Electronic Structure and Ferromagnetism Modulation in Cu/Cu2O Interface: Impact of Interfacial Cu Vacancy and Its Diffusion

Cu/Cu2O composite structures have been discovered to show sizable ferromagnetism (FM) with the potential applications in spintronic devices. To date, there is no consensus on the FM origin in Cu/Cu2O systems. Here, first principles calculations are performed on the interface structure to explore the microscopic mechanism of the FM. It is found that only the Cu vacancy (VCu) adjacent to the outermost Cu2O layer induces a considerable magnetic moment, mostly contributed by 2p orbitals of the nearest-neighbor oxygen atom (ONN) with two dangling bonds and 3d orbitals of the Cu atoms bonding with the ONN. Meanwhile, the charge transfer from Cu to Cu2O creates higher density of states at the Fermi level and subsequently leads to the spontaneous FM. Furthermore, the FM could be modulated by the amount of interfacial VCu, governed by the interfacial Cu diffusion with a moderate energy barrier (~1.2 eV). These findings provide insights into the FM mechanism and tuning the FM via interfacial cation diffusion in the Cu/Cu2O contact.

Scientific RepoRts | 5:15191 | DOi: 10.1038/srep15191 including long range double-exchange or super-exchange, are no longer suitable for depicting the FM in these systems. Therefore, a charge transfer Stoner model is proposed to fundamentally understand the FM induced by defects [17][18][19] . The criterion of Stoner model requires D(E F )J > 1, where D(E F ) is the density of states at the Fermi level (E F ) and J denotes the strength of exchange interaction. Spontaneous FM is triggered when a large D(E F ) occurs. Nevertheless, it is still not accessible how surface and interfacial defects introduce the localized states around Fermi level, and finally result in a large D(E F ) through the charge transfer. It is thus critical to unveil the connection between the FM and the defects states.
Relative to n-type ODMS, the p-type ODMS are much less explored. As a natural p-type material, cuprous oxide (Cu 2 O) is a promising material as catalyst, transistors, and etc 20,21 . If Cu 2 O could possess room-temperature FM, Cu 2 O would not only act as one spintronic material but also offer a fundamental platform to study the correlation between FM and structural properties. Actually, cuprous oxide (Cu 2 O) has shown room-temperature FM as other undoped oxides [9][10][11][12] . To date, there is no consensus of the origin of the FM in undoped Cu 2 O. Theoretically, the FM in undoped Cu 2 O is claimed to be induced by the oxygen interstitial in the bulk and by unsaturated Cu in the surface 22 . Experimentally, the undoped Cu 2 O fine powder 13 , nanowires 23 , and CuO/Cu 2 O interface 24 all exhibit the room-temperature FM relevant with the cation defects. Especially in our previous experimental work in Cu/Cu 2 O core-shell nanoparticles, the FM is found to be closely connected with the Cu vacancy (V Cu ) 25 . Besides, the magnetization can be tuned by modulating the V Cu amount through controlling the oxygen partial pressure and the annealing duration. Basically, it is critical to clarify the microscopic mechanism of V Cu induced FM and the feasibility to tune the FM through V Cu generation or compensation.
