First-Principles Study of Ir_n (n = 3–5) Clusters Adsorbed on Graphene and Hexagonal Boron Nitride: Structural and Magnetic Properties

Abstract

Magnetic clusters have attracted great attention and interest due to their novel electronic properties, and they have potential applications in nanoscale information storage devices and spintronics. The interaction between magnetic clusters and substrates is still one of the challenging research focuses. Here, by using the density functional theory (DFT), we study the structural stability and magnetic properties of iridium clusters (Ir_n, n = 3–5) adsorbed on two-dimensional (2D) substrates, such as graphene and hexagonal boron nitride (hBN). We find that the most favorable configurations of free Ir_n clusters change when adsorbed on 2D substrates. In the meantime, the magnetic moments of the most stable Ir_n reduce to 53% (graphene) and 23.6% (hBN) compared with those of the free−standing ones. Interestingly, about 12-times enlargement on the magnetic anisotropy energy can be found on hBN substrates. These theoretical results indicate that the cluster–substrate interaction has vital effects on the properties of Ir_n clusters.

1. Introduction

Owing to unexpected electronic and magnetic properties, atomic clusters are promising candidates for technological applications such as catalysis and magnetic storage. They have been becoming gradually more and more attractive in interdisciplinary fields since the 1990s [1,2,3]. The size and atomic structure-dependent properties of clusters present a huge opportunity for designing cluster-assembled materials and devices. Therefore, determining the ground state structure of a cluster directly by combining experimental and theoretical techniques is vital [1,4].

Magnetic clusters have attracted special attention, especially those composed of transition metals (TM) [5]. Because of the strong spin–orbital coupling (SOC), it is expected that nanostructures containing TM atoms will possess possibly greater magnetic anisotropy energy (MAE), which is a key parameter in nano-information storage devices. Generally, with the increase in the atom number n, the geometric structure of clusters will undergo a transition from line models (n = 2–3) to planar models (n = 3–5) and then to three-dimensional configurations (such as a pyramid, octahedron, icosahedron, cube or core-shell model) [6,7,8,9,10,11,12,13]. For instance, owing to the s(p)-d hybrid, there is a predominantly icosahedral growth for Fe₁₃ and Pd₁₃ clusters [14,15]. The electronic and magnetic properties of magnetic clusters highly depend on the atomic size. As the cluster size increases, an odd–even oscillation of vertical ionization potentials occurs in Ir_n (n < 8) and Rh_n (n < 13) clusters [16,17]. The strongly quenched orbital magnetic moment in size-dependent Fe_n (n = 3-20) clusters is obtained experimentally [14] and then confirmed by DFT calculations [18]. Furthermore, the size effects on magnetic moments have also been observed in Ni_n (n = 10–15) [19,20], Rh_n (n = 2–13) [3,16], Pd_n (n = 2–23, 55, 147) [15], Pt_n (n = 2–20) [21] and Ir_n (n = 1–13) clusters [22].

Generally, clusters can be experimentally prepared by several methods, such as magnetron sputtering [23], laser vaporization [24,25,26] and chemical vapor deposition (CVD) [27]. Normally, a substrate is necessary for many applications of the clusters. The interaction between the cluster and substrate can affect both the geometric structure and physical properties of a cluster. For instance, under the influence of the cluster–substrate interaction, Fe_n (n = 2–7), (Mn_n (n = 2–7) and Si_n (n = 2–6, 10)) clusters on graphene prefer different growth modes and various orientations [28,29]. Additionally, the electronic and magnetic properties of the substrate can be effectively modulated by the adsorption of clusters [30,31,32,33]. When the Mn₅ cluster is absorbed on graphene, the magnetic moment of the Mn₅ cluster is enhanced by 186% because of the electron redistribution [29]. On the contrary, for Fe_n (n = 1, 4–6) clusters, the magnetic moment is reduced by 2–4 μ_B [28]. Furthermore, magnetic clusters can turn into stable nonmagnetic clusters when adsorbed on 2D substrates [33]. Interestingly, a large MAE can be achieved by absorbing clusters on substrates. Among them, Ir_n is a suitable candidate for nano-information storage devices and has been investigated extensively. Hu et al. [34] put an Ir₂ dimer on the double vacancy site of 2D hexagonal boron nitride (hBN) and obtained an enlargement in MAE (~126 meV) [35]. Meanwhile, we have also investigated the substrate effect on MAE of Ir₂ and found that MAE depends on the adsorption site and density [36]. However, from our limited knowledge, the interactions between magnetic clusters and substrates are still far from well known, especially on the MAE of larger clusters.

