Profiles of oxygen and titanium point defects in ferromagnetic TiO2 films

Experimentally it is shown that without any oxygen manipulation for TiO2, a strong room temperature ferromagnetism could be expected only in ultra-thin films, with the ideal thickness below 100 nm. Both bulks and nano-powders of TiO2 are diamagnetic, indicating that the surface and its nano-sublayers play very important roles in tailoring the magnetic properties in this type of compound. To shed a new light on the defect-related magnetism in the typical case of anatase TiO2 surfaces, we have performed a series of quantum-mechanical calculations for TiO2 slabs containing Ti or O vacancies in different distances from the (001) surface. The lowest formation energies were obtained for the Ti vacancies in the first sub-surface layer and the O vacancies within the surface. The computed magnetic states reflect complicated structural relaxations of atoms influenced by both the surface and vacant atomic positions. O atoms cannot contribute much to magnetic moment when Ti vacancies are isolated and far from the surface. Ti vacancies in TiO2 are only metastable. The formation energy of Ti interstitials is lower than for Ti vacancies since high-temperature annealing, especially with a lot of O2 available that would fill up O-related defects, and as a result, eliminate most of Ti vacancies. Lower temperatures, less O2, and shorter exposure times may enable not only partial elimination of Ti vacancies but also can facilitate their diffusion into different states of aggregations. In the ferromagnetic films (i.e. thin films below 100 nm), it looks like that the O atoms are located closer to the Ti vacancies.


Introduction
The magnetic semiconducting oxide thin films of TiO 2 , SnO 2 , In 2 O 3 , ZnO, etc have been known to be potential materials for spintronic applications.The observed ferromagnetism (FM) at Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.room temperature found in pristine semiconducting oxide thin films [1][2][3][4] and nanoparticles [5] has been considered as an extraordinary phenomenon in the domain of magnetic materials for almost two decades.Oxygen vacancies and/or defects have been thought to be the origin of the observed FM due to the facts that (1) there is no 3d doping [1][2][3][4]6]; (2) annealing in oxygen atmosphere in most of the cases, reduced magnetic ordering [2,3].However, so far, the experimental results have not been thoroughly explained.This topic, therefore, remains focal and interesting for materials science and condensed matter physics community.It is important for applications if the physical picture of that phenomenon can be clarified.
In 2021, a model of oxygen vacancies was proposed to explain for the induced FM in undoped oxide films [7].An electronic structure calculation was carried out using the tight binding method in the confinement configurations, to show that a vacancy site in these oxides could create spin splitting and high spin state.The exchange interaction between the electrons surrounding the oxygen vacancy with the local field of symmetry could lead to a ferromagnetic ground state of the system.The paper has underlined the importance of having low dimensionality in the materials.Very recently, some other group also reported about the possibility of obtaining room temperature FM even in out-of-plane direction for ultrathin films TiO 2 with defects created by irradiating the samples using low-energy ions, exploiting both important features such as 2D and defects in TiO 2 films [8].
Since there are always conflicting viewpoints on this topic, such as (i) if the observed FM is intrinsic or not; (ii) what should be the profile of defects/vacancies; (iii) the real role of low dimensionality in inducing the FM, etc.We have done further experiments and simulations for TiO 2 as a representative for the diluted magnetic semiconducting oxides group, with hope to be able to clarify the origin of the induced FM in this family.

Samples fabrications and measurements
A TiO 2 target, and TiO 2 nanoparticles were synthesized by sol-gel route using chloride salt (TiCl 4 and SnCl 4 -Sigma-Aldrich) as the precursor.First, the precursors were added to the isopropanol (IPA) solution and stirred for 15 min to make them diffuse together, then the mixture solution was stirred for 4 h at room temperature.Then, the homogeneous solution was dried for 24 h at 120 • C. The obtained powders were separated into two parts.For the first part, powders were annealed in the air at 1100 • C for 1 h and pressed into the pellets to serve as targets for film fabrications.Then, it was sintered at 1300 • C for another 1 h.The second part was annealed at 500 • C-700 • C in the air for 1 h, to result in nanoparticles whose size is 9 nm.
