Oxygen Defect-Mediated Magnetism in FeC Codoped TiO 2

Themagnetic properties of the C doped and C-Fe codoped TiO 2 films fabricated by sol-gel and spin coating have been investigated combining experiments and first-principles calculations. All the samples exhibit the anatase crystal phase and the room temperature ferromagnetism.The values of the saturationmagnetizations are in the order of Fe-C codopedTiO 2 > Fe-C codopedTiO 2 (annealed in O 2 ) > C doped TiO 2 > C doped TiO 2 (annealed in O 2 ). The calculated net moment values are in the order of Fe-C codoped TiO 2 > C doped TiO 2 with oxygen vacancies existing, in accord with the experimental results. The hybridization of Fe 3d, C 2p, and O 2p (nearest to the Fe defect) led to the spin split of Fe 3d, C 2p, and O 2p which contributed to the ferromagnetism.


Introduction
Diluted magnetic semiconductors (DMSs) are promising candidates for the spin-polarized devices such as magnetooptical, nonvolatile storage and other spin logical devices [1].However, most of these DMSs have relatively low Curie temperatures (  ), reducing their practical usefulness.In the recent decades, oxide diluted magnetic semiconductors such as ZnO [2], SnO 2 [3], and TiO 2 [4] doped with magnetic transition metal elements have attracted considerable attention, due to the discovery of room temperature (RT) ferromagnetism (FM) in these systems.Several theoretical investigations have been reported, most of which focus on the cation vacancies in TiO 2 bulk materials [5][6][7][8][9][10].However, recent studies showed that the unexpected RT FM is closely related to the oxygen vacancies (Vos) instead of the cation vacancies [11][12][13][14][15][16][17].Vo is a type of defects in TiO 2 which can be manipulated relatively easily during the synthesis processing [17].Near the surface or in the bulk, Vos can lead to ferromagnetism enabling a possible application for TiO 2 as a magnetic semiconductor in spintronics [18].
In TiO 2 based DMSs, it is concluded that there are four factors related to the observed ferromagnetism: the Vos, cation vacancies, transition metal dopants, and the change of titanium oxidation state (Ti 3+ ) [16].On the one hand, the Vos can cause an obvious change in the band structure and make a significant contribution to the FM.On the other hand, the transition metal elements which have unpaired d-electrons can provide magnetic moment to the DMSs.In this paper, we have investigated the electronic and magnetic properties of transition metal (Fe), nonmetal C, and Vos codoped anatase TiO 2 (Ti 31 FeO 62 C) combining the experiments and the first-principles calculations based on the density-functional theory (DFT).The experimental results are consistent with the first-principles calculations.The magnetism induced by the Fe and C (Fe-C) codoping is investigated being associated with the V O defect electrons.The connections between doped Fe ions, C ions, and Vos are discussed to explain the ferromagnetism observed in these materials.