In this work, we have performed the density functional theory (DFT) calculations on the Cu/Cu 2 O interface in order to elucidate the origin and the modulation of FM. Our results indicate that the defect-free Cu/Cu 2 O interface is nonmagnetic, but in contrast, the interface containing specific site of V Cu possesses FM. The FM is not directly contributed by the V Cu but mostly contributed by the nearest-neighbor oxygen atom (O NN ) and the Cu atoms (Cu NN ) bonding with the O NN . As the anti-bonding states between the O NN and the Cu NN form localized states near the valence band maximum (VBM), the E F is pinned at the localized states and a large D(E F ) is satisfied through the charge-transfer from Cu to Cu 2 O at the interface. A moderate energy barrier (~1.2 eV) of the Cu diffusion guarantees the feasibility of modulating the FM through controlling the amount of interfacial V Cu . Our results provide an insight to understand the origin and the modulation of the FM in Cu/Cu 2 O contact. (111) surface is the most stable in terms of the surface coordination 26 Figure S1) of the Cu 2 O(111) contacts with the Cu(111) and the bottom Layer 5 is passivated. In practice, oxide surface reconstruction plays an important role to influence the interface quality. Thus, in order to capture this important structural information, we consider Cu 2 O surface reconstruction here. As a recent scanning tunneling microscopy (STM) result proposed, under different oxidation conditions, .°× .°R R 73 5 8 21 10 9 structure (also known as the "44" surface) is one of the stable Cu 2 O(111) surface reconstructions 26 . Therefore, in this work, we concentrate on the interface Cu/Cu 2 O based on this specific "44" surface reconstruction. Referring to Soon et al. 29 , we constructed the Cu/Cu 2 O interface by a 2 × 2 Cu(111) surface and a 4 × 4 Cu 2 O(111) surface. Due to the better ductibility of the metal Cu than semiconductor Cu 2 O, the lattice parameters of Cu 2 O are kept constant in Cu/Cu 2 O interface structures. The lattice mismatch for Cu is ~2.7%. According to the interfacial copper and oxygen contents, several candidate interface structures are considered. Figure 1(a,b) are top and side views of the pristine Cu/ Cu 2 O interface (int-pristine). Figure 1(c,d) present two and one Cu uns atoms in the Cu 2 O part, respectively (int-2Cu uns , int-1Cu uns ). Figure 1(e,f) are top and side views of the interface without Cu uns atoms in the Cu 2 O part (int-zero-Cu uns ). Figure 1(g,j) are interfaces with additional adsorbed oxygen atoms based on the int-zero-Cu uns . According to the O ads locations and amount, they are labeled as int-1O ads -A, int-1O ads -B and int-2O ads , respectively.

Stabilities of Cu/Cu 2 O interfaces with different interfacial Cu and O contents. The Cu
To determine the most stable interface, the interface free (formation) energy is calculated using the following equation, where E interface is the interface total energy. N Cu and N Cu O is the chemical potential of Cu in Cu 2 O. As we know, the maximum of chemical potential for one element occurs in its elemental phase. Combined with formula (2), μ O is restricted in following range: which can be rewritten as: Supplementary Information Table S1), which is consistent with generalized gradient approximation (GGA) result 29 . The µ O gas , half of an oxygen molecule energy, is  Figure S1), two types of Cu vacancy (Cu uns and Cu sat ) are called as "uns" and "sat" in Table 1. Through    Table 1, it is noticed that not all kinds of V Cu introduce a large magnetic moment into the interface system. Only vacancy at Cu sat in Layer 2 contributes a relatively large magnetic moment (0.4 to 0.5 μ B ) among all these structures. In order to unveil the FM mechanism, the interface band structures of defect-free int-2O ads and int-2O ads -V Cu (2) are calculated in Fig. 4(a,b). The green lines represent the total band structure of the interface. The dots and the triangles indicate the contribution from Layer 2 (see Supporting Information Figure S1) where the V Cu (2) locates, and the size denotes the weight. Compared with the bulk contribution, more localized surface states are observed near the E F , and the spin-up and spin-down states are splitted, indicating the Stoner instability. The existence of each V Cu leaves two dangling bonds with respect to its two nearest-neighbor oxygen atoms (O NN ). These dangling bonds may play a key role to introduce the FM. For more direct visual confirmation, the spin resolved projected density of states (PDOS) of O NN 2p and the 3d orbitals of the Cu atom (Cu NN ) bonding with the O NN are plotted in Fig. 4(c). Around the E F , the O NN -2p spin-up anti-bonding states (− 1 to 0 eV) are mostly occupied and the spin-down anti-bonding states are partially occupied. Meanwhile, due to the anti-bonding states composed by O NN -2p and Cu NN -3d orbitals, the Cu NN -3d orbitals show spin splitting as well. To compare the local magnetic moment within the same range, the spin-density distribution of int-2O ads -V Cu (2) is visualized within an atom sphere radius 0.8 Å which accords to the Wigner Seitz radius of oxygen atom (Fig. 4(d)). It demonstrates that the upper O NN contributes a relatively large proportion of magnetic moment (0.138 μ B ), while each Cu NN produces 0.075 μ B . Even when the radius is increased to 1.0 Å, the local magnetic moment on O NN and Cu NN are 0.147 μ B and 0.08 μ B , respectively, which is quite similar to the above results. In a word, in terms of the FM origin, the magnetic moment at the Cu/Cu 2 O interface is mainly from O NN and the Cu NN atoms. The magnetic moment on Cu NN results from the spin-splitting 3d orbitals which forms anti-bonding states with O NN -2p orbitals.