In this paper, by using first-principles calculations, we systematically study the interactions between Ir_n (n = 3–5) clusters and 2D substrates (graphene, hBN and germanene) [37]. Different ground state geometric structures of Ir_n and absorption sites of substrates are considered. We first investigate the geometric structures and stabilities with the help of cohesive and detachment energies. Then, we discuss the magnetic properties, including the magnetic moments and MAE, and explore the physics picture with the help of the local density of states and perturbation theory analysis. The present theoretical studies will provide insight into the substrate effect on larger magnetic clusters.

2. Materials and Methods

The structural, magnetic and electronic properties of Ir_n (n = 3–5) clusters adsorbed on 2D materials were studied by first-principles calculations, as implemented in the Vienna Ab-initio Simulation Package (VASP) code [38]. The ion–electron interaction was treated with the projector-augmented plane wave (PAW) potentials [39], and the exchange-correlation potential was described by generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) functional [40]. The wave functions were expanded in a plane wave basis set with an energy cut-off of 500 eV. The 2D substrates were chosen as 7 × 7 graphene, 7 × 7 hBN and 4 × 4 germanene supercells, respectively. To avoid the interaction between two neighboring layers, a vacuum space of 40 Å was added along the Z-direction. A k-mesh of 3 × 3 × 1 was used for the Brillouin zone. The atomic structures were fully relaxed without any symmetric constraints, with total energy and force convergence criteria of 10⁻⁴ eV and 0.01 eV/Å, respectively. For the calculations of the magnetic and electronic properties, the convergence criterion for the total energy was set to 10⁻⁶ eV, and the SOC effects were considered.

We employed binding energy (E_b, eV), cohesive energy (E_coh, eV/atom) and detachment energy (E_det, eV) to determine the most energetically favorable configuration of Ir_n/2D. E_b can be used to evaluate the interaction between the Ir_n cluster and the 2D substrate, which is defined as:

E_b = E_Irn + E_2D − E_Irn/2D

(1)

where E_Irn, E_2D and E_Irn/2D are the total energies of the free−standing Ir_n cluster, 2D substrate (graphene or hBN) and Ir_n/2D hybrid system, respectively. A larger E_b means a stronger interaction between Ir_n and the 2D materials. E_coh is the energy gain when isolated Ir atoms are assembled into the Ir_n cluster, which is defined as:

E_coh = (n × E_Ir − E_Irn)/n or E_coh = (E_2D + n × E_Ir − E_Irn/2D)/n

(2)

Here, n is the number of Ir atoms of the Ir_n cluster, E_Ir is the energy of an isolated Ir atom, E_Irn is the total energy of the free−standing Ir_n cluster and E_2D is the total energy of the 2D substrate, respectively. E_det is the energy gain when the Ir_n−1 cluster is transformed to Ir_n by adding one more Ir atom, which can be used to determine the most favorable cluster size n. For the free−standing cluster Ir_n or that on the 2D substrate, the detachment energy can be defined as:

E_det = E_Irn−1 + E_Ir − E_Irn or E_det = E_Irn−1/2D + E_Ir/2D − E_Irn/2D − E_2D

(3)

where E_Irn−1/2D and E_Ir/2D are the total energies of the Ir_n−1/2D and Ir/2D hybrid systems, respectively.

