Transition metal oxide (TMO) surfaces currently have a wide range of applications in energy and environmental science, such as catalysts for clean energy conversion, cleanup of air pollutants, and sensors for chemical and biomedical devices [1, 2]. Understanding the surface chemistry and structure–activity relationship of TMOs is therefore important for the further development of these applications [3]. In particular, 3d TMOs are notable because of their involved spin states and magnetism, which is sensitive to surface orientation and particle size [4-7]. For instance, the spin states of Co ions (rather than number of 3d electrons) in perovskite oxides play a critical role in their oxygen evolution activity [8]. In addition to oxides, the spin states of molecules such as O₂ influence their corresponding dissociation activity on oxides [9] and even simple metal surfaces [10]. Magnetism can be induced in metal oxides that are paramagnetic in bulk by surface adsorption and reaction [11, 12]. It is therefore interesting to study the influence of the spin states and magnetism of oxides on their surface chemistry.

Late 3d transition metal monoxides (MnO, FeO, CoO, and NiO) with cubic rock salt structure (Fm3m) [13, 14] are of particular importance in the study of antiferromagnetic (AFM) TMOs, and are often considered as model AFM systems. Besides their relatively high Neel temperature (T_N) and chemical stability, their large band gap (E_G) and insulating electronic structure allow their magnetic properties to be accurately described in terms of magnetic moments localized on transition metal cations [15, 16]. The anisotropic interaction between neighboring magnetic moments leads to long-range magnetic ordering, known as type-2 antiferromagnetism (AFM2), below T_N [17-20] and stacking of ferromagnetic (FM) (111) planes with opposite spin directions in adjacent layers, as identified by neutron diffraction [21]. Using magnetic exchange force microscopy, the magnetic order of surface nickel ions on the NiO(001) surface has been measured directly in real space [22-26]. Despite the definite AFM order of magnetic ions in the perfect bulk crystal below T_N, the ordering of magnetic ions on the surface can be changed under different conditions. For example, by engineering defects in the lattice of AFM NiO, a FM ordering dislocation can be introduced [27]. When the size of AFM NiO decreases to the nanoscale, the resulting decrease of coordination and lattice distortion can drive the phase transition to a FM-like phase [27, 28].

The magnetism of metal ions in late 3d TMOs originates from their partially filled 3d states, which are famous for their highly correlated nature [29]. It remains challenging to accurately describe strongly localized and correlated d electrons using standard density functional theory (DFT) approaches such as the local density approximation (LDA) or generalized gradient approximation (GGA) [30, 31]. Both the LDA and GGA often fail to predict E_G of these TMOs [32]. For instance, both CoO and FeO were predicted to be metallic. Although NiO and MnO were predicted to have E_G, the calculated values were severely underestimated [33]. Nevertheless, E_G of these materials can be opened in calculations by adding a Hubbard U term describing the strong on-site Coulomb repulsion to the LDA or GGA (DFT+U) [34, 35]. Compared to higher-level theories such as the hybrid functional or many-body perturbation [31, 36], DFT+U can substantially improve the calculation accuracy without increasing the computational cost, as demonstrated for the adsorption of CO and NO on NiO(001) [37, 38]. Simulation of water dissociative adsorption on NiO(111) was reported recently, and the calculation was found to be fairly insensitive to the choice of the DFT+U functional [39].

Chemically equivalent oxide surfaces may become inequivalent when considering the different symmetry of various long-range magnetisms. Because surface chemistry is largely decided by local environment (geometry and composition), it is currently unclear how the different magnetisms affect surface chemistry. Furthermore, the influence of different surfaces on magnetisms is still unknown. This influence may be mediated by reactants with different spin and/or magnetic moments. To clarify these issues, here NiO as a model system is studied by the GGA +U method. A number of magnetic phases, including AFM1, AFM2, AFM3, AFM4, AFM5, and FM, are considered. NiO(001) and NiO(110) surfaces are used to study the sensitivity of these magnetic phases to structure. While CO and NO adsorbed on NiO(001) of AFM2 has been studied to verify the DFT+U scheme treatment for strongly correlated systems [37, 38], here we use the adsorption of paramagnetic molecule NO and nonparamagnetic molecule CO to probe the influence of magnetism on molecule adsorption by NiO surfaces.

