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Possible origin of ferromagnetism in undoped monoclinic HfO2 film
Computational Materials Science 92 (2014) 120–126
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Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Possible origin of ferromagnetism in undoped monoclinic HfO2 film Min Wang a,⇑, Min Feng b, Yuan Lu a a b
College of Electronic Information and Optical Engineering, Nankai University, Tianjin 300071, People’s Republic of China School of Physics, Nankai University, Tianjin 300071, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 31 December 2013 Received in revised form 10 May 2014 Accepted 15 May 2014
Keywords: HfO2 Surface Oxygen vacancy Magnetism First principles
a b s t r a c t Using density functional theory calculations, we have studied the electronic structures and magnetic 1 1Þ surface. We find that the complex defects of oxyproperties of oxygen-deficient HfO2 (1 1 1) and ð1 gen vacancies (CDOV) may be responsible for the unexpected ferromagnetism in monoclinic HfO2 film without doping. The results show that each kind of oxygen vacancy (VO) alone can not introduce the mag 1 1Þ surface is magnetic with only one VO. When the CDOV netism on the surface, so neither (1 1 1) nor ð1 1 1Þ surface, the which are composed of two oxygen vacancies were introduced on the HfO2 (1 1 1) or ð1 system will be magnetic. However, the CDOV have to meet two prerequisites for the existence of a highspin defect ground state, i.e., one non-ground state of ferromagnetism exists for one VO in the CDOV, and the distance between the two oxygen vacancies in the CDOV should be less than or equal the critical distance. The spins induced by the special CDOV will form a ferromagnetic ground state, and they can produce a magnetic moment of 2.0lB. In addition, the magnetic moment mainly results from the d orbitals of low-charge-state Hafnium ions adjacent to the CDOV. The experimentally observed d0-ferromagnetism behavior in HfO2 system is in good agreement with our calculated results. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction Pristine hafnia (HfO2) is an insulator with a wide band gap (5.7 eV) and a high-k dielectric constant [1]. In addition, there is no evidence that it is magnetic in the ground state. However, surprisingly Coey et al. [2,3] observed the ferromagnetism (FM) of pristine HfO2 thin-film with the Curie temperature as high as 500 K. Since neither Hf4+ nor O2 is magnetic ion with open d or f shell, this phenomenon is coined as ‘‘d0 ferromagnetism’’. Obviously, it challenged our conventional understanding on the origin of magnetism and trigged a heated debate [4–6]. There has been a consensus that ‘‘d0 ferromagnetism’’ is induced by native defects, either cation or anion vacancy. In the experiments, Coey et al. [3] and Hong et al. [6–8] revealed that the observed unexpected ferromagnetism in HfO2 film is closely related to the oxygen vacancy (VO) instead of cation vacancy. They reported that the magnetic moments of the undoped HfO2 film decrease as the annealing time in oxygen atmosphere increases. Zenkevich et al. [9] studied the surface electronic structure in HfO2 film by low energy ion spectroscopy (LEIS). The results showed that a metal-like band will be formed on the HfO2 surface as a result of the produce of lots of defects that is believed to result
⇑ Corresponding author. Tel./fax: +86 22 23494893. E-mail address: [email protected] (M. Wang). http://dx.doi.org/10.1016/j.commatsci.2014.05.025 0927-0256/Ó 2014 Elsevier B.V. All rights reserved.
from the oxygen defects at the top layer of surface. This is related to Coey’s observation of d0-FM in HfO2 film, where they annealed HfO2 alternatively in vacuum and oxygen atmosphere, and observed FM after vacuum annealing. These studies mentioned above showed that the magnetism may be directly related to the oxygen vacancies in the undoped oxides. Existing first-principles calculations are mostly focused on hole-induced-FM which may result in the local magnetic state in HfO2 bulk material. Pemmaraju and Sanvito studied the HfO2 with Hafnium (Hf) vacancies using first-principles calculations [10]. The results show that isolated cation vacancy in HfO2 results in the high-spin defect state, and these states are ferromagnetically coupled with a rather short range magnetic interaction which leads to the ferromagnetic ground state. Weng and Dong investigated the FM in HfO2 doped by holes based on ab initio calculation [11]. The results showed that the observed FM in HfO2 could result from the holes that were doped in HfO2 system with nonmagnetic ions. The doped holes will enter the p bands of the oxygen atoms adjacent to the dopant and result in the p bands spin split. Obviously, the calculated results mentioned above are not consistent with the experiments. Moreover, previous researches focus on bulk magnetism, although the magnetization depends on the thickness of the undoped oxide thin films [6], which hints that surface or interface may impact the unexpected magnetism. In fact, the thinner the film is, the stronger the magnetization. Thus, the observed
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FM is clearly related to oxygen vacancies near to surface or interface. However, so far there were no calculations about the oxygen vacancies can induce the FM on HfO2 surface. 1 1Þ are For monoclinic HfO2, it is known that the (1 1 1) and ð1 the two most stable surfaces [12]. In this paper, we systematically study the electronic structures and magnetism of oxygen-deficient 1 1Þ surface. We firstly show that the oxygen HfO2 (1 1 1) and ð1 vacancies on the HfO2 surface can induce magnetism without magnetic doping. 2. Computational details The calculations in this article were carried out by using the Vienna ab initio simulation package (VASP) [13]. The projector augmented plane-wave (PAW) method with cutoff energy of 520 eV and the U-centered 2 2 1 k-mesh were used in the calculations. The generalized-gradient approximation (GGA) is used for treating the exchange and correlation potential [14]. The energy convergence error is 104 eV for the electronic loops and 103 eV for the ionic loops. In addition, forces on the atoms are less than 0.02 eV/Å when the structural relaxation cycles were terminated. 1 1Þ surfaces In this paper, we modeled the HfO2 (1 1 1) and ð1 by (2 2) surface cells consisting of four stoichiometric HfO2 monolayers (192 atoms in total). The thickness of vacuum layer above the slab was 10 Å. For comparison, the monoclinic HfO2 bulk is also modeled by 2 2 2 supercell, 96 atoms in total. The energy cutoff and convergence criteria are the same as above. The k-mesh was set to be 4 4 4 for the calculation of electronic properties. 3. Results and discussion
Fig. 1. Crystal structure of monoclinic HfO2. Deep yellow and red balls represent the Hf and O atoms (in all structural graphs), respectively. The geometries of O3c, O4c and Hf7c are also shown. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
were obviously symmetric in Fig. 2(d). So the oxygen vacancies can not induce the magnetism in HfO2 bulk. Our results are the same as previous study [10].