3. Results

3.1. Structural Properties

We investigated the structural, electronic and magnetic properties of the magnetic Ir_n clusters on different 2D substrates and then compared them with the free−standing ones. For the Ir_n (n = 3, 4, 5) clusters, we considered different isomers corresponding to the most stable configuration and the metastable ones. We then put the Ir_n cluster above three kinds of substates: graphene, hBN and germanene, respectively. Owing to the stronger interaction between the Ir and Ge atoms, the Ir_n cluster will dissociate and embed into the monolayer germanene, which can induce defected germanene. Taking Ir₃ clusters as the examples, we show the optimized configurations of Ir₃ adsorbed on germanene (see Supplementary Figure S1). Therefore, differently from our previous work in which the favorite adsorption site for the Ir₂ cluster was the single vacancy of germanene [36], we mainly discussed the graphene and hBN substrates. Three kinds of absorption sites have been considered: on the top of an atom (T), on the top of a C-C (B-N) bond (B) and on the top of a hexagonal-ring-center (H). Accordingly, the Ir_n cluster absorbed on the 2D substrate is named Ir_nm/2D-T (or B, H; see Figure 1), where n = 3, 4, 5 is the number of Ir atoms, m = a, b, c labels different isomers of free−standing Ir_n clusters, 2D is either graphene or hBN and T (or B, H) labels the absorption site of the nearest Ir atom.

As shown in Figure 1a,b, there are two relative stable configurations for the free−standing Ir₃ cluster: the line model (Ir_3a) and the triangle model (Ir_3b). Hereafter, we set the energy of the most stable configuration as zero and ΔE as the energy difference between the most stable and metastable configuration, as listed in

Table 1. The energy difference between the most stable configuration and its isomer (ΔE, eV), the binding energy (E_b, eV), the minimum distance between the cluster and the substrate (d, Å), the magnetic moment of the clusters (μ, μ_B) and the hybrid system (μ_tot, μ_B) and the transferred charge from the cluster to the 2D substrate (δ, e). The negative δ represents the electrons transferring from the cluster to the 2D substrate.

	ΔE	Eb	d	μ	μtot	δ
Ir3b/graphene-H	0	5.352	1.771	1.408	1.287	−0.163
Ir3b/graphene-BH	0.159	5.192	2.007	2.385	2.517	−0.221
Ir3a/graphene-HH	0.278	4.950	1.714	1.017	1.083	−0.269
Ir3b/hBN-TT	0	5.583	2.248	2.687	2.713	−0.0305
Ir3b/hBN-H	0.268	5.315	1.957	2.644	2.702	0.101
Ir3a/hBN-T	0.691	4.768	2.253	0.822	0.829	0.107
Ir4a/graphene-BB	0	4.818	2.662	4.929	4.973	−0.245
Ir4a/graphene-T	0.093	4.725	2.080	4.943	4.941	−0.104
Ir4b/graphene-H	0.462	5.607	1.895	0.548	0.259	−0.037
Ir4a/hBN-TT	0	5.546	2.363	1.535	1.519	−0.023
Ir4a/hBN-T	0.411	5.135	2.241	2.877	2.900	0.010
Ir4c/hBN-TTT	0.938	6.722	2.075	0	0	−0.133
Ir5a/graphene-H	0	5.434	1.989	4.516	4.539	−0.173
Ir5a/graphene-TTTT	0.586	4.847	2.374	2.181	2.196	−0.468
Ir5b/graphene-BB	0.645	5.029	2.595	2.452	2.452	−0.170
Ir5a/hBN-H	0	5.554	1.736	3.861	3.844	0.093
Ir5c/hBN-T	0.103	6.567	2.298	2.377	2.358	0
Ir5b/hBN-H	0.172	5.622	1.742	3.940	3.933	0.067

