eV.The intrinsically nonperiodic nature of NP systems, created by adding 12 Å of vacuum around each particle, restricted the Brillouin zone sampling to the G-point.Relaxations were carried out until a convergence criterion of 10 À6 eV between consecutive steps was reached, without any structural, symmetry, or magnetic constraints.
The tendency of the two elements to mix (or segregate) within the given morphology was quantified through mixing energies, using the expression proposed by Jellinek and Krissinel. 97Charge distribution was calculated using the Bader charge analysis approach of Henkelman et al. 98 Spin magnetic moments were determined iteratively through simultaneous optimisation during the self-consistent field (SCF) procedure.To predict spin-orbit-related properties (orbital magnetic moments and magnetic anisotropy energies), fully relativistic spin-orbit coupling (SOC) calculations 99,100 were performed within the non-collinear version of the VASP code developed by Hobbs et al. and Marsman and Hafner. 101,102To satisfy the requirements of extremely well-converged wave functions and charge densities, the criteria for termination of the SCF cycles was tightened to 10 À7 eV per cell and energy changes to less than a hundredth of a meV.Two sets of self-consistent SOC non-collinear calculations were performed, one for each easy and hard magnetisation axes, and the MAE was determined in terms of the difference in their total energies.In principle, such an approach, although time-consuming, is exact and straightforward.
Further details can be found in the ESI.†

Energy trends
The structures of the studied bimetallic AuCo NPs are shown in Fig. 1, with the corresponding energetic evolution with respect to the increasing NP size captured in Fig. 2. The L1 0 ordered cuboctahedra were chosen as a reference point for each size.All remaining morphologies are located at negative energies, meaning that the L1 0 ordered cuboctahedron is the least favourable morphology across the whole size range.Relaxations of the NPs of the smallest size considered, N =5 5( d o 1 nm), led to significant structural changes due to the disproportionate radii of Au and Co atoms, resulting in energies which are difficult to relate directly to the energetic trends of larger NPs.
For the NPs with diameters 41 nm, ordering within the icosahedral geometries showed improvement in stability over L1 0 cuboctahedra with energy differences of 0.050 eV per atom.Disordering of two metallic phases within the corresponding 147-and 309-atom NPs with icosahedral geometry showed further improvement in stability.L1 0 decahedra are energetically the most stable ordered AuCo NP structures, and calculated energy differences in reference to the L1 0 cuboctahedron are in the 0.062-0.075eV per atom range, whereas, when disordered, the difference reduces to B0.040 eV per atom.This behaviour is in contrast to the results of the PtCo NP study, 103 where disordered mixing of the two elements was always found to be less favourable compared to ordered atomic arrangements.Core-shell segregation is a dominant mechanism for all three geometries, similar to the PtCo icosahedra.Core-shell AuCo icosahedra have the most favourable energy difference with L1 0 cuboctahedra, between 0.210 and 0.268 eV per atom, followed by core-shell decahedra which are in the energy difference range of 0.194-0.239eV per atom.The separation between the two geometries decreases with the increase in the NP size.Complete segregation of Au and Co phases in cuboctahedral NPs was observed to lead to a spontaneous transformation to the core-shell icosahedron for all except the smallest 55-atom NP,which, in turn, was significantly distorted after geometry optimisation, giving a core-shell/L1 0 energy difference of 0.207 eV.
Calculated mixing energies per atom are given in Table 1.Only core-shell morphologies show negative mixing energies, indicating spontaneous segregation of the Au and Co metallic phases.However, the extent of the convenient core-shell miscibility reduces as the NPs grow in size.There is an average 40% decrease in segregation favourability of icosahedral and decahedral core-shell AuCo NPs when going from a 1.0 nm to a 2.5 nm diameter.Additionally, positive mixing energies of 1.0 and 1.5 nm L1 0 decahedra (0.044-0.072 eV per atom) are only a small portion of the mixing energies of ordered icosahedra or cuboctahedra of the same size, which reach up to 0.283 eV per atom for the 561-atom L1 0 cuboctahedron.
In order to gain insight into the physical reasons behind the stark differences in the energies of varying AuCo NP morphologies, structural, electronic, and magnetic features were examined on the atom-decomposed level.