3.1. Bulk properties 3.2. The (1 1 1) surface with oxygen vacancies The monoclinic crystal is the most stable phase for the HfO2 [12], space group P21/c, with lattice parameters, a = 5.1156 Å, b = 5.1722 Å, and c = 5.2948 Å, b = 99.18° [1]. The bulk is constructed by three types of ions (see Fig. 1). The threefold-coordinated oxygen ions (O3c) will form an almost planar trigonal structure with the peripheral Hf atoms. And an imperfection of tetrahedron is formed by the fourfold-coordinated oxygen ions (O4c) with the coordinating Hf atoms. In addition, each Hafnium atom in the bulk is sevenfold-coordinated (Hf7c) with the coordinating oxygen (O) atoms. Fig. 2(a) showed the density of states (DOS) within GGA for the perfect HfO2 bulk. In the case, the band gap is open between the O2p valence band maximum (VBM) and Hf-d conduction band minimum (CBM). And the calculated band gap is about 4.08 eV, smaller than the experimental values of 5.7 eV [1]. The underestimation of band gap is the well-known side effect of local density based approximations including GGA. The DOS of the HfO2 bulk with one vacancy of O3c or O4c (i.e., VO3c or VO4c), were shown in Fig. 2(b) and (c). Although the impurity states will be formed in the band gap about 1.30 eV and 1.60 eV below the CBM for VO3c and VO4c, respectively, the majority and minority spin channels are symmetric in both Fig. 2(b) and (c). Therefore, the systems are both nonmagnetic. Now, we consider the complex defects of oxygen vacancies (CDOV) that are induced by two oxygen vacancies (VO’s). Fig. 2(d) shows the DOS of the bulk with VO3c and VO4c (VO3c–VO4c). The distance between the VO3c and VO4c is 2.540 Å, which is the nearest distance between two oxygen vacancies in the bulk. However, the results show that the system is also nonmagnetic from Fig. 2(d) according to our calculations. The majority and minority channels of the impurity bands which are induced by the CDOV
The HfO2 (1 1 1) surface is a complicated surface. There are four inequivalent surface oxygen atoms and one kind of Hafnium atom on the top layer of (1 1 1) surface. Two types of oxygen ions are twofold-coordinated (i.e., O2c-a and O2c-b), which the bond angle of O2c-a is larger than O2c-b. Other two types of oxygen ions are both threefold-coordinated (i.e., O3c-a and O3c-b), which the bond angles are also different (see Fig. 3). The Hafnium atom on the top layer of the surface is sixfold-coordinated. In Fig. 4(a), we can see that the perfect HfO2 (1 1 1) surface keep the characteristic of insulator, and the band gap is open between the O-2p VBM and Hf-d CBM. The band gap of the perfect surface is about 4.15 eV, also smaller than the experimental value of 5.7 eV for the bulk. When one oxygen vacancy is produced on the (1 1 1) surface, the system is still an insulator (see Fig. 4(b–e)). And it is obviously shown that the majority and minority spin channels are symmetry in Fig. 4, so the systems are all nonmagnetic. One single oxygen vacancy can not induce the magnetism on the HfO2 (1 1 1) surface. Next, we consider the case of CDOV which are composed of two oxygen vacancies. The list of CDOV on (1 1 1) surface was shown in Table 1. Here, we only consider the nearestneighbor distance for each kind of CDOV. The CDOV which are composed of the same type of oxygen vacancies are not considered, because the distance between the two oxygen vacancies is very large (more than 7 Å). The calculated densities of states were shown in Fig. 5(a–f). The CDOV can induce the impurity bands in the band gap in Fig. 5. However, only the VO2c-a–VO2c-b can induce the ferromagnetic ground state on the HfO2 (1 1 1) surface (see Table 1). And the total magnetic moment is 2.0lB. The total DOS (TDOS) of (1 1 1) surface with VO2c-a–VO2c-b is partially shown in Fig. 6. It is shown that the majority and minority
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Fig. 2. Calculated densities of states of: (a) perfect monoclinic HfO2 bulk, (b) the bulk with one VO3c, (c) the bulk with one VO4c, (d) the bulk with VO3c and VO4c (VO3c–VO4c). Fermi energy is set to be zero (in all DOS graphs).
(i.e., O3c-a and O3c-b). The bond angles are different between O3c-a and O3c-b (see Fig. 7). In Fig. 8, we can see that the results are the same as the (1 1 1) surface. The single oxygen vacancy can not induce the magnetism 1 1Þ surface. The perfect ð1 1 1Þ surface is also an insulaon the ð1
Fig. 3. Perfect HfO2 (1 1 1) surface, only the stoichiometric HfO2 monolayer on the top layer of the surface is shown. The bond angles [unit (°)] of the oxygen ions (i.e., O2c-a, O2c-b, O3c-a and O3c-b) are also shown, the oxygen ions are at the apex positions.