DFT calculations were performed with the Vienna ab initio simulation package (VASP) [40] based on the projected augmented wave (PAW) method [41, 42]. The spin-polarized Perdew Burke Ernzerhof (PBE) [43] exchange-correlation functional and on-site Coulomb repulsion U term for d electrons in the spirit of Hubbard according to Dudarev's approach [35] were used to describe electron exchange and correlation. An effective U of 5.3 eV for Ni was used throughout the present work, because it could reproduce well bulk properties and CO/NO adsorption on NiO(001) surfaces [37].

Because partially occupied d orbitals are strongly localized at Ni²⁺, a net spin magnetic moment was assigned to each Ni²⁺. For the cubic sublattice of magnetic ions, all magnetic ions having parallel spin means there is FM order (Figure 1(a)). In contrast, the series of common AFM configurations of Ni²⁺ AFM1–AFM5 (as shown in Figure 1(b-f)) can be described as oppositely stacked FM layers in direction G with super lattice periodicity p in which Ni²⁺ maintain parallel spin within p layers [44]. Below T_N = 523 K, the ground-state magnetic configuration of NiO is AFM2 [21]. We considered AFM1–AFM5 and FM magnetic order as a starting point to construct surfaces with different surface magnetic order by truncation of bulk NiO.

Four layers of an NiO(001) slab surface supercell and five layers of an NiO(011) slab (4×4) surface supercell were used to model the adsorption of molecules on NiO(001) and NiO(011) surfaces, respectively. Slabs were separated by 12 Å of vacuum with the bottom two layers fixed at the bulk truncated structure, and dipole correction perpendicular to each slab was imposed. The layer thickness and vacuum size were found to converge for adsorption of CO/NO on AFM2. Surface energy was evaluated with symmetric slabs of the minimum surface cell for each surface until they converged to less than 1 meV/Ų with respect to slab thickness. A plane wave cutoff of 400 eV and k-point grids of (4×4×1) for NiO(001)- and (3×2×1) for NiO(011)-(2×4) were used. Geometrical optimization was performed until the force on relaxed atoms was less than 0.02 eV/Å.

Table 1 lists the optimized equilibrium lattice constant, energy difference per NiO formula with respect to the lowest energy state (AFM2), localized magnetic moment on Ni, and band gap for the various magnetic phases considered. The energetically most favorable long-range magnetic phase is AFM2, which is consistent with the structure of NiO below T_N determined by neutron diffraction. The energy difference between different magnetic phases can be as large as 102 meV/NiO. AFM2 has the smallest lattice constant (a = 4.19 Å) and magnetic moment of Ni (m =1.71 μ_B), but the largest E_G of 3.25 eV for the magnetic phases. The present work agrees well with the results of a previous SGGA+U calculation (a = 4.20 Å, m = 1.72 μ_B, E_G= 3.2 eV) [37]. For the other AFM phases, the lattice constant and magnetic moment increase by 0.02 Å and 0.10 μ_B at most, respectively, but E_G decreases by 1.16 eV. It is clear that the lower the energy of the magnetic phase, the smaller the lattice constant and magnetic moment and the larger the E_G. These trends originate from the superexchange interaction of the second nearest neighbor (NN) Ni²⁺, as rationalized in an earlier theory for rock salt transition metal monoxides [33, 45].

To understand the origin of the AFM behavior of NiO, we fitted the calculated energy in Table 1 to the Ising model of magnetic moment interaction [19]. The fitting result gives i-th NN magnetic moment exchange pair interactions J_i (i = 1, 2, 3, and 4) of 0.71, -15.58, -0.24, and 0.07 meV, respectively. This means that the second NN interaction (J₂) is the dominant interaction and the negative value indicates the preference for AFM order, similar to the behavior of CoO and MnO [18, 19]. Because J₁, J₃, and J₄ are much smaller than J₂, the number of second NN pairs determines the relative stability of the various AFM phases. For AFM2, all the second NN pairs are antiparallel, so it is energetically the most favorable state of NiO.