Structural parameters
By analysing the atomic distances in core-shell AuCo NPs, listed in Table 2, it can be seen that the average inter-shell nearest neighbour Co-Co distance is several percent shorter than the average Co-Co intra-shell distance for both icosahedral and decahedral NP geometries.This induced dense packing of Co shells allows the size mismatch between the atomic species to be compensated by radial accommodation of gold atoms on the surface and reduces the internal stress in comparison to the L1 0 ordering, where a certain portion of Au atoms is incorporated in the inner shells.The percentage difference in the inter-and intra-shell distances is greater in the icosahedron (3.8-5.7%)than in the decahedron NPs Fig. 2 Energetics of AuCo NPs of varying morphologies (core-shell, L1 0 ordered, and disordered cuboctahedron, decahedron, and icosahedron) as a function of the NP size (N = 55, 147, 309, and 561).All energies are expressed per atom, in respect to the energy of the L1 0 cuboctahedron.Corresponding geometries can be found in Fig. 1. (0.7-1.3%), resulting in longer Co-Au distances and more favourable energetics.Distances obtained for the L1 0 ordered morphologies are summarised in Table 3.In general, mixing of the two metallic phases within the inner shells of the NPs resulted in shorter average Co-Au and elongated inter-shell Co-Co distances compared to the core-shell counterparts.Single directional elongation of the decahedral geometry allowed for increased Co-Au distances in between the shells, which is possibly the most important contributor in the reduction of volumetric strain and leads to the improved stability over the L1 0 icosahedron and cuboctahedron.Owing to a particularly large difference in the radii of Co and Au atoms, it is not unusual that the mismatch in the average interatomic distances persists with the increase in the NP size.

Electronic structure
A qualitative understanding of energetic trends of distinct orderings can be gained through the analysis of electronic properties.Densities of state, DOS, of 147-atom L1 0 and coreshell structures, Fig. 3, show that both have the 3d majorityspin channel of Co atoms practically complete, which indicates that the stability difference comes from the filling up of the minority-spin channel and shifting of the contributions of the Co 3d states to lower energies.Calculated d-band energies of minority-spin Co 3d states are about two times lower in energy for the core-shell AuCo icosahedral and decahedral NPs (e d,ico = À0.36 eV, e d,deca = À0.42 eV) compared to the L1 0 counterparts (e d,ico = À0.18eV, e d,deca = À0.24eV).This improved filling of the Co minority-spin channel of the core-shell AuCo NPs reflects their increased stability.In addition, the Au 5d states of both spin channels within the L1 0 ordered structures are shifted to deeper energy levels, thereby decreasing the effective hybridisation with the Co 3d states as well as the exchange splitting of Au DOS.Differences in the DOS and d-band energies of varying L1 0 ordered AuCo NP geometries are less pronounced (De d = 0.00-0.06eV), providing only a general conclusion of the near degeneracy of L1 0 cuboctahedron, decahedron, and icosahedron.Similar behaviour is observed for core-shell icosahedral and decahedral AuCo NPs.DOS of disordered AuCo NP morphologies are presented in Fig. S2  (ESI †).Asymmetry of majority-and minority-spin channels of Co atoms is maintained throughout both the ordered and coreshell alloying with Au, indicating preserved magnetic moments.Minimal disruptions in the overlap of the two spin channels of Au were also captured.
In order to gain insight into the electron localisation, which can be correlated with variations in the reactivity of vertices, edges, and facets, Bader charges of Co and Au atoms have been analysed over different 147-atom AuCo NP morphologies, Table 4.The increased degrees of freedom on the NP surface naturally pull electrons from the core, whereas the difference in the electronegativity of Co and Au (w Co =1 .8 8 ,w Au = 2.54) additionally exacerbates this process, as is clearly reflected in the core-shell AuCo NPs, where Co cores show significant charge depletion (0.197 and 0.195 e À per Co atom for icosahedron and decahedron, respectively).The difference in the charge transferred from Co core atoms to Au shell atoms between the two morphologies, namely decahedral and icosahedral AuCo NPs, is very small (0.001-0.002 e À ), indicating only minimal dependence of t h ee l e c t r o nl o c a l i s a t i o no nt h eN Pg e o m e t r y .
For the L1 0 ordered AuCo NPs, depletion of charge from the NP core and subsequent accumulation in the shell is even more pronounced, and calculated charge transfer between the two atomic species is two times larger than for the core-shell counterparts (0.378 and 0.399 e À electron depletion per Co atom for L1 0 icosahedron and decahedron, respectively).In L1 0 structures, Co and Au atoms are both placed in the NP core as well as in the NP shell, and species-specific contributions have also been provided in Table 4. Core Co/Au atoms show increased levels of charge depletion/accumulation compared to those situated on the surface.The difference in charge per Co atom in the core and in the surface is 0.019 e À for L1 0 decahedron, 0.034 e À for L1 0 icosahedron, and 0.005 e À for L1 0 cuboctahedron, whereas the gain of electrons on the core Au atoms is 0.097, 0.056, and 0.047 e À , respectively, in comparison to Au atoms in the NP shell.Nevertheless, surface Co atoms consistently showed electron loss, and significant charge transfer was captured to both core and shell Au atoms, indicating that, for the AuCo NPs, regardless the NP morphology or atomic arrangement, the difference in electronegativity is more influential than the surface effect.Finally, in correlation with the NP shape, variations in the charge transfer are relatively small (0.008-0.029 e À ), similar to core-shell NPs, with a slight deviation of L1 0 decahedron possibly arising from the adaptation of excess Co atoms over Au anti-sites to comply with the chosen atomic composition.Atom-decomposed local Bader charges, represented in Fig. S3  (ESI †), show an even distribution of negative charge amongst Au atoms of core-shell structures, together with a more prominent contribution of interface Co atoms over deeper, core-centred spheres.Intermixing of atomic species in L1 0 AuCo NPs resulted in a greater localisation of electrons over gold atoms which are more highly coordinated to Co. Similar behaviour is seen in the disordered decahedron, whose atom-decomposed charge transfer has also been shown.