. Ir_3a is more stable than Ir_3b, with an energy difference of 0.124 eV. Ir_3a has an average bond length of 2.181 Å. These results are consistent with most previous PBE calculations [22,41] and PW91 calculations [33]. However, when absorbed on graphene or the hBN substrate, the Ir₃ cluster prefers the triangle model because of the substrate effect (see Figure 1c–h), which is similar to the Si₃ cluster absorbed on the graphene substrate [42]. ΔE is 0.159 eV (on graphene) and 0.268 eV (on hBN), respectively. For the graphene substrate, the most stable configuration is the Ir_3b/graphene-H (Figure 1c) hybrid system, in which the Ir₃ plane is perpendicular to the graphene sheet, the innermost Ir atom is located at the H site with a d (distance between the Ir atom and the substrate) of 1.771 Å and the other two Ir atoms are located at the B site. As opposed to Ir_3b/graphene-H, the most stable configuration is Ir_3b/hBN-TT (Figure 1f), in which the plane of the Ir₃ cluster has a tilt angle of 76.5° with a horizontal hBN sheet. Compared with Ir_3b/graphene-H, there is an inversion for the triangle model, in which two nearer absorbed Ir atoms form chemical bonds with N atoms with a d of 2.248 Å. Owing to two Ir-N bonds, Ir_3b/hBN-TT has an E_b of 5.583 eV, which is higher than that of Ir_3a/graphene-H (5.352 eV).

Figure 2 shows three kinds of relative stable Ir₄ configurations for the free−standing clusters, and those absorbed onto the graphene and hBN substrates, respectively. For the free−standing Ir₄ clusters, the square planar (Ir_4a, Figure 2a) is the most favorable configuration and has an average bond length of 2.338 Å. The most stable configuration and structure parameters are consistent with those in the previous report [22]. Unlike the Ir₃ cluster, the most stable configurations of Ir_4a remain unchanged on both the graphene and hBN substrate, along with a slight band angle deformation when they are adsorbed onto hBN. Figure 2e, h indicate that the metastable Ir₄ on either the graphene or hBN is still a square planar configuration. The difference is that that are two Ir atoms bonded with the substrate in the most stable configuration, but there is only one in the metastable structure. Therefore, ΔE decreases from 1.251 eV (free−standing Ir_4b) to 0.411 (Ir_4a/hBN-T) and 0.093 eV (Ir_4a/graphene-T), respectively. Similar to Ir_3b/hBN-TT, for Ir_4a/hBN-TT (Figure 2g), the Ir_4a cluster plane has a tilt angle of 75.1° with the hBN sheet because of the strong Ir-N interactions. As shown in Table 1, Ir₄/hBN has a higher E_b compared with Ir₄/graphene, which indicates a stronger interaction between the cluster and the substrate. Note that, because the configuration of the Ir_n cluster in Ir_n-2D may be different, a higher E_b indicates a stronger interaction between the cluster and the substrate and does not guarantee a higher stability. For example, as listed in Table 1, Ir_4c/hBN-TTT (Figure 2i) has a larger E_b, along with a higher total energy.

The free−standing Ir₅ isomers are listed in Figure 3a–c, in which Ir_5a (square pyramid model) is the most stable configuration, and the metastable ones are Ir_5b (square adding a co-plane triangle model, with an ΔE of 0.24 eV) and Ir_5c (triangular bipyramid model, with an ΔE of 1.117 eV), respectively. When it is absorbed on the 2D substrates, the square pyramid Ir_5a is still the most stable. A previous theoretical calculation also suggested that the square pyramid model of Ir₅ is more stable for both free−standing clusters [22,33,41] or on the monolayer graphene [43]. As shown in Figure 3d,g, the bottommost Ir atom of the cluster is located at the H site of the graphene (hBN) with a d of 1.989 (1.736) Å. Ir_5c/hBN-T is metastable owing to its higher E_b (6.567 eV), which is larger than that of Ir_5b/hBN-H (5.622 eV).