In this work, a Ni atom with an upward (or positive) magnetic moment (↑) means that the electron population of the spin-up component is larger than that of the spin-down, whereas a Ni atom with a downward (or negative) magnetic moment (↓) means that the electron population of the spin-down component is larger than that of the spin-up. The spin-resolved density of states (SDOS) of Ni (↑) in bulk NiO-AFM2 is illustrated in Figure 2. For the 3d_{xy, yz, xz}(t_2g) band, both the spin-up and spin-down components are distributed in the valence band. Compared with the spin-up component, the electrons in the spin-down component mainly populate the upper/top part of the valence band. For the 3d_{x²–y², z²} (e_g) band, the marked exchange splitting causes the e_g states to be well separated (by ~9.69 eV). In particular, the spin-down components are distributed in the conduction band. Most of the spin-up components are distributed in the lower part of the valence band, and a small amount are distributed close to the top of the valence band. The gap between the valence band maximum (VBM) and conduction band minimum (CBM) of the Ni 3d band is 3.23 eV, which is nearly same with as the E_G of bulk NiO (3.25 eV). For Ni(↓), the corresponding components are simply reversed. As shown below, these features are essential for the hybridization between Ni and CO/NO molecules.

For rock salt crystals, the (001) plane is chemically equivalent with (010), (100), (001), (010), and (100): all belong to the {001} plane family, and the corresponding primitive cell is (1×1). A long-range magnetic phase lowers the corresponding symmetry and decreases the degeneracy of the {001} plane family. The nonequivalent planes depended on the long-range magnetic phase (AFM1–AFM5), as classified in Table 2 and plotted in Figure 3. Each of AFM1, AFM3, AFM4, and AFM5 had two nonequivalent planes, whereas AFM2 had only one nonequivalent plane. This led to nine nonequivalent surfaces with different primitive cells, although they are all chemically equivalent.

Taking AFM1-(100) (Figure 3(b)) as an example, the magnetic moments of the first NN Ni pair are exclusively antiparallel (↑↓). Similar behavior was found for AFM3-(001) (Figure 3(d)). In contrast, for AFM1-(001) (Figure 3(a)) and AFM4-(001) (Figure 3(f)), the magnetic moments of the first NN Nipair are exclusively parallel (↑↑). For the remaining five surfaces shown in Figure 3, both the (↑↓) and (↑↑) configurations coexist in the first NN Ni pairs, forming different surface magnetism patterns. The different local magnetic pairs along with their long-range magnetic phases provide a good playground to investigate the influence of magnetism on surface properties. Figure 4 plots the SDOS of a surface Ni atom (↑) from AFM2-(001). The overall features remain the same as that of AFM2 bulk (Figure 2). The main difference is the gap between the VBM and CBM of the Ni 3d band, which decreases from the bulk value of 3.23 to 2.81 eV.

The calculated surface energies are presented in Table 2. The surface energies range from 49 to 54 meV/Ų, and the difference between different magnetic phases is less than 5 meV/Ų. To rationalize this small variation, we note that the surface energy increases mainly from the cost of Ni-O bond cleavage when creating a new surface. Considering the exchange coupling between magnetic cations, cleavage of the Ni-O bond might introduce an additional cost originating from the loss of the corresponding exchange interaction. Because the exchange interaction between Ni²⁺ is largely determined by J₂, the estimated cost of breaking the J₂ interaction when creating a new surface is ~1.7 meV/Ų. Namely, the contribution from the long-range AFM phases to the surface energy is indeed small. Compared to the calculated overall surface energy, the contribution from magnetism (~3%) is negligible.

CO and NO adsorption on these nonequivalent surfaces at a coverage of 0.25 monolayer with respect to surface Ni was studied. Various adsorption sites were considered, and the results for adsorption at the energetically most favorable sites are given in Table 3. For the nonequivalent surfaces considered, calculated CO adsorption energies varied from −0.33 to −0.37 eV, while NO adsorption energies were more exothermic and ranged from −0.42 to −0.46 eV. The small change of adsorption energies (0.04 eV; less than 10%) reveals the weak influence of the long-range magnetic phases on both CO and NO adsorption. The calculated adsorption energies are in good agreement with those obtained from a previous GGA+U calculation on a (001) surface of NiO with AFM2 magnetic order and thermodesorption and infrared experiments (−0.30 to −0.45 eV for CO and −0.52 to −0.57 eV for NO) [37, 38, 46-48].

