Introduction

Diluted magnetic semiconductors (DMS) are promising materials for spintronic devices due to the employment of the spin degree of freedom besides the charge property of carriers1,2. Among the III-V semiconductors doped by transition metals, spin polarization of carriers is achieved in Mn-doped GaAs, InAs and etc3,4. However, the low Curie temperature far below room temperature impedes the DMS-based device development5. In recent years, oxides diluted magnetic semiconductors (ODMS), such as Fe-ZnO, Cr-TiO2, Mn-TiO2 and etc, have attracted much attention due to their Curie temperature over 300 K in regards to DMS6,7,8. Unexpectedly, room temperature ferromagnetism (FM) has been observed in undoped oxides. After Venkatesan and Coey et al. pioneered in the finding of the room-temperature FM in undoped HfO29, other oxides without intentional magnetic impurities doping are subsequently discovered to show the FM behavior10,11,12.

Significant investigations of the FM mechanism are performed on the undoped nanoscaled ODMS systems, such as fine powder, heterostructures, core-shell nanoparticles and etc, where the surface and interfacial native point defects are supposed to be the origin of the FM13,14,15,16. However, without the contribution of magnetic transition metal ions, the traditional magnetic exchange interactions in oxides, 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 defects17,18,19. The criterion of Stoner model requires D(EF)J > 1, where D(EF) is the density of states at the Fermi level (EF) and J denotes the strength of exchange interaction. Spontaneous FM is triggered when a large D(EF) 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(EF) 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 (Cu2O) is a promising material as catalyst, transistors and etc20,21. If Cu2O could possess room-temperature FM, Cu2O 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 (Cu2O) has shown room-temperature FM as other undoped oxides9,10,11,12. To date, there is no consensus of the origin of the FM in undoped Cu2O. Theoretically, the FM in undoped Cu2O is claimed to be induced by the oxygen interstitial in the bulk and by unsaturated Cu in the surface22. Experimentally, the undoped Cu2O fine powder13, nanowires23 and CuO/Cu2O interface24 all exhibit the room-temperature FM relevant with the cation defects. Especially in our previous experimental work in Cu/Cu2O core-shell nanoparticles, the FM is found to be closely connected with the Cu vacancy (VCu)25. Besides, the magnetization can be tuned by modulating the VCu amount through controlling the oxygen partial pressure and the annealing duration. Basically, it is critical to clarify the microscopic mechanism of VCu induced FM and the feasibility to tune the FM through VCu generation or compensation.

In this work, we have performed the density functional theory (DFT) calculations on the Cu/Cu2O interface in order to elucidate the origin and the modulation of FM. Our results indicate that the defect-free Cu/Cu2O interface is nonmagnetic, but in contrast, the interface containing specific site of VCu possesses FM. The FM is not directly contributed by the VCu but mostly contributed by the nearest-neighbor oxygen atom (ONN) and the Cu atoms (CuNN) bonding with the ONN. As the anti-bonding states between the ONN and the CuNN form localized states near the valence band maximum (VBM), the EF is pinned at the localized states and a large D(EF) is satisfied through the charge-transfer from Cu to Cu2O 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 VCu. Our results provide an insight to understand the origin and the modulation of the FM in Cu/Cu2O contact.

Results and Discussion

Stabilities of Cu/Cu2O interfaces with different interfacial Cu and O contents

The Cu(111) surface is the most stable in terms of the surface coordination26. When the Cu(111) surface is oxidized, an intrinsic Cu(111)/Cu2O(111) interface forms27,28. In this work, we focus on the Cu(111)/Cu2O(111) intrinsic interface, labeled as Cu/Cu2O. The bulk and surface calculations ensure that five layers slab model is suitable for the further interface exploration (See Supplementary Information).