channels of the impurity bands are obviously asymmetric. The spin density map was shown in Fig. 6 inset. According to our calculations, the magnetic moments are mostly located at three Hf atoms adjacent to the CDOV. Projected DOS (PDOS) shows that the middle-gap impurity bands can be attributed to d-orbitals of the Hf atoms around the VO2c-a–VO2c-b. In addition, the calculations show that the total energy of ferromagnetic state for the (1 1 1) surface with VO2c-a–VO2c-b is lower than that of non-magnetic state by 200 meV. And we found that the calculations with antiferromagnetic initial states eventually converge to ferromagnetic states, so the ground state for the HfO2 (1 1 1) surface with VO2c-a–VO2c-b is ferromagnetic state. 1 1Þ surface with oxygen vacancies 3.3. The ð1 1 1Þ surface. On the Fig. 7 shows the structure of perfect HfO2 ð1 surface, there are two types of Hafnium atoms, i.e., sixfold-coordinated Hafnium ions (Hf6c) and sevenfold-coordinated Hafnium ions (Hf7c). One kind of oxygen ions is twofold-coordinated (O2c), and other two types are both threefold-coordinated oxygen ions
tor, with an open band gap of 3.84 eV, smaller than the (1 1 1) surface. Although the impurity states can be induced by VO2c, VO3c-a, or VO3c-b, the majority and minority spin channels are almost symmetric. Thus, the systems are all nonmagnetic. 1 1Þ surface. The list of Now, we will induce the CDOV on the ð1 1 1Þ surface was shown in Table 2. We also only conCDOV on ð1 sider the nearest-neighbor distance. The calculated results showed that VO2c–VO3c-a and VO2c–VO3c-b can induce the magnetism on the surface. And the magnetic moments are both 2.0lB. Fig. 9 shows 1 1Þ surface. It is obvithe calculated DOS for the CDOV on the ð1 ously that the surface with VO3c-a–VO3c-b is nonmagnetic. The surface with VO2c–VO3c-a or VO2c–VO3c-b will induce the impurity bands in the band gap. In addition, the majority and minority channels of the impurity bands are obviously asymmetric. So the system with VO2c–VO3c-a or VO2c–VO3c-b is magnetic. 1 1Þ with VO2c– Figs. 10 and 11 are the PDOS of the surface ð1 VO3c-a or VO2c–VO3c-b. The insets are the spin density maps in Figs. 10 and 11. For the surface with VO2c–VO3c-a, the magnetic moments mostly reside on five Hf atoms around the CDOV. And the magnetism can be attributed to d-orbitals of the Hf atoms. In Fig. 11, the magnetic moments are mostly located at three Hf 1 1Þ surface. And the atoms adjacent to the VO2c–VO3c-b on the ð1 magnetism also results from the d-orbitals of the Hf atoms. In addition, the calculations show that the total energy of ferro 1 1Þ surface with VO2c–VO3c-a (or VO2c– magnetic state for the ð1 VO3c-b) is lower than that of non-magnetic state by 366 meV (or 138 meV). And we also found that the calculations with antiferromagnetic initial states eventually converge to ferromagnetic states, 1 1Þ surface with VO2c–VO3c-a so the ground state for the HfO2 ð1 (or VO2c–VO3c-b) is also ferromagnetic state. 3.4. Discussion From the results mentioned above, we can get the conclusion that the CDOV play a key role in inducing the magnetism on the
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Fig. 4. Calculated densities of states of: (a) perfect HfO2 (1 1 1) surface, (b) the surface with one O2c-a vacancy (VO2c-a), (c) the surface with one O2c-b vacancy (VO2c-b), (d) the surface with one O3c-a vacancy (VO3c-a) and (e) the surface with one O3c-b vacancy (VO3c-b).
Table 1 The list of CDOV on the HfO2 (1 1 1) surface. The corresponding distances and magnetic moments are also shown. Type of complex defects
Nearest neighbor distance (Å)
Magnetic moment (lB)
VO2c-a–VO3c-a VO2c-a–VO3c-b VO2c-b–VO3c-a VO2c-b–VO3c-b VO3c-a–VO3c-b VO2c-a–VO2c-b
3.242 3.659 2.854 3.242 3.713 2.792
0 0 0 0 0 2.0
HfO2 surface. In the process of calculation, only VO2c-b on the (1 1 1) 1 1Þ surface can produce two energy surface and VO2c on the ð1 states in the system, see Fig. 12.
From Fig. 12, the two energy states are ferromagnetic state (FM) at Valley1 and nonmagnetic state (NM) at Valley2, respectively. And the Valley2 is the lowest position of energy, so NM is more stable than FM. For the HfO2 (1 1 1) surface with one VO2c-b, the energy difference DE for the two states is 29.7 meV, so the NM should be the ground state of the system. Similarly, the VO2c on the HfO2 1 1Þ surface can also produce FM and NM, and the DE is ð1 24.8 meV, thus the ground state of the system is also NM. If we induce another oxygen vacancy on the surface near the VO2c-b or VO2c, the ground state will be likely to become ferromagnetic ground state due to the interaction between the two VO’s. Furthermore, only the special CDOV can result in the ferromagnetic ground state, e.g., VO2c-a–VO2c-b, VO2c–VO3c-a and VO2c–VO3c-b. Other CDOV can not induce the magnetism, such as VO2c-a–VO3c-a, VO2c-a–VO3c-b and VO3c-a–VO3c-b and so on. One key factor is the
Fig. 5. Calculated densities of states of HfO2 (1 1 1) surface with: (a) VO2c-a and VO3c-a (VO2c-a–VO3c-a), (b) VO2c-a and VO3c-b (VO2c-a–VO3c-b), (c) VO2c-b and VO3c-a (VO2c-b–VO3c-a), (d) VO2c-b and VO3c-b (VO2c-b–VO3c-b), (e) VO3c-a and VO3c-b (VO3c-a–VO3c-b) and (f) VO2c-a and VO2c-b (VO2c-a–VO2c-b).