Experiments and Calculations
The C doped TiO 2 films, C doped TiO 2 films (annealed in O 2 ), Fe-C codoped TiO 2 films, and Fe-C codoped TiO 2 films (annealed in O 2 ) were prepared by sol-gel and spincoating methods.A clear solution was prepared by reacting tetrabutyl titanate (C 16 H 36 O 4 Ti) and nanotube carbon (C) with a mixture of water and hydrochloric acid (HCl) in an ethanol (C 2 H 5 OH) diluted medium.The C doped TiO 2 films were spin-coated on the fluorine doped tin oxide (FTO) substrates with the mentioned solution.After the prebaking at 70 ∘ C for 30 min, these films were annealed at 450 ∘ C for 2 h in O 2 gas and in air to obtain the C doped and the Vos-decreased C doped TiO 2 films, respectively.To get the Fe-C codoped samples, iron nitrate hydrate was added into deionized water; and the C doped TiO 2 films were immersed in the solution for 1 hour.Following the same procedure as that for the C doped and the Vos-decreased C doped TiO 2 samples, the Fe-C codoped and the Vos-decreased Fe-C codoped samples were prepared.
The crystal structures were characterized by X-ray diffraction (XRD, Bruker D8 Discover) with Cu K radiation ( = 1.54 Å).The electronic structures were measured by the X-ray photoelectron spectroscopy (XPS) and the binding energy of the XPS spectra was calibrated with reference to the C 1s peak at 284.6 eV.The optical absorption spectra in the wavelength range of 200-800 nm were measured by using ultraviolet-visible near infrared spectrophotometer (CARY5000, Varian) at RT under the diffuse reflection mode with the integrating sphere.The photoluminescence (PL) spectra were conducted by using the 325 nm He-Cd laser (20 MW) as an excitation light source.The magnetic properties were studied using a vibrating-sample magnetometer (VSM) equipped in the physical property measurement system (PPMS, Quantum Deign).The magnetization loops were recorded with the magnetic field from −1 T to 1 T (T is the abbreviation of Tesla) applied parallel to the samples surfaces.
First-principles calculations based on spin-polarized density-functional theory and projector augmented wave (PAW) pseudopotential technique are performed as implemented within the Vienna Ab-Initio Simulation Package (VASP) [19,20].The generalized gradient approximation (GGA-PBE) for the wave functions is used with a cutoff of 400 eV to model the exchange and correlation functional [21].The calculations have been carried out for three cases: (1) one oxygen (O) atom is substituted by a Vo (Ti 32 O 63 ); (2) two O atoms are substituted by a Vo and a C atom (Ti 32 O 62 C); (3) a titanium (Ti) atom and two O atoms are substituted by an Fe atom, a V O , and a C atom (Ti 31 FeO 62 C).The Monkhorst-Pack scheme -points grid sampling was set to be 2 × 2 × 5 for the 95-atom anatase supercell.The valence electrons configurations for the O, C, Ti, and Fe are 2s 2 2p 4 , 2s 2 2p 2 , 3s 2 3p 6 3d 2 4s 2 , and 3d 3 4s 2 , respectively.All the atomic positions are fully optimized until the atom forces drop below the value 0.02 eV/ Å. referred to as FTO (110), ( 101), (211), and (301).No signals of impurities such as rutile, FeTiO 3 , or Fe cluster are detected.In addition, for the C doped TiO 2 films (annealed in O 2 ) and Fe-C codoped TiO 2 films (annealed in O 2 ), the XRD diffraction peaks show a relative lower intensity and a wider full width at half maximum (FWHM) comparing with the XRD data of C doped TiO 2 films and Fe-C codoped TiO 2 films.The average particle sizes of all the films were calculated and estimated using Scherrer equation choosing the Brag angle at (101), (004), and (200) diffraction peak.It is shown that the values of average particle size are 24.5 nm and 26.8 nm, for the C doped TiO 2 films and Fe-C codoped TiO 2 films, respectively.After the sample was annealed in O 2 gas, the values of average particle size decreased to 18.2 nm and 23.6 nm for the C doped TiO 2 films and Fe-C codoped TiO 2 films.The variation of the particle size originates from the difference of the doped element (Fe or C) and annealing gas (O 2 ).