Magnetic properties
Average magnetic moments per atom for studied AuCo NP morphologies and sizes are plotted in Fig. 4. In general, the isomers are ferromagnetic with the average magnetic moments in the range of 0.80-0.90m B , i.e. slightly lower than 1.12 m B averages obtained for CoPt NPs. 104The highest deviations are encountered between the core-shell and L1 0 decahedra and icosahedra, where the core-shell mediated reduction mostly results from the lower magnetic moments of compressed centre-most neighbouring cobalt atoms and decreased magnetisation of shell-segregated gold atoms.For the largest sizes considered, this yields a total magnetic moment of L1 0 morphologies which is more than 30 m B higher than their core-shell counterparts.
For the 147-atom L1 0 cuboctahedron, two antiferromagnetic variations of the magnetic structure were considered: a layered antiferromagnet, with Co and Au layers of alternating spin-up and spin-down orientation, and a staggered antiferromagnet, where the orientation of the atomic spins alternates between nearest neighbour pairs and thus the total magnetic moment is nearly cancelled within each layer.Both structures were allowed to relax, without restrictions on the orientation of the magnetic  spins, upon which the layered antiferromagnetic structure spontaneously relaxed to the ferromagnetic ordering.This behaviour is likely due to the induced exchange splitting experienced by the naturally low magnetic Au sites.The structure with the staggered antiferromagnetism, Fig. S4 (ESI †), was found to be less stable than the original ferromagnetic NP by 0.034 eV per atom.
The site-and element-resolved distributions of the atomic spin magnetic moments for the 147-atom L1 0 ordered and core-shell morphologies are shown in Fig. 5 and Fig. 6, respectively.In all cases, Co atoms exhibit stable spin moments comparable to those of bulk phases.Site-dependency is most pronounced in the L1 0 icosahedron, where the centre atom experiences a substantial magnetic moment reduction, with a calculated spin magnetic moment of 0.   Co atoms of around 0.1-0.3m B , which is also reflected in the induced moments of the Au atoms.Gold atoms were shown to be more sensitive to the local environment, displaying a spread of spin magnetic moments for each morphology.The vertex Au atoms, i.e. the atoms positioned farthest from the NP centre, generally show below-average spin magnetic moments, which are already fairly low in the 0.018-0.033m B range.
Average orbital magnetic moments of both Co and Au atoms within the core-shell orderings showed soothed site-dependence compared to the L1 0 ordered AuCo NPs for both icosahedron and decahedron.However, obtained averages of the Au orbital moments within the core-shell icosahedron and decahedron of 0.011 and 0.010 m B were found to be about half of those measured for the L1 0 orderings, namely 0.021 m B for the L1 0 icosahedron and 0.025 m B for the L1 0 decahedron.Averages for Co were, on the other hand, slightly higher for the core-shell icosahedron and decahedron NPs; 0.080 m B compared to the 0.074 m B obtained for the L1 0 icosahedron, and 0.073 m B compared to 0.068 m B calculated for the L1 0 decahedron.Despite the fluctuations in the average values with increasing distance from the central atom, the orbital contribution remains in the direction of spin magnetisation for all sites.The minimal variance in the orbital moments of Co atoms within the two distinct morphologies and the increase in the orbital moments of Au atoms situated in the L1 0 layers indicates the particular relevance of the incorporation of gold atoms in the non-surface positions in the NP anisotropy.
Magnetic anisotropy energies were calculated for the 55-and 147-atom AuCo core-shell and L1 0 ordered NPs of varying morphologies, and the results are presented in Fig. 7.In the case of core-shell AuCo NPs, considered directions of magnetisation were along the growth vectors of low Miller index facets and along the vertex sites.Both the core-shell icosahedron and decahedron were found to have the former as an easy magnetisation axis.For the L1 0 ordered AuCo NPs, the easy magnetisation axis is aligned perpendicular to the stacking of the Au and Co atomic layers, while the direction of the layer elongation forms a hard magnetisation plane.MAE values of corresponding 147-atom monometallic decahedron, icosahedron, and cuboctahedron Co NPs are 471.3,65.6, and 211.8 kJ m À3 , respectively, as presented in our previous work. 105The core-shell arrangement within the icosahedral AuCo NP morphology more than triples the initial Co NP anisotropy to 239.9 kJ m À3 ,whereas the opposite effect is observed for the core-shell decahedron, which showed a reduced MAE value of 278.2 kJ m À3 .L1 0 ordered AuCo NPs of all three morphologies showed an order of magnitude higher MAE, which is a substantial improvement of monometallic Co NP anisotropy energies.Calculated MAE for the 147-atom L1 0 AuCo NPs are 928.3kJ m À3 for the cuboctahedral morphology, 1011.7 kJ m À3 for the decahedron,  and 1038.2 kJ m À3 for the icosahedron.The 55-atom L1 0 decahedron and icosahedron NPs were also found to have very high MAE values of 762.1 and 1160.7 kJ m À3 , respectively.The anisotropy of disordered alloy structures was calculated to be fairly low, e.g.][108] An important aspect is the intrinsic connection of the anisotropy energies with the local atomic anisotropies of the orbital magnetic moments, L z À L x p E z À E x . 109Although the direct proportionality between MAE and the orbital anisotropies from the monometallic case to the alloys containing heavy metals might not be completely confirmed, 110,111