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M. Wang et al. / Computational Materials Science 92 (2014) 120–126 Table 2 1 1Þ surface. The corresponding distances and magnetic The list of CDOV on the ð1 moments are also shown.
Fig. 6. Projected DOS of Hafnium atoms adjacent to the VO2c-a–VO2c-b on the surface (1 1 1) is shown. The inset shows the spin density map for HfO2 (1 1 1) surface with one VO2c-a–VO2c-b.
1 1Þ surface, it was only shown the top layer of the Fig. 7. Perfect HfO2 ð1 stoichiometric HfO2 monolayer. The bond angles [unit (°)] of the oxygen ions (i.e., O2c, O3c-a and O3c-b) are also shown, the oxygen ions are at the apex positions.
Type of complex defects
Nearest neighbor distance (Å)
Magnetic moment (lB)
VO3c-a–VO3c-b VO2c–VO3c-a VO2c–VO3c-b
3.713 2.957 2.854
0 2.0 2.0
distance between two oxygen vacancies in CDOV (dCDOV). As we know, if the dCDOV is far enough, the effect is equivalent to two isolated oxygen vacancies and the system will be nonmagnetic. Thus, dCDOV could not be too large, otherwise the interaction between the two V0O s will be too weak. In Table 1, it was shown that the critical distance is about 2.792 Å on (1 1 1) surface. According to our calculations, the surface with VO2c-a–VO2c-b will be nonmagnetic when the distance between VO2c-a and VO2c-b is 5.267 Å which is the second nearest-neighbor distance. Therefore, when the dCDOV is larger than 2.792 Å, the CDOV can not induce the magnetism on the (1 1 1) surface. Similarly, the results show that the critical distance 1 1Þ is 2.957 Å in Table 2. Therefore, of the CDOV on surface ð1 when the distance is 2.854 Å, obviously, the VO2c–VO3c-b can also result in the ferromagnetic state. And when the distance between the two oxygen vacancies exceed 2.957 Å, e.g., the second nearest-neighbor distances are 4.056 Å and 4.624 Å for VO2c–VO3c-a and VO2c–VO3c-b, respectively, the CDOV also do not induce the magnetism. So it can be concluded that the interaction between the two oxygen vacancies in CDOV is short-range. Fig. 13 showed the schematic diagram of the spin state. When only one oxygen vacancy was produced on the surface, the total spin S = 0. The oxygen vacancy is an n-type defect, the two electrons which are released by the VO as compensating charge will fill in the molecular orbitals. And when the exchange energy (P) between the two lowest states is smaller than the split (D0) between them, the two spins will occupy the lowest state and they are antiparallel. This will result in a low spin state. This is the case of only one VO (see Fig. 13(a)). When the CDOV were produced on the surface, obviously, four electrons will be induced in the system. Two electrons will fill in
1 1Þ surface, (b) the surface with one O2c vacancy (VO2c), (c) the surface with one O3c-a vacancy (VO3c-a) and (d) the Fig. 8. Calculated densities of states of: (a) perfect HfO2 ð1 surface with one O3c-b vacancy (VO3c-b).
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1 1Þ surface with: (a) VO3c-a and VO3c-b (VO3c-a–VO3c-b), (b) VO2c and VO3c-a (VO2c–VO3c-a), (c) VO2c and VO3c-b (VO2c–VO3c-b). Fig. 9. Calculated densities of states of HfO2 ð1
1 1Þ) surface with Fig. 12. The diagram of state of energy for the HfO2 (1 1 1) (or ð1 one VO2c-b (or VO2c).
Fig. 10. Projected DOS of Hafnium atoms adjacent to VO2c–VO3c-a on the surface 1 1Þ is shown. The inset shows the spin density map for HfO2 ð1 1 1Þ surface ð1 with one VO2c–VO3c-a.
Fig. 13. Schematic diagram of the spin state, low-spin S = 0 and high-spin S = 1 states. (a) The surface with only one VO was shown, (b) and (c) show the surface with the CDOV.
1 1Þ Fig. 11. Projected DOS of Hafnium atoms around VO2c–VO3c-b on the surface ð1 1 1Þ surface with one is shown. The inset shows the spin density map for HfO2 ð1 VO2c–VO3c-b.
the lowest molecular orbital and they are antiparallel. Other two electrons, when the distance is larger than the critical distance, then P < D0, the two electrons will be antiparallel and occupy the second excited state and lead to a low spin state (see Fig. 13(b)). Because the interaction between the two oxygen vacancies was strong when the distance is less than or equal the critical distance, this will result in P > D0. Thus, the two spins will occupy the second and the third excited states, respectively. And it will result in a high-spin state (S = 1, see Fig. 13(c)). From the discussion mentioned above, the CDOV can result in the ferromagnetic ground state based on the following facts: (1)
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there was a non-ground state of FM for one oxygen vacancy in the CDOV; (2) the distance of two oxygen vacancies in CDOV should be less than or equal the critical distance, or else, the interaction is too weak to result in the high-spin state. These findings provide a new way to explain the d0-ferromagnetism in pristine oxides.
This research is sponsored by National Natural Science Foundation of China (Grant No. 10970499), and National Basic Research Program of China (973 Program, Grant No. 2011CB606405).
4. Conclusion
References
In conclusion, based on first-principle calculations we systematically studied the oxygen vacancies on the HfO2 surface. The results show that a single VO can not induce the magnetism on 1 1Þ surface. The CDOV can result in a high-spin the (1 1 1) and ð1 state, and produce the magnetic moment of 2.0lB. However, they have to meet two conditions. That is presence of a non-ground state of FM for one VO in the CDOV, and the dCDOV is less than or equal the critical distance. So our results suggest a useful mechanism which can interpret well that the local magnetic moments could be produced in HfO2 film without any doping. It is important to note, however, whether the local magnetic moment induced by the CDOV can produce macroscopic magnetism in the experiment, the magnetic coupling between the two CDOV’s in different distances would be further investigated.