Five sandwich-like layers of Cu2O(111) surface and five layers of Cu(111) surface are included in a slab model with a 15 Å vaccum space, where the top Layer 1 (see Supplementary Information Figure S1) of the Cu2O(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 Cu2O surface reconstruction here. As a recent scanning tunneling microscopy (STM) result proposed, under different oxidation conditions, structure (also known as the “44” surface) is one of the stable Cu2O(111) surface reconstructions26. Therefore, in this work, we concentrate on the interface Cu/Cu2O based on this specific “44” surface reconstruction. Referring to Soon et al.29, we constructed the Cu/Cu2O interface by a 2 × 2 Cu(111) surface and a 4 × 4 Cu2O(111) surface. Due to the better ductibility of the metal Cu than semiconductor Cu2O, the lattice parameters of Cu2O are kept constant in Cu/Cu2O 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/Cu2O interface (int-pristine). Figure 1(c,d) present two and one Cuuns atoms in the Cu2O part, respectively (int-2Cuuns, int-1Cuuns). Figure 1(e,f) are top and side views of the interface without Cuuns atoms in the Cu2O part (int-zero-Cuuns). Figure 1(g,j) are interfaces with additional adsorbed oxygen atoms based on the int-zero-Cuuns. According to the Oads locations and amount, they are labeled as int-1Oads-A, int-1Oads-B and int-2Oads, respectively.

Figure 1
figure 1

Top and side views of Cu/Cu2O interface with pristine structure, int-pristine in (a) and (b). Part of the interfacial Cuuns atoms present, two and one Cuuns in (c) int-2Cuuns and (d) int-1Cuuns). Top and side views of interface without interfacial Cuuns, int-zero-Cuuns in (e,f). Interfaces with additional adsorbed oxygen atoms based on the int-zero-Cuuns. According to the Oads locations and amount, they are labeled as int-1Oads-A in (g), int-1Oads-B in (h) and int-2Oads in (i,j). Large silver balls are Cu atoms in Cu(111) surface. Green and blue balls denote the Cuuns and Cusat in Cu2O, respectively. Small red balls are oxygen atoms.

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To determine the most stable interface, the interface free (formation) energy is calculated using the following equation,

where Einterface is the interface total energy. NCu and denote the amount of Cu atom and Cu2O primitive unit, respectively. and μO are the chemical potentials of bulk Cu and oxygen in bulk Cu2O. Here, represents the energy of one Cu2O primitive cell. lO is the number of the excess or deficient oxygen atoms in the interface. A is the interface area. The chemical potentials and μO in Cu2O possess the relationship of:

where is the chemical potential of Cu in Cu2O.

As we know, the maximum of chemical potential for one element occurs in its elemental phase. Combined with formula (2), μO is restricted in following range:

which can be rewritten as:

The calculated is −1.24 eV (See Supplementary Information Table S1), which is consistent with generalized gradient approximation (GGA) result29. The , half of an oxygen molecule energy, is −4.92 eV. The interface formation energies of different interfaces are plotted in Fig. 2. All structures tend to become more stable as μO increases. The int-2Oads structure possesses the lowest interface energy when is in the range of −1.2 to 0.0 eV, which agrees with the reference work29.

Figure 2
figure 2

Dependence of interface free (formantion) energy for different structures on the oxygen chemical potential.

The int-2Oads structure is found to be the most stable interface structure.

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Microscopic mechanism of the ferromagnetism induced by Cu vacancy

Since the Cu vacancies are closely correlated with the interface FM25, one VCu is introduced into in the most stable int-2Oads interface. The possible VCu locations are labeled as int-2Oads-VCu(n) in Fig. 3, where n denotes the location number. Following the definition of Cu atom in the Cu2O surface (see Supplementary Information Figure S1), two types of Cu vacancy (Cuuns and Cusat) are called as “uns” and “sat” in Table 1. Through the collinear spin-polarized calculations, the charge transfer from Cu to Cu2O is characterized based on the Bader charge analysis (Table 1)30, from which we find that Cu2O gains ~2.6 electrons. Such charge transfer originates from the different work functions (WF) between Cu (WF: 4.6 eV) and Cu2O (WF: 4.8 eV)31,32. Among the int-2Oads-VCu(n) systems, int-2Oads-VCu(1) exhibits the largest charge transfer (~2.8 e) owing to the new bond formation between the Cu2O and the Cu surface.

Table 1 Total magnetic moment and the amount of charge transfer from Cu to Cu2O in int-2Oads with one VCu at different locations.
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Figure 3
figure 3

The numbers from 1 to 9 demonstrate the possible VCu locations in Cu/Cu2O int-2Oads interface after introducing one VCu.