Conclusions
The interest in nanoalloys of noble and transition metals is associated with their enhanced electronic and magnetic properties, which could be valuable and tuneable assets in versatile applications.A combination of highly magnetic cobalt and inert and easy-to-functionalise gold could be an opportune solution for many magnetisation-based biomedical NP treatments.DFT calculations were performed to establish the relation between the morphology factors of AuCo NPs (NP geometry, size, and atomic arrangement) and their structural, energetic, and magnetic properties.
In particular, L1 0 ordered AuCo NPs of varying geometries (cuboctahedron, decahedron, and icosahedron) show high magnetic anisotropy energy in comparison to monometallic Co NPs, as well as a slight improvement of magnetic moments compared to the core-shell alloyed counterparts.However, analysis of the stability trends and mixing favourability highlighted the dominance of core-shell morphologies over a wide NP size range, especially that of the core-shell AuCo icosahedron, owing to the advantageous hybridisation of Au 5d and Co 3d states and low positioning of the minority spin channel centre.Nevertheless, energy separation between different morphologies can be reduced by embedding the NPs in a matrix or placing them in a carrier gas to facilitate diffusion processes during the NP growth.For example, a recent synthesis of 3 nm L1 0 CoPt NPs was achieved by creating samples of diluted CoPt layers embedded in amorphous carbon, 112 and the results provided here are expected to stimulate similar efforts in the synthesis of ordered AuCo NPs.
This DFT study has captured favourable magnetic properties of L1 0 ordered AuCo NPs, which are hence suggested to be promising candidates for applications such as magnetic nanoparticle hyperthermia.Further work on the passivation-mediated changes in the energetic and magnetic properties of AuCo NPs is our next step, whereas we trust that this work will encourage experimental research into AuCo NP synthesis.