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Acknowledgements
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Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Possible origin of ferromagnetism in undoped monoclinic HfO2 film Min Wang a,⇑, Min Feng b, Yuan Lu a a b
College of Electronic Information and Optical Engineering, Nankai University, Tianjin 300071, People’s Republic of China School of Physics, Nankai University, Tianjin 300071, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 31 December 2013 Received in revised form 10 May 2014 Accepted 15 May 2014
Keywords: HfO2 Surface Oxygen vacancy Magnetism First principles
a b s t r a c t Using density functional theory calculations, we have studied the electronic structures and magnetic 1 1Þ surface. We find that the complex defects of oxyproperties of oxygen-deficient HfO2 (1 1 1) and ð1 gen vacancies (CDOV) may be responsible for the unexpected ferromagnetism in monoclinic HfO2 film without doping. The results show that each kind of oxygen vacancy (VO) alone can not introduce the mag 1 1Þ surface is magnetic with only one VO. When the CDOV netism on the surface, so neither (1 1 1) nor ð1 1 1Þ surface, the which are composed of two oxygen vacancies were introduced on the HfO2 (1 1 1) or ð1 system will be magnetic. However, the CDOV have to meet two prerequisites for the existence of a highspin defect ground state, i.e., one non-ground state of ferromagnetism exists for one VO in the CDOV, and the distance between the two oxygen vacancies in the CDOV should be less than or equal the critical distance. The spins induced by the special CDOV will form a ferromagnetic ground state, and they can produce a magnetic moment of 2.0lB. In addition, the magnetic moment mainly results from the d orbitals of low-charge-state Hafnium ions adjacent to the CDOV. The experimentally observed d0-ferromagnetism behavior in HfO2 system is in good agreement with our calculated results. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction Pristine hafnia (HfO2) is an insulator with a wide band gap (5.7 eV) and a high-k dielectric constant [1]. In addition, there is no evidence that it is magnetic in the ground state. However, surprisingly Coey et al. [2,3] observed the ferromagnetism (FM) of pristine HfO2 thin-film with the Curie temperature as high as 500 K. Since neither Hf4+ nor O2 is magnetic ion with open d or f shell, this phenomenon is coined as ‘‘d0 ferromagnetism’’. Obviously, it challenged our conventional understanding on the origin of magnetism and trigged a heated debate [4–6]. There has been a consensus that ‘‘d0 ferromagnetism’’ is induced by native defects, either cation or anion vacancy. In the experiments, Coey et al. [3] and Hong et al. [6–8] revealed that the observed unexpected ferromagnetism in HfO2 film is closely related to the oxygen vacancy (VO) instead of cation vacancy. They reported that the magnetic moments of the undoped HfO2 film decrease as the annealing time in oxygen atmosphere increases. Zenkevich et al. [9] studied the surface electronic structure in HfO2 film by low energy ion spectroscopy (LEIS). The results showed that a metal-like band will be formed on the HfO2 surface as a result of the produce of lots of defects that is believed to result
⇑ Corresponding author. Tel./fax: +86 22 23494893. E-mail address: [email protected] (M. Wang). http://dx.doi.org/10.1016/j.commatsci.2014.05.025 0927-0256/Ó 2014 Elsevier B.V. All rights reserved.
from the oxygen defects at the top layer of surface. This is related to Coey’s observation of d0-FM in HfO2 film, where they annealed HfO2 alternatively in vacuum and oxygen atmosphere, and observed FM after vacuum annealing. These studies mentioned above showed that the magnetism may be directly related to the oxygen vacancies in the undoped oxides. Existing first-principles calculations are mostly focused on hole-induced-FM which may result in the local magnetic state in HfO2 bulk material. Pemmaraju and Sanvito studied the HfO2 with Hafnium (Hf) vacancies using first-principles calculations [10]. The results show that isolated cation vacancy in HfO2 results in the high-spin defect state, and these states are ferromagnetically coupled with a rather short range magnetic interaction which leads to the ferromagnetic ground state. Weng and Dong investigated the FM in HfO2 doped by holes based on ab initio calculation [11]. The results showed that the observed FM in HfO2 could result from the holes that were doped in HfO2 system with nonmagnetic ions. The doped holes will enter the p bands of the oxygen atoms adjacent to the dopant and result in the p bands spin split. Obviously, the calculated results mentioned above are not consistent with the experiments. Moreover, previous researches focus on bulk magnetism, although the magnetization depends on the thickness of the undoped oxide thin films [6], which hints that surface or interface may impact the unexpected magnetism. In fact, the thinner the film is, the stronger the magnetization. Thus, the observed
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FM is clearly related to oxygen vacancies near to surface or interface. However, so far there were no calculations about the oxygen vacancies can induce the FM on HfO2 surface. 1 1Þ are For monoclinic HfO2, it is known that the (1 1 1) and ð1 the two most stable surfaces [12]. In this paper, we systematically study the electronic structures and magnetism of oxygen-deficient 1 1Þ surface. We firstly show that the oxygen HfO2 (1 1 1) and ð1 vacancies on the HfO2 surface can induce magnetism without magnetic doping. 2. Computational details The calculations in this article were carried out by using the Vienna ab initio simulation package (VASP) [13]. The projector augmented plane-wave (PAW) method with cutoff energy of 520 eV and the U-centered 2 2 1 k-mesh were used in the calculations. The generalized-gradient approximation (GGA) is used for treating the exchange and correlation potential [14]. The energy convergence error is 104 eV for the electronic loops and 103 eV for the ionic loops. In addition, forces on the atoms are less than 0.02 eV/Å when the structural relaxation cycles were terminated. 1 1Þ surfaces In this paper, we modeled the HfO2 (1 1 1) and ð1 by (2 2) surface cells consisting of four stoichiometric HfO2 monolayers (192 atoms in total). The thickness of vacuum layer above the slab was 10 Å. For comparison, the monoclinic HfO2 bulk is also modeled by 2 2 2 supercell, 96 atoms in total. The energy cutoff and convergence criteria are the same as above. The k-mesh was set to be 4 4 4 for the calculation of electronic properties. 3. Results and discussion
Fig. 1. Crystal structure of monoclinic HfO2. Deep yellow and red balls represent the Hf and O atoms (in all structural graphs), respectively. The geometries of O3c, O4c and Hf7c are also shown. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
were obviously symmetric in Fig. 2(d). So the oxygen vacancies can not induce the magnetism in HfO2 bulk. Our results are the same as previous study [10].