In line with its weak binding strength, CO adsorption induces little change of the magnetism (less than 0.02 μ_B) of CO and coordinated Ni atom. As shown in Figure 5(a), CO adsorbed nearly perpendicularly at the top of a Ni atom. The optimized Ni−C bond length varied from 2.02 to 2.07 Å, where a shorter bond length indicates stronger binding. Meanwhile, the C−O bond length of 1.14 Å was the same as that of gas-phase CO. Small tilting of the angle between the Ni−C and C−O bonds could be energetically favorable; however, the variation of the corresponding potential energy surface was less than 10 meV for tilt angles up to 30° [37].

The bonding mechanism between CO and a coordinated Ni atom can be inferred from the corresponding SDOS plotted in Figure 5(b). The hybridization is mainly between the CO 5σ orbital and Ni 3d_z² band in the bottom of the valence band (donation). In addition, there is weak hybridization between CO 2π^* and Ni 3d_x²–y² in the conduction band (back donation). The fact that both hybridizations appear far from the Fermi level rationalizes well the weak binding strength of adsorbed CO. Direct visualization of the bonding between CO and Ni can be better seen from the difference of electron density (Figure 5(c) and (d)). Pronounced charge accumulation between CO and coordinated Ni is observed, which indicates the dominating role of the donation interaction in CO adsorption on a NiO(001) surface.

Compared with the case for CO adsorption, NO binds more strongly to Ni with a tilted configuration (Figure 6(a)), in agreement with previous studies of NO adsorption on NiO(100) [38] and transition metal surfaces [49, 50]. For instance, on AFM2-(001), the tilt angle is 10.7° for the Ni−N bond and 49.5° for the N−O bond. Depending on the magnetic phase (Table 4), the optimized Ni-N bond length varies in the range of 1.98–2.05 Å, and the configuration with a shorter Ni−N bond length is consistent with stronger binding. The N−O bond length (1.17–1.18 Å) is nearly the same as that of the gas phase (1.17 Å). After NO adsorption, the magnetic moments of NO and coordinated Ni decrease by about 0.10 and 0.20 μ_B, respectively. Interestingly, the magnetic moment of adsorbed NO is always antiparallel with coordinated Ni irrespective of the surfaces magnetic phase; this will be discussed further later.

Upon NO adsorption, the hybridization between the NO 5σ orbital and Ni 3d_z² band in the bottom of the valence band decreases slightly (Figure 6(b)). Compared to the CO 2π^* orbital, which is completely unoccupied, the NO 2π^* orbital in the top of the valence band is partially occupied. For Ni(↑), it is mainly the Ni 3d_{xz, yz} spin-down component populated in the top/upper part of the valence band. To maximize the hybridization between NO 2π^* and Ni 3d_{xz, yz} in the top/upper part of the valence band, the occupied NO 2π^* must populate the spin-down component. In other words, the favorable configuration of magnetic moment between NO and coordinated Ni is antiparallel, namely, NO(↓) and coordinated Ni(↑), which is also found for NO adsorption on NiO(011).

Regarding the decrease of the magnetic moment of adsorbed NO, we note that the peak intensity of NO 2π^* at the top of the valence band is smaller than those of the three other peaks of NO 2π^* in the conduction band. This indicates the electron depletion in the corresponding states (spin-down component), and accordingly, the NO magnetic moment decreases. Similarly, the decrease of the magnetic moment of coordinated Ni can be rationalized by the depletion of Ni 3d_z² states (lower peak intensity) at the bottom of the valence band (spin-up component).

Compared to CO adsorption, the extra hybridization between NO 2π^* and Ni 3d_{xz, yz} in the valence band strengthens the binding between NO and the coordinated Ni atom. The direct participation of the NO 2π^* orbital can be clearly seen from the difference of electron density plotted in Figure 6(c) and (d). Moreover, the magnitude of the difference of electron density induced by NO adsorption is about five times larger than that of CO (Figure 6(d) versus Figure 5(d)). The larger extent of electron redistribution induced by NO than by CO corroborates well with its stronger binding strength. For both CO adsorption (Figure 6(c) and (d)) and NO adsorption (Figure 5(c) and (d)), the adsorption-induced charge redistribution is limited to the singly coordinated Ni atom, and electrons of the NN Ni are hardly affected. In other words, the long-range magnetic phase has little influence on NO and CO adsorption on NiO(001).