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According to Table 1, it is noticed that not all kinds of VCu introduce a large magnetic moment into the interface system. Only vacancy at Cusat in Layer 2 contributes a relatively large magnetic moment (0.4 to 0.5 μB) among all these structures. In order to unveil the FM mechanism, the interface band structures of defect-free int-2Oads and int-2Oads-VCu(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 VCu(2) locates and the size denotes the weight. Compared with the bulk contribution, more localized surface states are observed near the EF and the spin-up and spin-down states are splitted, indicating the Stoner instability. The existence of each VCu leaves two dangling bonds with respect to its two nearest-neighbor oxygen atoms (ONN). 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 ONN 2p and the 3d orbitals of the Cu atom (CuNN) bonding with the ONN are plotted in Fig. 4(c). Around the EF, the ONN-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 ONN-2p and CuNN-3d orbitals, the CuNN-3d orbitals show spin splitting as well. To compare the local magnetic moment within the same range, the spin-density distribution of int-2Oads-VCu(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 ONN contributes a relatively large proportion of magnetic moment (0.138 μB), while each CuNN produces 0.075 μB. Even when the radius is increased to 1.0 Å, the local magnetic moment on ONN and CuNN are 0.147 μB and 0.08 μB, respectively, which is quite similar to the above results. In a word, in terms of the FM origin, the magnetic moment at the Cu/Cu2O interface is mainly from ONN and the CuNN atoms. The magnetic moment on CuNN results from the spin-splitting 3d orbitals which forms anti-bonding states with ONN-2p orbitals.

Figure 4
figure 4

(a) The spin-restricted band structure of defect-free int-pristine interface and the dots from the contribution by Cu2O-Layer 2. (b) The spin-polarized band structure of int-2Oads-VCu(2). The up (down) triangles represent the spin-up (down) states of Cu2O-Layer 2. (c) The projected DOS of the ONN and CuNN in int-2Oads-VCu(2) interface. (d) The spin-densities of the ONN and CuNN and the corresponding magnetic moments within the atom sphere of radius 0.8 Å.

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To further illustrate the origin of the FM contributed by the ONN, the PDOS of the ONN-2p and CuNN-3d orbitals in different locations of VCu are presented in Fig. 5. Referring to Fig. 3, the PDOS for two types of VCu locations, one “uns” and one “sat” in each layer, are provided here. Each VCu has two ONN atoms and for clarity, only the PDOS of ONN with more dangling bonds are shown here. In the bulk Cu2O, the ONN-2p and CuNN-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 EF indicates that the hole produced by VCu and occupies a valence band like perturbed-host state (PHS)33. Comparing with the bulk Cu2O, the ONN-2p and CuNN-3d orbitals also create localized bonding states from −5.0 eV to −4.0 eV below the EF and delocalized states around the EF when VCu is not at site 2. However, besides the deep localized states in int-2Oads-VCu(2) moving up to the range from −4.0 eV to −3.0 eV, the prominently localized states appear around the EF. 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 EF and the VBM of Cu2O. For the defect-free int-2Oads interface, this energy difference is 0.12 eV. However in the int-2Oads-VCu(2) interface, ∆E is also ~0.12 eV. Since the localized defect states induced by the VCu(2) would pin the EF at the certain location and the charge transfer would not obviously shift EF, the FM occurs consequently.

Figure 5
figure 5

(a) The PDOS of ONN-2p and corresponding CuNN-3d orbitals in int-2Oads-VCu(n) interface. For clarity, the PDOS for two types of VCu structures, “uns” and one “sat” in each layer in Fig. 5 and the ONN with the more dangling bonds are presented. (b) The relaxed int-2Oads-VCu(2) interface structure. Two dangling bonds of ONN are observed due to the natural presence of “uns” type VCu in Layer 1. (c) The relaxed int-2Oads-VCu(1) structure. The ONN actually forms a new bond with one Cu atom from upper Cu surface, resulting only one dangling bond of ONN. The dotted circles represent the location of VCu.