3.1. Bulk properties 3.2. The (1 1 1) surface with oxygen vacancies The monoclinic crystal is the most stable phase for the HfO2 [12], space group P21/c, with lattice parameters, a = 5.1156 Å, b = 5.1722 Å, and c = 5.2948 Å, b = 99.18° [1]. The bulk is constructed by three types of ions (see Fig. 1). The threefold-coordinated oxygen ions (O3c) will form an almost planar trigonal structure with the peripheral Hf atoms. And an imperfection of tetrahedron is formed by the fourfold-coordinated oxygen ions (O4c) with the coordinating Hf atoms. In addition, each Hafnium atom in the bulk is sevenfold-coordinated (Hf7c) with the coordinating oxygen (O) atoms. Fig. 2(a) showed the density of states (DOS) within GGA for the perfect HfO2 bulk. In the case, the band gap is open between the O2p valence band maximum (VBM) and Hf-d conduction band minimum (CBM). And the calculated band gap is about 4.08 eV, smaller than the experimental values of 5.7 eV [1]. The underestimation of band gap is the well-known side effect of local density based approximations including GGA. The DOS of the HfO2 bulk with one vacancy of O3c or O4c (i.e., VO3c or VO4c), were shown in Fig. 2(b) and (c). Although the impurity states will be formed in the band gap about 1.30 eV and 1.60 eV below the CBM for VO3c and VO4c, respectively, the majority and minority spin channels are symmetric in both Fig. 2(b) and (c). Therefore, the systems are both nonmagnetic. Now, we consider the complex defects of oxygen vacancies (CDOV) that are induced by two oxygen vacancies (VO’s). Fig. 2(d) shows the DOS of the bulk with VO3c and VO4c (VO3c–VO4c). The distance between the VO3c and VO4c is 2.540 Å, which is the nearest distance between two oxygen vacancies in the bulk. However, the results show that the system is also nonmagnetic from Fig. 2(d) according to our calculations. The majority and minority channels of the impurity bands which are induced by the CDOV
The HfO2 (1 1 1) surface is a complicated surface. There are four inequivalent surface oxygen atoms and one kind of Hafnium atom on the top layer of (1 1 1) surface. Two types of oxygen ions are twofold-coordinated (i.e., O2c-a and O2c-b), which the bond angle of O2c-a is larger than O2c-b. Other two types of oxygen ions are both threefold-coordinated (i.e., O3c-a and O3c-b), which the bond angles are also different (see Fig. 3). The Hafnium atom on the top layer of the surface is sixfold-coordinated. In Fig. 4(a), we can see that the perfect HfO2 (1 1 1) surface keep the characteristic of insulator, and the band gap is open between the O-2p VBM and Hf-d CBM. The band gap of the perfect surface is about 4.15 eV, also smaller than the experimental value of 5.7 eV for the bulk. When one oxygen vacancy is produced on the (1 1 1) surface, the system is still an insulator (see Fig. 4(b–e)). And it is obviously shown that the majority and minority spin channels are symmetry in Fig. 4, so the systems are all nonmagnetic. One single oxygen vacancy can not induce the magnetism on the HfO2 (1 1 1) surface. Next, we consider the case of CDOV which are composed of two oxygen vacancies. The list of CDOV on (1 1 1) surface was shown in Table 1. Here, we only consider the nearestneighbor distance for each kind of CDOV. The CDOV which are composed of the same type of oxygen vacancies are not considered, because the distance between the two oxygen vacancies is very large (more than 7 Å). The calculated densities of states were shown in Fig. 5(a–f). The CDOV can induce the impurity bands in the band gap in Fig. 5. However, only the VO2c-a–VO2c-b can induce the ferromagnetic ground state on the HfO2 (1 1 1) surface (see Table 1). And the total magnetic moment is 2.0lB. The total DOS (TDOS) of (1 1 1) surface with VO2c-a–VO2c-b is partially shown in Fig. 6. It is shown that the majority and minority
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Fig. 2. Calculated densities of states of: (a) perfect monoclinic HfO2 bulk, (b) the bulk with one VO3c, (c) the bulk with one VO4c, (d) the bulk with VO3c and VO4c (VO3c–VO4c). Fermi energy is set to be zero (in all DOS graphs).
(i.e., O3c-a and O3c-b). The bond angles are different between O3c-a and O3c-b (see Fig. 7). In Fig. 8, we can see that the results are the same as the (1 1 1) surface. The single oxygen vacancy can not induce the magnetism 1 1Þ surface. The perfect ð1 1 1Þ surface is also an insulaon the ð1
Fig. 3. Perfect HfO2 (1 1 1) surface, only the stoichiometric HfO2 monolayer on the top layer of the surface is shown. The bond angles [unit (°)] of the oxygen ions (i.e., O2c-a, O2c-b, O3c-a and O3c-b) are also shown, the oxygen ions are at the apex positions.