Without considering the magnetic phases, the {011} plane family consists of twelve equivalent planes. When taking into account the magnetism, the symmetry and degeneracy are broken. As listed in Table 5 and plotted schematically in Figure 7, for AFM1, AMF2, AFM3, and AFM4, there are two nonequivalent surfaces, and for AFM5, there are three inequivalent surfaces. This gives a total of eleven nonequivalent surfaces. For nonequivalent AFM1-(011), AFM2-(011), AFM3-(110), and AFM5-(101) surfaces, the local magnetic moments of the two adjacent surface Ni atoms are exclusively antiparallel (↑↓). Conversely, for nonequivalent AFM1-(110), AFM2-(011), AFM4-(110), and AFM5-(101) surfaces, the local magnetic moments of two adjacent surface Ni atoms are exclusively parallel (↑↑). For the nonequivalent AFM3-(011), AFM4-(011), and AFM5-(011) surfaces, both (↑↓) and (↑↑) pairs (noted as X1 and X2, respectively) coexist.

The calculated energies of {011} surfaces are summarized in Table 5. For the nonequivalent surfaces, the calculated surface energies vary from 162 to 172 meV/Ų. These energies are about three times larger than those of NiO{001}, because more Ni−O bonds (per unit area) are broken to create the new surface from the bulk material. In contrast, the surface energies of the nonequivalent surfaces belonging to the same AFM phase differ only by 1 meV/Ų. This means that the variation of the surface energies by 10 meV/Ų mainly originates from the different long-range magnetic phases. Although the absolute variation of surface energies is about twice that of NiO{001} surfaces, the contribution to the overall surface energies remains small (~6%). This shows again the weak effect of the magnetic phases on surface energies.

Figure 8 plots the SDOS of a surface Ni atom (↑) of AFM2-(011). The 3d_x²–y² and 3d_yz states are populated mainly in the bottom of the valence band (spin up) and the lower part of the conduction band (spin down), while 3d_z², 3d_xz, and 3d_xy are populated in the valence band. The upper part of the valence band originates largely from Ni 3d_{xy, xz} (spin down). Another prominent feature is the gap between the VBM and CBM of the Ni 3d band of 1.40 eV, which is much smaller than that of AFM2-(001) (2.81 eV) and AFM2 bulk (3.23 eV). The smaller 3d band gap of the surface Ni might facilitate its hybridization with adsorbed molecules, which will be discussed below.

CO adsorption on these nonequivalent surfaces was studied, and the results at the most favorable sites are listed in Table 6. CO prefers to adsorb exclusively via the end of the C atom at the bridge site of two adjacent Ni atoms, labeled as A and B (Figure 9(a) and (c)). Irrespective of the nonequivalent surfaces and different bridge sites (↑↑ and ↑↓) considered, CO has similar adsorption energies at the (↑↓) bridge sites (Figure 9(e)); the calculated adsorption energies vary from −0.73 to −0.75 eV. Conversely, for CO adsorption at the (↑↑) bridge sites (Figure 9(b)), the calculated adsorption energies are smaller (−0.71 to −0.72 eV). Thus, the local magnetic moment and its relative direction of two coordinated Ni atoms are responsible for the variation of the calculated adsorption energies rather than the long-range magnetic phases. The calculated binding strengths of CO on NiO {011} are about twice that of CO on NiO{001}, which possibly arises from the greater number of Ni−C bonds involved and the lower coordination number of surface Ni atoms.

Important geometrical parameters and the bond lengths between C and two coordinated Ni atoms are given in Table 6. The optimized C-Ni bond lengths are in the range of 2.13–2.23 Å, and longer than those of CO adsorbed on NiO(001) (2.02–2.07 Å). Irrespective of the magnetic phases considered, the C−O bond lengths stayed at a constant value of 1.15 Å, which is 0.01 Å longer than that of gas-phase CO. CO adsorption has little influence on the surface magnetism: the magnetic moment for CO and coordinated Ni atoms decreased by only about 0.02 and 0.05 μ_B, respectively.