Films of TiO 2 were deposited by a pulsed-laser deposition system (KrF, 248 nm) from a ceramic target on (100) LaAlO 3 (LAO) substrates with an energy density as of 2 J cm −2 , and a repetition rate as of 10 Hz.The growth conditions for those undoped oxide films are the optimal conditions we had found for our systems with the substrate temperature kept at 650 • C, the oxygen pressure as of 0.01 mbar, and the O 2 : Ar flow ratio was 50:50.The typical thickness of TiO 2 films varies from 40 nm to 500 nm, depending on our purposes.A typical deposition time for a film of 100 nm thick was about 20 min.All films of TiO 2 are colorless, shiny, and highly transparent.The thickness of thin film was determined by x-ray reflectivity measurements with the beam aligned parallelly, with Cu-K α wavelength, and an acceleration voltage of 40 kV.The data was then fitted by the GenX software to determine the thickness, density, and roughness of thin film.
For the TiO 2 powders, target and films, structural studies were done by x-ray diffractions (XRD) at room temperature.
Measurements of magnetic moment (M) versus magnetic field (H) from 0 to 0.5 T, and versus temperature (T) from 5 K up to 400 K were performed by using a VSM magnetometer.The magnetic field was applied parallel to the film plane.

Computational methodology
For our quantum-mechanical calculations we used the density function theory implemented in the Vienna Ab-initio simulation package (VASP) [9,10] with the projector-augmentedwave (PAW) pseudopotentials (10-electron Ti_pv, which treats also 3p electrons as valence ones, and 6-electron O potentials) [11] and the generalized gradient approximation for the exchange-correlation energy.Based on the previous results in the materials project database (mp-390_TiO 2 ), the plane-wave energy cut-off was set to 520 eV.We performed the convergence tests to confirm that the accuracy of the calculations is high enough for our current study.Additional computational details are in the appendix.

Results and discussions
All TiO 2 films are single phase, well crystallized, and c-axis oriented (see a typical XRD pattern shown in figure 1).The lattice parameters of anatase TiO 2 were determined to be a = b = 3.782 ± 0.0004 Å, c = 9.532 ± 0.0004 Å.
From our previous report, it was shown that TiO 2 bulk is diamagnetic at room temperature [2].Based on what was observed in various undoped semiconducting oxides, it suggested that the room temperature FM could be induced only in low dimensional configurations [2][3][4][5]7].Thus, we will carefully clarify the case of low dimensional TiO 2 .
In figure 2, the magnetization (M) versus magnetic field (H) curves of TiO 2 powders (of about 9 nm in size) and thin films with various thickness are shown.According to the previous assumptions for room temperature FM in nano-sized TiO 2 , then one should expect to see an induced FM in both configurations, nano-powders, and thin films.However, from figure 2(a), it is clearly seen that nano-powders of TiO 2 are well diamagnetic.We would like to note here that our nanoparticles were synthesized in air, with free oxygen and there was no control.Thus, this condition of having a large quantity of oxygen available would not favor FM in particles.It is supposed that FM is expected in low dimensional TiO 2 but should be due to oxygen vacancies and defects.However, in the case of TiO 2 particles, O vacancies could not exist, and an atmosphere with lots of oxygen will eliminate Ti vacancies as well.
From figure 2(b), one can see that only films of TiO 2 show ferromagnetic behavior.When the thickness is below 100 nm, films are strongly ferromagnetic at room temperature.When the thickness increases, the magnetic ordering degrades, and almost disappears when reaching 300 nm.The magnitude of saturated magnetization of 100 nm thick film is very great, about five times larger than the greatest value reported so far in [2].Since the induced FM in TiO 2 is assumed to probably come from Ti defects and oxygen vacancies [2], it is likely that our deposition conditions for TiO 2 films favor the formations of those defects/oxygen vacancies on the surface, or more precisely to say, within the layer of 100 nm taken from the surface of the TiO 2 films.Note that all films have the same area size.The almost vanishing magnetic moment in the thickest film of 300 nm is rather consistent with a 3D-like behavior of the TiO 2 bulk (ceramic piece) reported in [2] showing that TiO 2 bulk is well diamagnetic at room temperature.It appears to us that the observed room temperature FM has something related to the surface.What we see in here is that, having a flat surface is important, but there should be some constraints going together with it, in the perpendicular direction along the thickness (e.g. in very thin films), because the FM indeed does not appear in thick films.One may note that the saturated magnetization for the 45 nm thick film is smaller than that of the 100 nm thick one.We must say that if the FM originates from oxygen or titanium point defects, then the profile of those is certainly not linear, and the specific fabrication conditions (PO 2 , temperature, as well as Ar:O ratio) may cause some point defects that are not distributed homogenously along the depth.Note that as higher vacuum (such as PO 2 as of E-6 Torr), this profile seems to be more linear, resulting in larger saturated magnetization for thinner films of 5-10 nm [2].