channels of the impurity bands are obviously asymmetric. The spin density map was shown in Fig. 6 inset. According to our calculations, the magnetic moments are mostly located at three Hf atoms adjacent to the CDOV. Projected DOS (PDOS) shows that the middle-gap impurity bands can be attributed to d-orbitals of the Hf atoms around the VO2c-a–VO2c-b. In addition, the calculations show that the total energy of ferromagnetic state for the (1 1 1) surface with VO2c-a–VO2c-b is lower than that of non-magnetic state by 200 meV. And we found that the calculations with antiferromagnetic initial states eventually converge to ferromagnetic states, so the ground state for the HfO2 (1 1 1) surface with VO2c-a–VO2c-b is ferromagnetic state. 1 1Þ surface with oxygen vacancies 3.3. The ð1 1 1Þ surface. On the Fig. 7 shows the structure of perfect HfO2 ð1 surface, there are two types of Hafnium atoms, i.e., sixfold-coordinated Hafnium ions (Hf6c) and sevenfold-coordinated Hafnium ions (Hf7c). One kind of oxygen ions is twofold-coordinated (O2c), and other two types are both threefold-coordinated oxygen ions
tor, with an open band gap of 3.84 eV, smaller than the (1 1 1) surface. Although the impurity states can be induced by VO2c, VO3c-a, or VO3c-b, the majority and minority spin channels are almost symmetric. Thus, the systems are all nonmagnetic. 1 1Þ surface. The list of Now, we will induce the CDOV on the ð1 1 1Þ surface was shown in Table 2. We also only conCDOV on ð1 sider the nearest-neighbor distance. The calculated results showed that VO2c–VO3c-a and VO2c–VO3c-b can induce the magnetism on the surface. And the magnetic moments are both 2.0lB. Fig. 9 shows 1 1Þ surface. It is obvithe calculated DOS for the CDOV on the ð1 ously that the surface with VO3c-a–VO3c-b is nonmagnetic. The surface with VO2c–VO3c-a or VO2c–VO3c-b will induce the impurity bands in the band gap. In addition, the majority and minority channels of the impurity bands are obviously asymmetric. So the system with VO2c–VO3c-a or VO2c–VO3c-b is magnetic. 1 1Þ with VO2c– Figs. 10 and 11 are the PDOS of the surface ð1 VO3c-a or VO2c–VO3c-b. The insets are the spin density maps in Figs. 10 and 11. For the surface with VO2c–VO3c-a, the magnetic moments mostly reside on five Hf atoms around the CDOV. And the magnetism can be attributed to d-orbitals of the Hf atoms. In Fig. 11, the magnetic moments are mostly located at three Hf 1 1Þ surface. And the atoms adjacent to the VO2c–VO3c-b on the ð1 magnetism also results from the d-orbitals of the Hf atoms. In addition, the calculations show that the total energy of ferro 1 1Þ surface with VO2c–VO3c-a (or VO2c– magnetic state for the ð1 VO3c-b) is lower than that of non-magnetic state by 366 meV (or 138 meV). And we also found that the calculations with antiferromagnetic initial states eventually converge to ferromagnetic states, 1 1Þ surface with VO2c–VO3c-a so the ground state for the HfO2 ð1 (or VO2c–VO3c-b) is also ferromagnetic state. 3.4. Discussion From the results mentioned above, we can get the conclusion that the CDOV play a key role in inducing the magnetism on the
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Fig. 4. Calculated densities of states of: (a) perfect HfO2 (1 1 1) surface, (b) the surface with one O2c-a vacancy (VO2c-a), (c) the surface with one O2c-b vacancy (VO2c-b), (d) the surface with one O3c-a vacancy (VO3c-a) and (e) the surface with one O3c-b vacancy (VO3c-b).
Table 1 The list of CDOV on the HfO2 (1 1 1) surface. The corresponding distances and magnetic moments are also shown. Type of complex defects
Nearest neighbor distance (Å)
Magnetic moment (lB)
VO2c-a–VO3c-a VO2c-a–VO3c-b VO2c-b–VO3c-a VO2c-b–VO3c-b VO3c-a–VO3c-b VO2c-a–VO2c-b
3.242 3.659 2.854 3.242 3.713 2.792
0 0 0 0 0 2.0
HfO2 surface. In the process of calculation, only VO2c-b on the (1 1 1) 1 1Þ surface can produce two energy surface and VO2c on the ð1 states in the system, see Fig. 12.
From Fig. 12, the two energy states are ferromagnetic state (FM) at Valley1 and nonmagnetic state (NM) at Valley2, respectively. And the Valley2 is the lowest position of energy, so NM is more stable than FM. For the HfO2 (1 1 1) surface with one VO2c-b, the energy difference DE for the two states is 29.7 meV, so the NM should be the ground state of the system. Similarly, the VO2c on the HfO2 1 1Þ surface can also produce FM and NM, and the DE is ð1 24.8 meV, thus the ground state of the system is also NM. If we induce another oxygen vacancy on the surface near the VO2c-b or VO2c, the ground state will be likely to become ferromagnetic ground state due to the interaction between the two VO’s. Furthermore, only the special CDOV can result in the ferromagnetic ground state, e.g., VO2c-a–VO2c-b, VO2c–VO3c-a and VO2c–VO3c-b. Other CDOV can not induce the magnetism, such as VO2c-a–VO3c-a, VO2c-a–VO3c-b and VO3c-a–VO3c-b and so on. One key factor is the
Fig. 5. Calculated densities of states of HfO2 (1 1 1) surface with: (a) VO2c-a and VO3c-a (VO2c-a–VO3c-a), (b) VO2c-a and VO3c-b (VO2c-a–VO3c-b), (c) VO2c-b and VO3c-a (VO2c-b–VO3c-a), (d) VO2c-b and VO3c-b (VO2c-b–VO3c-b), (e) VO3c-a and VO3c-b (VO3c-a–VO3c-b) and (f) VO2c-a and VO2c-b (VO2c-a–VO2c-b).
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M. Wang et al. / Computational Materials Science 92 (2014) 120–126 Table 2 1 1Þ surface. The corresponding distances and magnetic The list of CDOV on the ð1 moments are also shown.