SDOS for CO adsorption at the (↑↑)-bridge sites of AFM2 NiO(011) are plotted in Figure 10(a). The magnetic moments of both Ni(A) and Ni(B) point upwards, which are denoted as Ni(A, ↑) and Ni(B, ↑), respectively. Figure 10(a) reveals that the spin-up components of Ni(A, ↑) and Ni(B, ↑) are nearly completely occupied. The hybridization occurs mainly via Ni(A, ↑)/Ni(B, ↑) back-donation towards CO. In contrast, the spin-down components of Ni(A, ↑) and Ni(B, ↑) are partially occupied, and hybridization occurs via CO donation to Ni(A, ↑)/Ni(B, ↑). Back donation in the spin-up component but donation in the spin down can be easily visualized in the spin-resolved difference of electron density results plotted in Figure 10(b) and (c). For the spin-up case, there is pronounced charge depletion from both Ni(A, ↑) and Ni(B, ↑) and accumulation in CO 2π^* (back donation). For the spin-down component, there is charge depletion caused by CO 5σ donation and accumulation mainly between CO and Ni(A, ↑)/Ni(B, ↑).

SDOS for CO adsorption at the (↑↓) bridge sites of AFM2(011) are plotted in Figure 10(d), where the magnetic moments of Ni(A) and Ni(B) respectively point upwards (↑) and downwards (↓), and are denoted as Ni(A, ↑) and Ni(B, ↓), respectively. For the spin-up component, Ni(A, ↑) is nearly fully occupied and Ni(B, ↓) is partially occupied. Accordingly, the hybridization takes place via Ni(A, ↑) back donation toward CO, but CO donation toward Ni(B, ↓). This can be observed in the spin-resolved difference of electron density of the system (Figure 10(e) and (f)). There is modest charge depletion at Ni(A, ↑) for back donation and pronounced charge accumulation between CO and Ni(B, ↓) for CO donation. The relative larger extent of charge accumulation between CO and Ni(B, ↓) than that of charge depletion at Ni(A, ↑) indicates that donation rather than back donation plays a dominant role in the overall hybridization between CO and Ni. For the spin-down component (Figure 10(d)), Ni(B, ↓) is nearly fully occupied and Ni(A, ↓) is partially occupied. Accordingly, the hybridization takes place via Ni(B, ↓) back donation toward CO and CO donation toward Ni(A, ↑). The distinct hybridization and charge redistribution for CO at the (↑↓) bridge sites from that of the (↑↑) bridge sites is in contrast to their similar adsorption energies (which differ by less than 0.03 eV).

NO adsorption also occurs preferentially at the bridge site of two adjacent Ni atoms via the end of the N atom (Figure 9(c) and (f)). For all nonequivalent surfaces considered, the calculated adsorption energies for NO at the (↑↓) bridge sites are in the range of −0.99 to −1.05 eV and in the range of −1.21 to −1.30 eV at the (↑↑) bridge sites. Different from CO, the binding strengths at the (↑↑) bridge sites are about 0.3 eV stronger than those at the (↑↓) bridge sites. Moreover, the NO binding strength on NiO(011) is about three times stronger than that of NiO(001). For adsorption on (↑↑) or (↑↓) bridge sites, the difference of adsorption energy with variation of bulk magnetic order and surface index is less than 0.10 eV. In contrast, the variation of NO adsorption energy on all studied NiO(001) surfaces did not exceed 0.04 eV. This indicates that the larger variation of binding strength at all (↑↑) bridge sites (or (↑↓) bridge sites) of NiO(011) than that of NiO(001) may be simply caused by the higher surface activity of NiO(011). However, the difference of binding strength between adsorption at (↑↑) bridge sites and that at (↑↓) bridge sites of NiO(011) cannot be attributed to this reason. Again, the importance of the local magnetic order rather than the long-range magnetic phase is found here.