To further illustrate the origin of the FM contributed by the O NN , the PDOS of the O NN -2p and Cu NN -3d orbitals in different locations of V Cu are presented in Fig. 5. Referring to Fig. 3, the PDOS for two types of V Cu locations, one "uns" and one "sat" in each layer, are provided here. Each V Cu has two O NN atoms, and for clarity, only the PDOS of O NN with more dangling bonds are shown here. In the bulk Cu 2 O, the O NN -2p and Cu NN -3d orbitals generate large localized defect states in the range from − 5.0 eV to − 4.0 eV below the VBM. Meanwhile, a delocalized band near the VBM is also created. The state around the E F indicates that the hole produced by V Cu and occupies a valence band like perturbed-host state (PHS) 33 . Comparing with the bulk Cu 2 O, the O NN -2p and Cu NN -3d orbitals also create localized bonding states from − 5.0 eV to − 4.0 eV below the E F and delocalized states around the E F when V Cu is not at site 2. However, besides the deep localized states in int-2O ads -V Cu (2) moving up to the range from − 4.0 eV to − 3.0 eV, the prominently localized states appear around the E F . In other words, the Femi level could be pinned by these localized states. To understand this pinning phenomenon, we calculate the energy difference (∆E) between the E F and the VBM of Cu 2 O. For the defect-free int-2O ads interface, this energy difference is 0.12 eV. However in the int-2O ads -V Cu (2) interface, ∆E is also ~0.12 eV. Since the localized defect states induced by the V Cu (2) would pin the E F at the certain location and the charge transfer would not obviously shift E F , the FM occurs consequently.
To investigate why only certain V Cu could create localized states around the E F , we focus on the dangling bonds character of the O NN . Generally, the O atoms in Cu 2 O bulk form four bonds with the nearest  (2) interface, the upper O NN is merely bonding with two Cu atoms due to the natural "uns"-V Cu presence in Layer 1 (Fig. 5(b)). Therefore, the unique int-2O ads -V Cu (2) interface structure provides O NN one more dangling bonds, which leads to the weaker p-d hybridization and a more localized O-2p wave functions. For int-2O ads -V Cu (1), a new bond between the O NN and the Cu atom in above Cu(111) surface in the relaxed structure, as shown in Fig. 5(c). The new bond length is 1.95 Å, which is shorter than that in other int-2O ads -V Cu (n) structures (~2.07 Å). Thus, the new bond formation leads to the delocalized O NN -2p orbitals and the quenching of spin magnetic moment. It implies that once the dangling bonds are compensated, the larger magnetic moment shrinks.

Modulation of the ferromagnetism driven by interfacial Cu diffusion. The FM in Cu/Cu 2 O
interface is sensitive to the annealing process, in which the amount of the V Cu responsible for the FM could be tunable. It is important to investigate the feasibility of the Cu diffusion through the interface. Actually, the Cu diffusion from Cu into Cu 2 O is observed in previous experiments 34,35 . Such diffusion may degrade the electrical performance in Cu 2 O thin-film transistors 36 and modulate the magnetism during the Cu oxidation. Up to date, the theoretical Cu diffusion process and the energy barrier (E b ) in Cu/Cu 2 O contact are not well understood. Hence, a thoroughly study on the energy barrier related to the Cu diffusion and its influence on the FM is performed by climb image nudge elastic band (CI-NEB) calculations. As the int-2O ads -V Cu (2) structure has the largest magnetic moment, we focus on the Cu diffusion in this structure. As the V Cu in int-2O ads -V Cu (2) structure is located in Layer 2 (see Fig. 3), the diffusion process could be divided into two steps as shown in Fig. 6(a). The first step is one Cu atom moving from the Cu(111) surface into the natural V Cu located in Layer 1, leaving a vacancy on Cu(111) surface behind. Following the first step, this specific Cu atom further diffuses into V Cu (2) in Layer 2 (see Fig. 3).