Besides the fact that not all low dimensional TiO 2 configurations can be ferromagnetic (seeing from figure 2 that our TiO 2 nano-powders, so-called 0D, are not ferromagnetic at all), one should note that a strong FM must be unique for ultra-thin films only.In previous reports, some semiconducting oxide nano-powders such as CeO 2 , Al 2 O 3 , ZnO, In 2 O 3 (not TiO 2 ) could be ferromagnetic, but some special oxygen treatments were indeed applied [12][13][14][15], or in the case of TiO 2 , artificial defects must be created by irradiations for films [8] and for rutile single-crystal [16].To summarize better, a plot of saturated magnetization versus thickness for TiO 2 fabricated under the same conditions is shown in figure 3.One can see clearly that if one should say the room temperature FM in TiO 2 films comes from oxygen or titanium vacancies/defects, then those vacancies and defects must be located favorably on the surface and within the sub-layer of 100 nm taken from the surface.It is likely that having a surface and a nano sub-surface layer impacted, should play a very important role in inducing room temperature FM in this family of compounds.One can conclude that creating oxygen vacancies and defects are key points, but it is even more important is that those must be compacted in a 2D structure, let say, ultra-thin films.The XPS spectra of the 100 nm thick TiO 2 film are shown in figure 4. Normally XPS technique is only sensitive to the surface, however, concerning this study, when we are considering the surface, then we can rely on the XPS spectra, not only qualitatively but also quantitatively.One can see that Ti +3 vacancies (figure 4(a)) as well as of O vacancies (figure 4(b)), exist well in the 100 nm thick TiO 2 film.The interpretations for these Ti and O vacancies peaks could be referred from [17][18][19].We can also mention that the ratio of O:Ti in the 45 nm and 100 nm films is about 3.13:1 and 3.14:1, respectively, while theoretically it should be 2:1, i.e. our films are indeed lacking Ti 3+ .In the thicker film (200 nm), the O:Ti ratio is a bit smaller (e.g.3:1) in comparison to the thinner films.Referring to the M-H curves, a small change in this O:Ti ratio might result in a very different magnetic behavior indeed.One can interpret that in the ferromagnetic films (i.e.thin films below 100 nm), it looks like that the O atoms are located closer to the Ti vacancies.
As a complement to our experiments, we have performed a series of quantum-mechanical calculations of the (001) surfaces with vacancies in different positions.We used 94-atom slab supercells (see figure 5).The lattice parameters of the supercells were derived from our previous calculations of lattice parameters of the bulk TiO 2 with the anatase structure, see [11].In particular, the tetragonal-lattice parameters of the bulk TiO 2 are equal to a = b = 3.822 Å and c = 9.724 Å, i.e. neatly matching experimental data.The supercells in figure 5 have the lateral lattice parameters (within the (001) plane) twice greater than the bulk value, i.e. (2 × 2) surface unit cell, while the slab size in the direction perpendicular to the (001) surfaces was four times greater than the c parameter of the bulk (the vacuum width is about half of this value).The supercells contained 32 TiO 2 formula units reduced by either two Ti or O missing atoms (94 atoms in total then).
Our computed energies for Ti vacancies indicate that the Ti vacancies prefer the first subsurface layer, figure 5(b), with the total magnetic moment of the slab supercell equal to 5.12 µ B .The other positions of the Ti vacancies exhibit higher energies (by 0.25 eV, 2.08 eV and 1.64 eV for atomic configurations in figures 5(a), (c) and (d), respectively) but higher magnetic moment (7.99 µ B , 5.64 µ B and 8.00 µ B for figures 5(a), (c) and (d), respectively).The actual magnetic states are characterized by spin-polarization of the oxygen atoms which may result in local magnetic moments as high as 0.96 µ B (see figure 5(d), when the O atoms are close to two Ti vacancies).This fits to what have seen in the XPS data.Importantly, spin-polarized oxygen atoms may have their local magnetic moments to be oriented antiparallel to those at other atoms, see brown O atoms at lower surface of figures 5(b) and (c).The antiparallel orientation is also indicated by the negative sign of the magnitude of these local magnetic moments.As the positions of the two vacancies are not exactly symmetric, rather complex structural relaxations of atoms due to the existence of the surfaces as well as vacant atomic positions result in the asymmetry in the atomic positions of the two surfaces inside of our computational slab supercells.The magnetic states are, consequently, rather complex, too.