Results and Discussions
Figure 2 demonstrates the XPS core levels for O-1s, C-1s, and Fe-2p of the Fe-C codoped TiO 2 films.As it is shown in Figure 2(a), the core level spectrum of O-1s is fitted with two peaks at 530.14 eV and 531.70 eV, attributed to O 1s in Ti-O linkages and Ti-O-C bonds of TiO 2 , respectively.Figure 2(b) shows the core level spectrum of C-1s which can be fitted by four peaks at 284.84 eV, 286.71 eV, 283.6 eV, and 288.60 eV, respectively.The peak of 284.84 eV clearly arises from adventitious element carbon which also exists in the case of pure TiO 2 samples.The peaks at 286.71 eV, 283.6 eV, and 288.60 eV are attributed to C-O and C-Ti and COOH binding, respectively.Therefore, multiple carbon species, namely, substitutional and interstitial carbon atoms and carbonate species, coexist in the lattice of TiO 2 .Figure 2(c) reveals the Fe 2p core level XPS spectrum.Apparently, there are two main peaks of Fe 2p 3/2 and Fe 2p 1/2 located at 710.71 eV and 724.52 eV, respectively, close to the binding energy of Fe 3+ ion which indicates the existence of Fe 3+ [22].It is noticed that there is no weak peak at binding energy around 709 eV introduced by the contribution of Fe 2+ ion in the spectrum.The PL spectra are very sensitive to the stoichiometry and surface states for materials, which can provide information on electronic and optical properties [25,26].All the PL spectra of the specimens show two strong emission peaks at 468 nm and 480 nm, which are attributed to the Vos [27,28].The emission peaks corresponding to the defects are largely enhanced after annealing in O 2 gas.
Figure 4 shows the plots of magnetization () versus applied magnetic field () which demonstrate hysteresis behaviour in all samples measured by a VSM with the magnetic field from −1 to 1 T at RT.The values of the saturation magnetization (  ) are in the following order: the C doped TiO 2 (annealed in O 2 ) < C doped TiO  In order to understand the origin of RT FM in the Fe-C codoped TiO 2 films, the first-principles calculations are performed.The positions of V O , Ti, Fe, C, and O for V O -Fe-C codoped TiO 2 are the same as those of the V O doped TiO 2 and the V O -C codoped TiO 2 .Firstly, when there exists only one Vo in the supercell, each Vo is assumed to donate two electrons.The result indicates that the two electrons created by one Vo are shared by three equivalent Ti 3+ ions with up-spin of three different directions, which is similar to the results reported by Yang et al. [29].The calculated net magnetic moment of the system is about 0.533   , which is related to the denoted two electrons that occupy the three neighboring Ti sites.The second and the third scenarios are V O -C codoped TiO 2 (Ti 32 O 62 C) and V O -Fe-C codoped TiO 2 (Ti 31 FeO 62 C), respectively.
Figure 5 shows the TDOS and PDOS of Vo-C codoped TiO 2 and Vo-Fe-C codoped TiO 2 , respectively.The calculated band gaps using the GGA functional are about 2.09 eV for the Vo-C codoped TiO 2 and Vo-Fe-C codoped TiO 2 , which is lower than the experimental value of 3.20 eV.However, the reduced band gap has nearly no influence on the magnetic state of C doped anatase TiO 2 and Fe-C codoped TiO 2 .
Figure 5(a) shows the TDOS and PDOS of C 2p electrons for Vo-C codoped TiO 2 samples.It can be seen from Figure 5(a)I that there is no spin splitting around the Fermi level, which illustrates that the Vo-C codoped TiO 2 samples have no magnetic property.For the PDOS of C 2p electrons (in Figure 5(a)II) nearest to the Vo, there are also no exchange splitting around the Fermi level between the spin-up and spin-down states, lying within the band gap.With respect to the local Cartesian coordinate, the up-spin and downspin of C 2  , C 2  , and C 2  states are all occupied.This indicates that the two electrons, created by one Vo, were trapped by the doped C atom.As a result, the valence electrons configuration for doped C atom is 1s 2 2p 6 , which produces 0   net magnetic moment.
Figure 5(b)I exhibits the TDOS for Vo-Fe-C codoped TiO 2 sample.It can be seen that a part splitting between the spin-up and spin-down states around the Fermi level is shown illustrating the existence of magnetism.For the PDOS of Fe 3d electrons (in Figure 5 codoped TiO Combining all the results presented above, we introduced a defect electron based model for the observed ferromagnetism.The magnetic moment is associated with a Vo, C 2− /Vo/Ti 4+ , and C 2− /Fe 3+ /Vo complex for Vo-C codoped TiO 2 and Vo-Fe-C codoped TiO 2 , respectively.The magnetic orbitals extend to nearest neighbor and second neighbor around the complex.In the two models, the two electrons denoted by Vo mediate the coupling of C 2− /Vo/Ti 4+ and C 2− /Fe 3+ /Vo complex, possessing the characteristics of 3d electrons of Ti 4+ and Fe 3+ , occupying C 2p site, partly O 2p sites, and Fe 3+ site.This is the original signal of the C 2− and Fe 3+ , which also can be used to explain the reason that there is only Ti 4+ signal appearing in XPS spectra.The value of total magnetic moment for Vo-Fe-C codoped TiO 2 and Vo-C doped TiO 2 is in the same order of   for Fe-C codoped TiO 2 and C doped TiO 2 .

Conclusions
In summary, the RT FM properties of the C doped TiO

Figure 3 (
Figure 3(a) illustrates the UV-Vis absorption spectra for these samples, which exhibit the characteristic spectrum of TiO 2 with its fundamental absorption edge around 384 nm (3.2 eV of band-gap energy).The absorption edges of the C doped TiO 2 films, C doped TiO 2 films (annealed in O 2 ), Fe-C codoped TiO 2 films, and Fe-C codoped TiO 2 films (annealed in O 2 ) are 387 nm, 370 nm, 399 nm, and 392 nm, with calculated band-gap energy of 3.20 eV, 3.35 eV, 3.11 eV, and 3.16 eV, respectively, similar to those reported in [23, 24].Comparing with the samples annealed in O 2 atmosphere, the absorption edges of the C doped and Fe-C codoped TiO 2 films both shifted slightly toward the visible light range.The values of the band gap are in the following order: Fe-C codoped TiO 2 > Fe-C codoped TiO 2 (annealing in O 2 ) > C doped TiO 2 > C doped TiO 2 (annealing in O 2 ).The spectrum of Fe-C codoped sample yields the largest red shift which indicates the doping of Fe or C element may narrow the band gap.

