DFT calculations of Cu doped TiO 2 ferromagnetic study

. There is still some controversy about the room-temperature ferromagnetism generated by transition metal-doped TiO 2 and its magnetic generation. In this paper, the samples with different doping ratio were prepared to verify the magnetism of doped TiO 2 , and then the geometry of copper-doped Ti16O32 supercell system was optimized by using the overall energy density function theory (DFT) and generalized gradient approximation (GGA). The results show that the doped energy band diagram shows electron self-selective cleavage near the Fermi energy level and the addition of Cu atoms does produce ferromagnetism. The magnitude of the induced magnetic moment is related to the distance of Cu atoms and oxygen vacancies. The system with a doped Cu-Cu distance of 3.82 A is more stable, and the ferromagnetism of the doped phase is more stable and lower 29 meV than the antiferromagnetic state in the absence of oxygen vacancies (Cu 2 Ti 14 O 32 ), while a magnetic burst occurs in Cu 2 Ti 14 O 30 after the formation of oxygen vacancies. Magnetic Cu-TiO 2 may become a promising adsorbent to be applied in the field of pollutant control.


1.Introduction
Magnetic adsorbent is a magnetic solid material that can be used to separate, enrich and extract target substances in solution. It has wide application prospects in environmental governance, biomedicine, chemical analysis and other fields.
Whether CuO or TiO 2 nanoparticles, their use for wastewater treatment has the disadvantage of being difficult to separate from the treated wastewater. To address this issue, magnetic composite particles containing TiO 2 have been developed as multiphase catalysts in recent years [1] .Usually, copper-doped titanium dioxide is not magnetic. However, some studies have found that under certain conditions, copper-doped titanium dioxide will show a behavior similar to ferromagnetism, that is, showing characteristics such as hysteresis loop and saturation magnetization under an applied magnetic field. The magnetic properties of this copper-doped TiO 2 mainly comes from the change in its electronic structure. The d-electron level of copper couples with the t 2g electron level of titanium dioxide, leading to the enhanced electron spin polarization effect, which gives the material a behavior similar to ferromagnetism.Cu doped TiO 2 nanoparticles were prepared by sol-gel method and their magnetic properties were studied. The results showed that when the Cu concentration was 8%, the samples exhibited the maximum saturated magnetization and the area of the hysteresis loop, indicating a pronounced magnetic behavior. Meanwhile, the authors also explored the influence of Cu doping concentration and sample size on the magnetic properties of the materials [2] . These magnetic catalysts can be recovered and reused by an applied magnetic field [3] . Doping of transition metals generates magnetism because of electron spin [4] . In the research of Cu-doped TiO 2 films, ferromagnetism was reported by Hau et al. at room temperature, where the ferromagnetic coupling strength is based on the distance of doped atoms and decreases with increasing concentration of dopants [5] . Both experimental and theoretical results have shown that both cationic and anionic vacancies induce room temperature ferromagnetism [6] . However, the sources of magnetism in copper-doped systems in these studies are sometimes contradictory. Therefore, further studies are needed to understand the details of this process. Based on its properties, TiO 2 can be used as an excellent carrier to address agglomeration and recovery issues, thus to obtain better adsorption.

2.First-principles calculation
The Cu-doped crystalline phase structure was studied using CASTEP software based on density functional theory [7,8] . The TiO 2 space group of the anatase phase is I41/amd with lattice constants of a=b=3.822 nm and c=9.846 nm. The calculations were performed using the Monkonhorst-Pack method, in which, K-space grid points were selected with a plane wave truncation energy (Ecut) of 400 eV and an accuracy of 2.0×10 -6 eV/ atom, and the K-network in the Brillouin zone is chosen as 3×3×2. Cu, as a transition metal, has a strong electron correlation in the 3d orbitals. Therefore, the local density approximation (LDA) calculation is questionable for 3d ferromagnetic-doped oxides. The LDA+U [9] (U Cu 3d = 2.5 eV, U is the effective on-site Coulomb interaction between 3d electrons) is used in this work to correct the Coulomb interaction term of Cu 3d electrons.
According to the periodicity of the atoms in anatase TiO 2 , representative sites of doped Cu and V o (O vacancies) are shown in Fig. 1. The formation energies can be obtained according to the following formula:

Experimental
Firstly, Cu(NO 3 ) 2 ·3H 2 O and 20 ml of deionized water were added to beaker for dissolution. After stirring for 0.5 h, 4.0 g of anatase titanium dioxide was added to the solution and stirred enough in a heated environment to obtain a homogeneous slurry. Secondly, the homogeneous slurry was moved into a drying oven and dried at 80 ℃ for 12 h. Thirdly, the solid precursor was crushed, put into a muffle furnace, heated to 500 ℃ at a rate of 5 ℃/min, and baked during this temp for 4 h. Later, the solid precursor was crushed and finely ground to successfully prepare different copper oxide doped titanium dioxide adsorbents. The doped conditions: m(Cu):m(TiO 2 ) = 0.01:1 (CT1), 0.10:1 (CT10), 0.20:1 (CT20). For comparison, plain copper oxide without titanium dioxide was prepared using a similar method.

Results
The X-ray diffraction (XRD) spectra of anatase TiO 2 , Cu/TiO 2 adsorbent with different doping ratios and pure CuO were shown in Fig. 1.
and (204) crystal planes of anatase, respectively [10] . The characteristic peaks of rutile TiO 2 were not found in the XRD patterns of CT1, CT10, and CT20, demonstrating that the high temperature calcination at 500 ℃ during the material preparation did not convert anatase TiO 2 to rutile TiO 2 . No obvious Cu peak was observed in CT1, but with the increase of Cu content, the diffraction peak located at 35.5 ° gradually intensifies, in full agreement with the (-111) crystallographic plane of CuO [11] . Although no new diffraction peaks were detected in the doped sample, the peak position of Cu-doped TiO 2 was marginally moved to the right compared to that of pure anatase TiO 2 , indicating some Cu 2+ have entered into the TiO 2 lattice. The shift may be due to the substitution of Cu 2+ (ionic radius 87 pm) for Ti 4+ (ionic radius 74.5 pm) [12] .Therefore, we further analyzed the average particle size of TiO 2 and doped samples by XRD, TiO 2 , CT1, CT10 and CT20 are 22.5nm,22.9nm,23.1nm and 23.6nm, respectively; FT-IR spectroscopy results. As shown in fig.2.(b), the absorption cone of TiO 2 is at 532cm -1 , with Cu doping, the Cu-O has shifted the peak at about 632cm -1 . These phenomena fully proved the existence of the doped phase in the doped samples. The results of the VSM studies at room temperature for different samples are shown in fig.2.(c), and the M-H measurements for all samples were performed by changing the magnetic field from -90 kOe to +90 kOe. TiO 2 The sample showed a very weak room-temperature ferromagnetism, which may be related to the presence of trace amounts of Ti 3+ in the sample. It can be seen that both CT1 and CT10 have PM behavior, and interestingly, both CT10 and CT20 have a diamagnetic tail, which may be attributed to the presence of diamagnetic CuO in the sample, and the amount of CuO present in CT20 is much larger than that in CT10. Therefore, the amount of Cu doping is a key factor in determining the magnetic properties of the Cu/TiO samples. Meanwhile, which would indicate that Cu/TiO 2 may have more widespread in the adsorbent field. In the doped system of TiO 2 , some defects may exist, such as oxygen vacancy, Ti vacancy, metal interstitials, and the production of Oions on the lattice [13] . However, the oxygen vacancy is considered inherent defect caused by doping. The substitution of Cu 2+ for Ti 4+ causes a charge imbalance in the cell, which is compensated by oxygen vacancy according to the principle of electrical neutrality. For this reason, Cu-doped TiO 2 systems containing oxygen vacancy were included in our study. Based on the periodicity of Ti atoms in the TiO 2 cell, the doping sites in this work are shown in Fig. 1 in conjunction with the study by S Roy et al. [14] .The formation energy (E f ) of substitutional doping of individual Cu atoms was calculated in this work, and it was found that the lowest formation energy was found at substitutional position 4, which was 10.07 eV. The higher E f shows that the reaction of doping is not spontaneous and requires external energy to form, which also explains that the CuO and Cu 2 O in the as-prepared sample are mostly loaded on the surface of TiO 2 .