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To investigate why only certain VCu could create localized states around the EF, we focus on the dangling bonds character of the ONN. Generally, the O atoms in Cu2O bulk form four bonds with the nearest four Cu atoms. Hence one ONN around the VCu forms bonds with three other Cu atoms, generating one dangling bond. The spin-polarized calculation for a 2 × 2 × 2 bulk Cu2O supercell with one Cu vacancy gives the magnetic moment per atom less than 0.0001 μB, indicating a non-magnetic state. However, in the int-2Oads-VCu(2) interface, the upper ONN is merely bonding with two Cu atoms due to the natural “uns”-VCu presence in Layer 1 (Fig. 5(b)). Therefore, the unique int-2Oads-VCu(2) interface structure provides ONN one more dangling bonds, which leads to the weaker p-d hybridization and a more localized O-2p wave functions. For int-2Oads-VCu(1), a new bond between the ONN 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-2Oads-VCu(n) structures (~2.07 Å). Thus, the new bond formation leads to the delocalized ONN-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/Cu2O interface is sensitive to the annealing process, in which the amount of the VCu 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 Cu2O is observed in previous experiments34,35. Such diffusion may degrade the electrical performance in Cu2O thin-film transistors36 and modulate the magnetism during the Cu oxidation. Up to date, the theoretical Cu diffusion process and the energy barrier (Eb) in Cu/Cu2O 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-2Oads-VCu(2) structure has the largest magnetic moment, we focus on the Cu diffusion in this structure. As the VCu in int-2Oads-VCu(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 VCu located in Layer 1, leaving a vacancy on Cu(111) surface behind. Following the first step, this specific Cu atom further diffuses into VCu(2) in Layer 2 (see Fig. 3). Once the VCu in Layer 2 is compensated, the FM almost vanishes. Within the CI-NEB calculations, the energy barrier (Eb) 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 (Ea) in the Cu2O growth by oxidation (~1.0 eV)37,38. The Cu2O growth from Cu oxidation is closely related with the Cu diffusion from Cu to Cu2O39:

Figure 6
figure 6

(a) Cu diffusion route from Cu(111) surface to the VCu site in int-2Oads-VCu(2) structure. The energy curves in (b,c) corresponding to the first and the second step during the diffusion. The dotted circles represent the different reaction coordinates in NEB calculations.

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where α and DCu are the degree of ionization of defects and diffusion coefficient of Cu, respectively. kp denotes the parabolic rate which could be obtained by:

where is a prefactor and represents the partial pressure in oxidation. Actually, the activation energy (Ea) is the energy barrier (Eb) 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 DCu and the diffusion energy barrier (Eb) can be written in the following equation:

Thus,

in which λ is a dimensionless factor, ν and d indicate the vibration frequency (normally 1012 ~ 1013 s−1) and the jump distance, respectively. When (0.2 Pa)25, ( in ref. 40), d should be several angstroms to make DCu compatible for both sides of Eq. (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 Eb in the second step is 1.18 eV which is slightly less than that in the first step. The lower Eb in the second step implies that the Cu further moves easily to the VCu in the second layer of Cu2O(111) as well once it reaches the Cu2O 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 μB, indicates that the diffused Cu suppresses the FM. At the “Mid” site, the diffused Cu forms bonds with the ONN and the local magnetic moment drops significantly because partial dangling bonds of ONN are compensated. A higher D(EF) of the Stoner criterion is no longer satisfied, which leads to the quenching of the FM. Thus during the growth of Cu2O under Cu oxidation, the annealing treatment would influence the Cu diffusion. To further quantify the diffusion feasibility, the approximated diffusion time can be solved by39:

where L denotes the obtained oxidized layer (Cu2O) thickness after the oxidization duration of t. When Eb = 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 observation25. Therefore, the FM modulated by the annealing process in experiment is actually realized by controlling the amount of interfacial VCu through Cu diffusion within the Cu/Cu2O interface.

Conclusion

To summarize, the FM in Cu/Cu2O contact is induced by VCu around the Cu/Cu2O interface. Only the interface structure with the “sat” type VCu in the second layer possesses a relatively large magnetic moment due to two dangling bonds of ONN. The EF is pinned in the ONN-2p and CuNN-3d localized states and a large D(EF) is achieved by the charge transfer from Cu to Cu2O. Once the VCu 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 VCu in Cu/Cu2O 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 chosen40. 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 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) method41.

Additional Information

How to cite this article: Li, H.-B. et al. Electronic Structure and Ferromagnetism Modulation in Cu/Cu2O Interface: Impact of Interfacial Cu Vacancy and Its Diffusion. Sci. Rep. 5, 15191; doi: 10.1038/srep15191 (2015).