We employ E_coh and E_det to further discuss the favorable Ir_n clusters on the substrates. As shown in Figure 4a, E_coh increases with the number of cluster atoms (n) for both the free−standing Ir_n [33] and Ir_n/2D hybrid systems. Compared with the free−standing Ir_n cluster, Ir_n/2D possesses a higher E_coh, suggesting that the substrate effect can make the Ir_n cluster energetically stable. The E_coh of Ir₅ on graphene (hBN) is 5.19 (5.34) eV/atom, which is comparable with that from Ghazi’s works [43,44]. As plotted in Figure 4b, for free−standing clusters, that the maximum of E_det belongs to the Ir₄ configuration indicates that Ir₄ is the favorite Ir_n cluster. After being absorbed on the substrates (either graphene or hBN), Ir₃/2D turns out to be the most stable configuration due to it having the largest E_det.

3.2. Magnetic Properties

We next discuss the magnetic properties of Ir_n clusters on graphene and hBN. By setting different spin directions in Ir_n, we can determine what the magnetic ground state (ferromagnetic or anti-ferromagnetic) is. For all the stable configurations, including the free−standing Ir_n and Ir_n on the substrates, the ferromagnetic ground state is more energetically favorable, as shown in Supplementary Table S1. The total magnetic moments of the free−standing Ir_3a and Ir_3b are 0.947 μ_B and 2.654 μ_B, respectively. The total magnetic moments of Ir_4a, Ir_4b and Ir_4c are 6.509 μ_B, 3.583 μ_B and 0 μ_B, respectively. These results are consistent with the previous calculations [22,33]. Moreover, the total magnetic moments of Ir_5a, Ir_5b and Ir_5c change to be 5.574 μ_B, 7.641 μ_B and 7.562 μ_B, respectively. As listed in Table 1, except for Ir_3a/graphene-HH and Ir_3b/hBN-TT, the magnetic moments of the Ir_n clusters on the 2D substrates decrease more or less. Compared with the free−standing Ir_n cluster, the magnetic moments of the most stable Ir_n clusters adsorbed onto the substrates were reduced to 53% (Ir_3b/graphene-H) and 23.6% (Ir_4a/hBN-TT), respectively. Furthermore, for metastable Ir_4b/graphene-H, the magnetic moment of the Ir_4b cluster is only 0.548 μ_B (84.7% reduction). The variation of the magnetic moment caused by the substrate effect or adsorption site can be understood by the charge transfer between the cluster and the 2D sheet.

Table 1 lists the charge transfer (d) between Ir_n and the substrates from the Bader analysis [45]. Interface bonds may form between the Ir_n cluster and the substrate due to the electron transferring. Firstly, the magnitude of d on graphene is generally larger than that on hBN and relies on the absorption site. Secondly, for the considered Ir_n/graphene, electrons transfer from the Ir_n cluster to the graphene sheet, corresponding to a negative d. On the contrary, the transfer direction depends on the bonded atom number when the clusters are absorbed onto the hBN substrate. Specifically, if one Ir atom is attached to the substrate, such as in Ir_3b/hBN-H (as shown in Figure 1), the charges transfer from hBN to Ir_n (d > 0). If two or more atoms are attached to the substrate, such as in Ir_3b/hBN-TT, the transfer direction is reversed (d < 0).

The density of states (DOS) of the most stable free−standing Ir_n and Ir_n/2D hybrid systems is shown in Figure 5. Generally speaking, the DOS of the Ir_n cluster is perturbed due to the substrate effect. The substrate effect can be divided into two parts: energy level repulsion and charge transfer. From the DFT calculations, the projected DOS indicated that d_xz states are induced from the energy level repulsion between the d_z² states of Ir_n and the p_z of C (N) atoms. Meanwhile, the energy level repulsion shifts the states and increases or decreases the magnetic moments of Ir_n. Taking Ir₃ as an example, the magnetic moment of Ir_3b (2.654 mB) is increased to 2.687 μ_B on hBN but decreased to 1.408 μ_B on graphene. Similar changes can also be found for the Ir₄ and Ir₅ clusters (see Table 1). The charge transfer can be quantitatively characterized by the Bader analysis (Table 1) and qualitatively characterized by the Charge Density Difference (CDD). The CDD in Figure 6 demonstrates that charge redistribution takes place at both the interface region and the Ir_n cluster. Note that, differently from other Ir_n/2D hybrid systems, the electrons in the Ir_5a/hBN-H structure transfer from hBN to Ir atoms, as listed in Table 1. Accordingly, positive charge density dominates the interface region in Figure 6f.