Once the V Cu in Layer 2 is compensated, the FM almost vanishes. Within the CI-NEB calculations, the   energy barrier (E b ) is found to be 1.23 eV in the first step, and the total energy drops by 0.79 eV in the final stage, as plotted in Fig. 6(b). Such energy barrier is ~0.2 eV higher than the activation energy (E a ) in the Cu 2 O growth by oxidation (~1.0 eV) 37,38 . The Cu 2 O growth from Cu oxidation is closely related with the Cu diffusion from Cu to Cu 2 O 39 : where α and D Cu are the degree of ionization of defects and diffusion coefficient of Cu, respectively. k p denotes the parabolic rate which could be obtained by: where k p 0 is a prefactor and p O 2 represents the partial pressure in oxidation. Actually, the activation energy (E a ) is the energy barrier (E b ) in the Cu oxidation process, which determines the Cu diffusion. Please refer to the link "http://en.wikipedia.org/wiki/Activation_energy" for the definition of activation energy. According to the Arrhenius formula, the relationship between D Cu and the diffusion energy barrier (E b ) can be written in the following equation: Thus, in which λ is a dimensionless factor, ν and d indicate the vibration frequency (normally 10 12 ~ 10 13 s −1 ) and the jump distance, respectively. When = . p 0 0015Torr  8), which demonstrates that the Cu diffusion (~4 Å in the first step and ~3 Å in the second step) could be achievable. In Fig. 6(c), the E b in the second step is 1.18 eV which is slightly less than that in the first step. The lower E b in the second step implies that the Cu further moves easily to the V Cu in the second layer of Cu 2 O(111) as well once it reaches the Cu 2 O surface.
At the middle location (labeled as "Mid" in Fig. 6) in the whole diffusion process, the spin-polarized calculation is performed. The total magnetic moment, only 0.0003 μ B , indicates that the diffused Cu suppresses the FM. At the "Mid" site, the diffused Cu forms bonds with the O NN and the local magnetic moment drops significantly because partial dangling bonds of O NN are compensated. A higher D(E F ) of the Stoner criterion is no longer satisfied, which leads to the quenching of the FM. Thus during the growth of Cu 2 O under Cu oxidation, the annealing treatment would influence the Cu diffusion. To further quantify the diffusion feasibility, the approximated diffusion time can be solved by 39 : where L denotes the obtained oxidized layer (Cu 2 O) thickness after the oxidization duration of t. When E b = 1.2 eV and oxygen partial pressure is 0.2 Pa, the first step diffusion (~4 Å) would be finished in about 40 minutes. This result explains the experimental observation 25 . Therefore, the FM modulated by the annealing process in experiment is actually realized by controlling the amount of interfacial V Cu through Cu diffusion within the Cu/Cu 2 O interface.

Conclusion
To summarize, the FM in Cu/Cu 2 O contact is induced by V Cu around the Cu/Cu 2 O interface. Only the interface structure with the "sat" type V Cu in the second layer possesses a relatively large magnetic moment due to two dangling bonds of O NN . The E F is pinned in the O NN -2p and Cu NN -3d localized states and a large D(E F ) is achieved by the charge transfer from Cu to Cu 2 O. Once the V Cu is compensated by the diffused Cu atom, the number of dangling bonds reduces and the FM vanishes. A moderate energy barrier (~1.2 eV) guarantees the feasibility to modulate the FM by controlling Cu diffusion in experiment. These results offer a comprehensive understanding about the microscopic mechanism of the FM and its modulation by V Cu in Cu/Cu 2 O interface. Also, our calculations provide an insight to understand and tune the FM relevant with defects in other metal/oxides contacts.

Calculation methods
All the calculations are performed using Vienna ab initio simulation package (VASP). The generalized gradient approximation (GGA) with exchange-correlation function of Perdew-Burke -Ernzerhof (PBE) is chosen 40 . The energy cutoff of 400 eV is selected and the electronic optimization stops when the total energies of neighboring optimization loops differ below 10 −5 eV in all the calculations. A 7 × 7 × 7 Monkhorst-Pack k-point mesh is set up in the bulk calculations. To avoid the interaction between periodic images, the vacuum thickness is set up to 15 Å for the surface and interface slab structures. The Scientific RepoRts | 5:15191 | DOi: 10.1038/srep15191 Γ -centered 5 × 5 × 1 k-point mesh is adopted in slab calculations. For the structural relaxation, the force on each atom is chosen to be less than 0.001 eV/Å in bulk calculations and less than 0.05 eV/Å in surface and interface calculations. The Cu diffusion paths are calculated by the climb image nudge elastic band (CI-NEB) method 41 .