Fig. 1
Fig. 1 Structures and cross sections showing outer and inner arrangement of Au and Co atoms in core-shell, L1 0 ordered, and disordered cuboctahedron, decahedron, and icosahedron AuCo bimetallic NPs.

Fig. 3
Fig. 3 Total, 5d Au and 3d Co projected densities of state, DOS, of 147-atom cuboctahedron (grey), decahedron (green), and icosahedron (yellow) AuCo NPs of L1 0 (left) and core-shell (right) orderings.Both majority-and minority-spin states are shown.d-band energy centres, e d , are given for Au 5d and Co 3d states in corresponding colours.
59 m B compared to the NP average of 1.87 m B ; the first complete shell surrounding the central Co atom has an average moment of 1.68 m B .There is a clear enhancement of spin magnetic moments in the surface

Fig. 4
Fig. 4 Average magnetic moments per atom for various AuCo NP morphologies as a function of the NP size.Lines are to guide an eye only.

Fig. 5
Fig. 5 Element-resolved spin, S i , and orbital, L i , magnetic moment as a function of the distance to the NP centre of 147-atom cuboctahedron (&), decahedron (D), and icosahedron (}) AuCo NPs with L1 0 ordering.Co magnetic moments are in grey, and Au in yellow.The number of overlapping symbols, arising from the NP symmetries, is represented by the saturation of colours as indicated in the top right.Dotted lines are connecting average moments for complete geometrical shells.The arrows denote the respective NP averages.

Fig. 6
Fig. 6 Element-resolved spin, S i , and orbital, L i , magnetic moment as a function of the distance to the NP centre of 147-atom decahedron (D) and icosahedron (}) AuCo NPs with core-shell arrangements.Co magnetic moments are in grey, and Au in yellow.The number of overlapping symbols, arising from the NP symmetries, is represented by the saturation of colours as indicated in the top right.Dotted lines are connecting average moments for complete geometrical shells.The arrows denote the respective NP averages.Core-shell cuboctahedron is omitted because of the relaxation-induced rearrangement into icosahedral shape.
this relationship can still give an indication on the sites which exhibit a pronounced dependence on the direction of magnetisation for varying AuCo NP morphologies.Atom-resolved orbital anisotropies are shown in Fig. 8.For core-shell AuCo NPs, the intermixing interface contains atoms with the highest DL values, whereas core Co atoms and under-coordinated Au atoms exhibit minimal orbital anisotropy.On the other hand, Co atoms populating the surface L1 0 sites of ordered AuCo NPs are the main contributors to the overall anisotropy.The MAE of the core-shell alloyed icosahedron is hence increased in comparison to the monometallic Co icosahedron owing to the induced orbital anisotropy at the Co-Au interface, in contrast to the almost complete lack of any anisotropy over the pure 55-atom Co NP (Fig. S5, ESI †).The contrast in behaviour of the decahedral core-shell alloyed AuCo NP is due to the highest local anisotropy present at under-coordinated surface sites of the 55-atom Co decahedron (Fig. S5, ESI †), which are saturated by the Au shell in AuCo NPs.This is not the case for L1 0 ordering, which allows for surface Co atoms to maintain their local anisotropy, at the same time facilitating the advantage of the Au-Co interface as an additional source of orbital anisotropy.

Fig. 8
Fig.8Atom-resolved local anisotropies of 147-atom AuCo NPs: core-shell decahedron and icosahedron (top panel) and L1 0 ordered cuboctahedron, decahedron, and icosahedron (bottom panel), in that order.Blue and red shades indicate positive and negative differences in the easy and hard magnetisation direction of orbital moments, respectively; a scale is provided on the top left.The larger spheres refer to Au atoms, while smaller ones denote Co atoms.

Table 2
Average inter-and intra-shell atomic distances in AuCo NPs of core-shell ordered icosahedral (ico) and decahedral (deca) morphologies for varying NP sizes