Figure 3 (
Figure 3(b) presents the PL spectra of C doped TiO 2 films, C doped TiO 2 films (annealing in O 2 ), Fe-C codoped TiO 2 films, and Fe-C codoped TiO 2 films (annealing in O 2 ) at RT.The PL spectra are very sensitive to the stoichiometry and surface states for materials, which can provide information on electronic and optical properties[25,26].All the PL spectra of the specimens show two strong emission peaks at 468 nm and 480 nm, which are attributed to the Vos[27,28].The emission peaks corresponding to the defects are largely enhanced after annealing in O 2 gas.Figure4shows the plots of magnetization () versus applied magnetic field () which demonstrate hysteresis behaviour in all samples measured by a VSM with the magnetic field from −1 to 1 T at RT.The values of the saturation magnetization (  ) are in the following order: the C doped TiO 2 (annealed in O 2 ) < C doped TiO 2 < Fe-C codoped TiO 2 (annealed in O 2 ) < Fe-C codoped TiO 2 .

2
films and Fe-C codoped TiO 2 films have been investigated.The values of the saturation magnetizations are in the order of Fe-C codoped TiO 2 > Fe-C codoped TiO 2 (annealed in O 2 ) > C doped TiO 2 > C doped TiO 2 films (annealed in O 2 ).The calculated net moment values are in the order of Fe-C codoped TiO 2 > C doped TiO 2 with Vos existing, which are in accord with the experimental results.These calculations suggest the key factor for the formation of ferromagnetic ordering is the Vo which contributes two electrons to the doped C atom and neighboring O sites.The hybridization of Fe 3d, C 2p (nearest to the Fe atom), and O 2p (nearest to the Fe defect) led to the spin splitting of Fe 3d, C 2p, and O 2p which contributed to the magnetism.The unique characteristic of the defect electrons denoted by a Vo in Fe-C codoped TiO 2 and C doped TiO 2 is that they provide the means for the percolation of the magnetic complexes to achieve magnetization in the Fe-C codoped samples.
2. With respect to the local Cartesian coordinate, the spin-up and spin-down states of Fe 3  are occupied, while for Fe 3  , Fe 3  , and Fe 3  2 the spin-up states are occupied; for Fe 3d xy , only a few spin-down states are occupied.Noticeably, there are no spin-up and spin-down states of Fe 3  2 occupied.This indicates that each doped Fe atom at the Ti site produces the net magnetic moments of 2.538   , and its electron configuration can be resembled as Fe 3+ (3d 5 ).For the PDOS of C 2p electrons (in Figure5(b)III), the C 2p states are spin-polarized and lie within the band gap of Vo-Fe-C codoped TiO 2 .With respect to the local Cartesian coordinate, the spin-up and spin-down states of C 2  and C 2  are all occupied, while, for C 2  , the spin-down C 2  states are occupied and partly spin-up 2  states are not; as a result, the valence electrons configuration for the doped C atom is 1s 2 2p 5 .This indicates that each doped C atom at the O site produces −0.025net magnetic moments.For the PDOS of O 2p electrons (in Figure 5(b)IV), the C 2p states are partly spin-polarized and lie within the band gap of Vo-Fe-C codoped TiO 2 .With respect to the local Cartesian coordinate, the spin-up and spin-down states of O 2  , O 2  , and C 2  are all occupied, but the slightly spin-up states of O 2  appear around Fermi level energy; as a result, the valence electrons configuration for O atom is 1s 2 2p 6 .The calculated net magnetic moment of O atom nearest to doped Fe atom is 0.075   .To analyze the spin polarization induced by the doped Fe atom and C atom, we calculated the spin density distribution Fe and C atom.The calculated results are that the magnetic moment is mainly delocalized around the Fe atom, namely, about 2.538   on the Fe atom, about −0.025   on the C atom, about 0.079   on the nearest-neighbor O atom, and about 0.029   on the second-neighbor O atom.The calculated result indicates that the magnetic orbital describing the doped Fe, Vo, and C center extends to the second-nearest-neighbor O atoms.One of the two electrons created by the Vo is trapped by the doped C atom, and the other one is shared by Fe, C, and O atoms surrounding it.The total magnetic moment is 3.216   for the Vo-Fe-C codoped TiO 2 .