Cu with 3d 10 4s 1 electron configuration provides two electrons to the surrounding six O atoms, producing s-p-d orbital hybridization, so Cu tends to behave as a valence of +2 in the oxide doped system. According to the energy splitting theory in the crystal field, the Cu 3d orbital can split into two e g orbitals and three t g orbitals. From the perspective of energy, the energy of the three t 2g orbitals is lower than that of the two e g orbitals, so the remaining nine electrons on the Cu 3d orbital will preferentially occupy the lower energy t 2g , forming t 3 2g+ t 3 2g-e 2 g+ e 1 g-, and in turn cause an asymmetry between e g+ and e g-, thus generating a magnetic moment of 1 μB. Almost in agreement with the above hybridization theory, the calculation results demonstrate that a magnetic moment of 1.01 μB is indeed generated in the doped system of CuTi 15 O 32 . As shown in Fig. 3, two spin-up electrons and one spin-down electron are produced in the energy band of CuTi 15 O 32 . Compared to Ti (Fig. 4c), the PODS peaks of Cu 3d (Fig. 4b) and O 2p are close to each other in the range of -5eV-0eV, indicating a strong p-d coupling between Cu 3d and O 2p. Fig. 4a shows the spin asymmetry at the upper and lower spin density of the state diagram at the Fermi energy level in the CuTi 15 O 32 structural system, where spin splitting occurs as the root cause of the magnetic moment. The density of states diagrams by Cu (Fig. 4b) and O (Fig. 4d) illustrate that the magnetic moments in the cell are mainly contributed by Cu 3d orbitals and O 2p orbitals. The peak of Cu 3d in PDOS is larger than that of O 2p, indicating that the magnetic moments are mainly contributed by Cu-3d orbitals. The PDOS diagram of Ti (Fig. 4c) is almost completely symmetric, indicating that Ti does not contribute to the overall cell magnetic moments. The calculations show that Cu produces 0.4 μB of the magnetic moment, which accounts for 40% of the overall magnetic moment, meaning that the remaining 60% of the magnetic moment is provided by the six O around Cu.
The detailed results of the calculations for the doping of single Cu atoms at different spots and two Cu atoms at different spots in this work are shown in Table 1. In Cu 2 Ti 14 O 32 , the doping positions (1,2) and (3,4) are calculated in perfect agreement, so it can be determined that the magnitude of the magnetic moment is related to the distance between the two Cu atoms. The optimal distances that produce the largest magnetic moments are 3.11 Å versus 5.40 Å, which is similar to the results for Cu-doped rutile TiO 2 [15] . It seems that the Cu-Cu distance is the key to determining the magnitude of the magnetic moment, and the more distant distance tends to produce a larger magnetic moment, but this is not absolute, where the doping position (1,3) produces a magnetic moment of 2.06 μB. Interestingly, the magnetic moment is larger when two Cu atoms are in diagonal positions: (1,3), (1,4) and (3,5). When the distance of Cu-Cu is 3.82A, the doping formation energy is the lowest, indicating that the structure (3,4) is more stable. The magnetic moment of structure (3,4) is 1.34 μB. The difference between the ferromagnetic and antiferromagnetic formation energy of Cu 2 Ti 14 O 32 is -29 meV, which confirms that the Cu-doped TiO 2 ferromagnetic state is more stable. To maintain the electronrutral local environment within the cell, the O vacancies are generally around the Cu atoms. In CuTi 15 O 32 , as shown in Fig. 3

. Conclusion
The results show that the doped energy band diagram shows electron self-selective cleavage near the Fermi energy level and the addition of Cu atoms does produce ferromagnetism. The ferromagnetism of the Cu doped TiO 2 is calculated by DFT and shows that the magnitude of the induced magnetic moment is dependent to the distance of Cu atoms and the oxygen vacancies. The system with the Cu-Cu distance of 3.82 A in the doped phase is more stable, and the ferromagnetism of the doped phase is more stable than the antiferromagnetic state in the absence of oxygen vacancy (Cu 2 Ti 14 O 32 ). However, magnetic quenching occurred in Cu 2 Ti 14 O 30 after oxygen vacancy formation. The theoretical magnetic study of titanium dioxide can provide some theoretical basis for titanium dioxide in the field of pollutant control.