Important geometrical parameters for NO adsorption on NiO(011) are given in Table 7. Irrespective of the different magnetic phases considered, the N−O bond lengths stay constant at 1.19 Å, 0.02 Å longer than that of gas-phase NO. For NO adsorption at the (↑↑) bridge sites, the two N−Ni bond lengths are nearly same (1.96–1.97 Å). The corresponding NO magnetic moment prefers to align antiparallel with the two coordinated Ni(↑), namely, as NO(↓), as also found for NO adsorption on NiO(001). The magnetic moments of NO and coordinated Ni atoms decreased by at most 0.25 and 0.13 μ_B, respectively. For NO adsorption at the (↑↓) bridge sites, the two N−Ni bond lengths were not the same. The shorter one varied from 1.93 to 1.97 Å. The magnetic moments of NO and Ni corresponding to the shorter N−Ni bond pointed downwards (↓) and upwards (↑), decreasing by at most 0.43 and 0.20 μ_B, respectively. The longer N−Ni bond length varied from 2.03 to 2.09 Å, and there was little change of the magnetic moment of coordinated Ni(↓), which is understandable because of its relative longer N−Ni bond length.

Calculated SDOS for NO at the (↑↑) bridge sites of AFM2 NiO(011) is plotted in Figure 11(a), where the magnetic moments of both Ni(A) and Ni(B) point upwards and are denoted as Ni(A, ↑) and Ni(B, ↑), respectively. As noted above, the NO magnetic moment prefers to point downward (↓); namely, there are more electrons occupied in the NO spin-down component than in the spin-up component. More electrons in the NO spin-down component would facilitate the corresponding donation process. This was verified in the spin-resolved difference of electron density results plotted in Figure 11(b) and (c), where charge accumulated between NO and coordinated Ni(A, ↑)/Ni(B, ↑). For the spin-up component, less electron occupation of the NO orbital would facilitate the corresponding back donation. This can be found in Figure 11(b) and (c), where charge depleted from coordinated Ni(A, ↑)/Ni(B, ↑) and accumulated in the NO molecule.

Calculated SDOS for NO adsorbed at the (↑↓) bridge sites of AFM2(011) is plotted in Figure 11(d), where the magnetic moments of Ni(A) and Ni(B) point upwards and downwards and are denoted as Ni(A, ↑) and Ni(B, ↓), respectively. The N−O bond length with Ni(A, ↑) is shorter than that with Ni(B, ↓), and the NO magnetic moment points downward accordingly. The hybridization between NO(↓) and Ni(A, ↑) with antiparallel magnetic configuration is essentially the same as that for NO adsorption on AFM2(011) because the electronic and magnetic configurations are the same. This can be seen further in the corresponding difference of electron density plots (Figure 11 (e) and (f)). Conversely, for NO(↓) and Ni(B, ↓) with same orientation of magnetic moments, the electronic hybridization between NO and Ni(B) is limited. Indeed, the difference of electron density (Figure 11(e) and (f)) between NO and Ni(B) becomes negligible, particularly in the spin-down component. This rationalizes well the weaker binding strength of NO adsorption at the (↑↓) bridge sites than that of NO at the (↑↑) bridge sites.

By constructing surface models of NiO with different magnetic phases, and using the paramagnetic molecule NO and nonparamagnetic molecule CO to probe the reactivity on (001) and (011) surfaces, we investigated the influence of magnetism on the surface chemistry of NiO. When the favorable adsorption sites involve only a single Ni cation, such as NO/CO adsorption at the top site of a Ni cation on the (001) surface, the long-range magnetic phases make little contribution to the overall adsorption behavior. The adsorption strength is primarily determined by chemical environment (such as surface orientation, coordination number, and adsorbed species). When the favorable adsorption site involves two adjacent Ni cations, such as NO/CO adsorption at the bridge site of two Ni cations in NiO(011), the local magnetic order of Ni ions coordinated to the adsorbed molecule rather than the long-range magnetism makes a considerable contribution to the overall adsorption behavior. For nonparamagnetic molecule CO, the orbital hybridization for adsorption at the (↑↑) bridge sites is very different from that at the (↑↓) bridge sites, despite their incidental similar adsorption energies. For paramagnetic molecule NO, the hybridization at the (↑↑) bridge sites is different from that at the (↑↓) bridge sites, and the binding strength of the former is about 0.3 eV stronger than that of the latter. The present work highlights the importance of the local magnetic order of TMO surfaces on molecule adsorption, particularly for paramagnetic molecules, at multi-fold sites.

Acknowledgments

We are grateful for the fruitful discussion with Prof. Hong Jiang.