Finally, we discuss the substrate effect on the magnetic anisotropy energy (MAE) of the Ir_n clusters. MAE is defined as the energy difference between different easy axes (parallel (//) and perpendicular (⊥) to the 2D substrate) per Ir atom, i.e., MAE (in meV/Ir atom) = E_// − E_⊥. The MAE values of the free−standing Ir_3b, Ir_4a and Ir_5a are 11.57, 10.05 and 32.43 meV, respectively, which are consistent with previous theoretical calculations [22]. However, owing to the slight structural difference, the MAE of the free−standing Ir_4b (9.32 meV) is lower than that yielded from Ge’s calculation (40.26 meV) [41]. Figure 7 plots the MAE of the free−standing Ir_n clusters, Ir_n/graphene and Ir_n/hBN. Clearly, with the increase in n (from 3 to 5), the Ir_n clusters experience an easy-axis direction change. More importantly, under the influence of the substrate effect, the MAE is enlarged by about 4 times for the Ir_3b/graphene and by 12 times for the Ir_4a/graphene.

MAE can be understood with the help of the second-order perturbation approach [46], which is defined as:

$$\mathrm{MAE}={\xi }^2{\displaystyle \sum }_{\mathrm{U},\mathrm{O}}\frac{{\left|<\mathrm{O}\left|l_{\mathrm{z}}\right|\mathrm{U}>\right|}^2-{\left|<\mathrm{O}\left|l_{\mathrm{x}}\right|\mathrm{U}>\right|}^2}{E_{\mathrm{U}}-E_{\mathrm{O}}}$$

(4)

where $\xi$ is the SOC constant, O (U) stands for the occupied (unoccupied) states, E_O (E_U) stands for the corresponding energy eigenvalues and l_z (l_x) is the orbital angular momentum operator. As described by Equation (4), the coupling spin orbital matrix element difference, i.e., |<O|l_z|U>|² − |<O|l_x|U>|², contributes to the value of MAE, including different coupling orbitals and various coupling factors. Figure 8 shows the d orbital-resolved MAE of the free−standing Ir_n cluster and Ir_n/graphene (Ir_n/hBN). As shown in Figure 8b, the main contribution of the free−standing Ir_3b cluster to the MAE comes from the matrix element difference between the d_xz and d_z² orbitals. However, Figure 8a,c indicate that the main contributions on the substrate changed to d_xy and d_x²_−y² orbitals for both the hBN and graphene, owing to the d_z²-to-d_xy orbitals transition, as discussed above. For Ir_4a, Figure 8e (free−standing) and Figure 8f (Ir_4a/hBN) suggested that the interaction between d_xz and d_xy is the main contribution for MAE, which results in a smaller MAE. In Ir_4a/graphene, we found that the d orbital is closer to the Fermi level, resulting in a higher MAE. Finally, the interactions between d_x²_−y² and d_xz (d_xy) determine the MAEs of the free−standing (on substrates) Ir_5a clusters. The positive (negative) contributions given by the matrix element difference between different orbitals and coupling factors result in different MAE values, as discussed in reference [46].

4. Conclusions

In conclusion, the structural and magnetic properties of Ir_n (n = 3–5) clusters adsorbed on 2D substrates (graphene and hBN) were systematically investigated using the DFT method. The calculated results show that, after the structure relaxation, the stability order of Ir_n may change on 2D substrates. The detachment energies suggest that, for the free−standing Ir_n, the most favorite cluster is the one of n = 3. After being absorbed on 2D substrates, the most stable cluster changes to n = 4. The magnetic moments of Ir_n generally decrease owing to the charge transfer between the Ir_n and the substrates, which depends on the substrate type and adsorption site. The MAE of the Ir_n cluster can be enlarged by 12 times for Ir_4a/graphene, which is understood with the help of the second-order perturbation approach.