Fig. 6. Projected DOS of Hafnium atoms adjacent to the VO2c-a–VO2c-b on the surface (1 1 1) is shown. The inset shows the spin density map for HfO2 (1 1 1) surface with one VO2c-a–VO2c-b.
1 1Þ surface, it was only shown the top layer of the Fig. 7. Perfect HfO2 ð1 stoichiometric HfO2 monolayer. The bond angles [unit (°)] of the oxygen ions (i.e., O2c, O3c-a and O3c-b) are also shown, the oxygen ions are at the apex positions.
Type of complex defects
Nearest neighbor distance (Å)
Magnetic moment (lB)
VO3c-a–VO3c-b VO2c–VO3c-a VO2c–VO3c-b
3.713 2.957 2.854
0 2.0 2.0
distance between two oxygen vacancies in CDOV (dCDOV). As we know, if the dCDOV is far enough, the effect is equivalent to two isolated oxygen vacancies and the system will be nonmagnetic. Thus, dCDOV could not be too large, otherwise the interaction between the two V0O s will be too weak. In Table 1, it was shown that the critical distance is about 2.792 Å on (1 1 1) surface. According to our calculations, the surface with VO2c-a–VO2c-b will be nonmagnetic when the distance between VO2c-a and VO2c-b is 5.267 Å which is the second nearest-neighbor distance. Therefore, when the dCDOV is larger than 2.792 Å, the CDOV can not induce the magnetism on the (1 1 1) surface. Similarly, the results show that the critical distance 1 1Þ is 2.957 Å in Table 2. Therefore, of the CDOV on surface ð1 when the distance is 2.854 Å, obviously, the VO2c–VO3c-b can also result in the ferromagnetic state. And when the distance between the two oxygen vacancies exceed 2.957 Å, e.g., the second nearest-neighbor distances are 4.056 Å and 4.624 Å for VO2c–VO3c-a and VO2c–VO3c-b, respectively, the CDOV also do not induce the magnetism. So it can be concluded that the interaction between the two oxygen vacancies in CDOV is short-range. Fig. 13 showed the schematic diagram of the spin state. When only one oxygen vacancy was produced on the surface, the total spin S = 0. The oxygen vacancy is an n-type defect, the two electrons which are released by the VO as compensating charge will fill in the molecular orbitals. And when the exchange energy (P) between the two lowest states is smaller than the split (D0) between them, the two spins will occupy the lowest state and they are antiparallel. This will result in a low spin state. This is the case of only one VO (see Fig. 13(a)). When the CDOV were produced on the surface, obviously, four electrons will be induced in the system. Two electrons will fill in
1 1Þ surface, (b) the surface with one O2c vacancy (VO2c), (c) the surface with one O3c-a vacancy (VO3c-a) and (d) the Fig. 8. Calculated densities of states of: (a) perfect HfO2 ð1 surface with one O3c-b vacancy (VO3c-b).
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1 1Þ surface with: (a) VO3c-a and VO3c-b (VO3c-a–VO3c-b), (b) VO2c and VO3c-a (VO2c–VO3c-a), (c) VO2c and VO3c-b (VO2c–VO3c-b). Fig. 9. Calculated densities of states of HfO2 ð1
1 1Þ) surface with Fig. 12. The diagram of state of energy for the HfO2 (1 1 1) (or ð1 one VO2c-b (or VO2c).
Fig. 10. Projected DOS of Hafnium atoms adjacent to VO2c–VO3c-a on the surface 1 1Þ is shown. The inset shows the spin density map for HfO2 ð1 1 1Þ surface ð1 with one VO2c–VO3c-a.
Fig. 13. Schematic diagram of the spin state, low-spin S = 0 and high-spin S = 1 states. (a) The surface with only one VO was shown, (b) and (c) show the surface with the CDOV.
1 1Þ Fig. 11. Projected DOS of Hafnium atoms around VO2c–VO3c-b on the surface ð1 1 1Þ surface with one is shown. The inset shows the spin density map for HfO2 ð1 VO2c–VO3c-b.
the lowest molecular orbital and they are antiparallel. Other two electrons, when the distance is larger than the critical distance, then P < D0, the two electrons will be antiparallel and occupy the second excited state and lead to a low spin state (see Fig. 13(b)). Because the interaction between the two oxygen vacancies was strong when the distance is less than or equal the critical distance, this will result in P > D0. Thus, the two spins will occupy the second and the third excited states, respectively. And it will result in a high-spin state (S = 1, see Fig. 13(c)). From the discussion mentioned above, the CDOV can result in the ferromagnetic ground state based on the following facts: (1)
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there was a non-ground state of FM for one oxygen vacancy in the CDOV; (2) the distance of two oxygen vacancies in CDOV should be less than or equal the critical distance, or else, the interaction is too weak to result in the high-spin state. These findings provide a new way to explain the d0-ferromagnetism in pristine oxides.
This research is sponsored by National Natural Science Foundation of China (Grant No. 10970499), and National Basic Research Program of China (973 Program, Grant No. 2011CB606405).
4. Conclusion
References
In conclusion, based on first-principle calculations we systematically studied the oxygen vacancies on the HfO2 surface. The results show that a single VO can not induce the magnetism on 1 1Þ surface. The CDOV can result in a high-spin the (1 1 1) and ð1 state, and produce the magnetic moment of 2.0lB. However, they have to meet two conditions. That is presence of a non-ground state of FM for one VO in the CDOV, and the dCDOV is less than or equal the critical distance. So our results suggest a useful mechanism which can interpret well that the local magnetic moments could be produced in HfO2 film without any doping. It is important to note, however, whether the local magnetic moment induced by the CDOV can produce macroscopic magnetism in the experiment, the magnetic coupling between the two CDOV’s in different distances would be further investigated.
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Acknowledgements