The structural complexity is illustrated in the changes in the position of Ti atoms within slabs with Ti vacancies in figure 6.We analyzed vertical positions of Ti atoms, i.e. their coordinates along the z direction which is perpendicular to the studied surfaces.These z-coordinates of Ti atoms form groups of either four or three values, see full black circles in figure 6 because our 96-atom slabs are 2 × 2 multiples of TiO 2 unit cell within the (001) plane.Therefore, a group of four similar values indicates an atomic plane without any Ti vacancy while When inspecting the z-coordinates in figure 6(a), see full black circles, it is obvious that the biggest variations of the z-coordinates within a plane, i.e. a single group of similar values, correspond to (i) the surface with the Ti vacancy and (ii) the first sub-surface plane of Ti atoms.The other groups of four values with z-coordinates of Ti atoms are nearly identical.Moreover, in the case of the Ti-atom planes in the center of the slab, the values are not only nearly identical but also equal to the bulk value.As the Ti vacancies move into the first sub-surface planes of Ti atoms, see full black circles in figure 6(b), the neighboring two planes above and below, i.e. the surface plane and the second sub-surface plane, exhibit the biggest modulations in the values of z-coordinates of Ti atoms.The two planes of Ti atoms in the center of the slab still show nearly identical values of z-coordinates.With the Ti vacancies moving yet deeper under the surface, to the second sub-surface plane of Ti atoms, see full black circles in figure 6(c), the two planes of Ti atoms above and below the vacancy-containing plane possess the biggest differences in their z-coordinate values and it is also the case of the two central planes of Ti atoms.In contrast, the two surface planes of Ti atoms become nearly planar (the four values of z coordinates are nearly identical).These relations are even more pronounced in the case of Ti vacancies located in the two central atomic planes, see full black circles in figure 6(d), which become the most distorted while the surface and sub-surface planes of Ti atoms are nearly planar.
To further analyze the structural relaxations, we have analyzed the inter-planar distances in the case of Ti atoms.We proceeded in two steps.First, the z-coordinates for each of the groups of three or four Ti atoms were averaged to get a single averaged z-coordinate for each plane of Ti atoms.Second, a distance was determined between (i) a studied plane of Ti atoms and (ii) the neighboring plane of Ti atoms which is in the direction towards the nearest surface.The inter-planar distance was computed as the difference between the averaged z-coordinates of these two planes.The inter-planar distances are then indicated by full red circles in figure 6.Each full red circle in figure 6 indicates (i) the averaged z-coordinate of a particular group of Ti atoms by the vertical position of full red circle and (ii) the inter-planar distance to the neighboring plane of Ti atoms in the direction towards the nearest surface by the horizontal position of the full red circle.
The inter-planar distances visualized by full red circles in figure 6(a) indicate that the inter-planar distance between the surface and the first sub-surface planes of Ti atoms is reduced when compared with the bulk value, which is marked by the vertical black dashed line.The inter-planar distance between the first and second sub-surface plane of Ti atoms is slightly expanded and the distances between the planes of Ti atoms in the center of the slab are nearly equal to the bulk value.Interestingly, quite opposite trends are obtained when the Ti vacancy moves to the first sub-surface plane of atoms, see full red circles in figure 6(b).The distance between the surface and the first sub-surface planes of Ti atoms is expanded when compared with the bulk value while the distance between the first and second sub-surface planes of Ti atoms is reduced.As the Ti vacancies are deeper, the inter-planar distances become affected also in the case of the two Ti planes in the center of the slab.This trend is even more pronounced when the vacancies are deeper, see full red circles in figures 6(c) and (d), when the inter-planar distance becomes the most different from the bulk in the case of atomic planes in the center of the slab.
Regarding the oxygen vacancies, we have in fact computed four different slab supercells but only the one shown in figure 7 exhibits spin-polarization (the other three are not included).The magnetic state is only weak with surface Ti atoms next to the surface oxygen vacancy possessing the local magnetic moment of about 0.12 µ B .

Conclusions
Our experiment data have shown that as for pristine semiconducting oxides such as TiO 2 , room temperature ferromagnetism could be expected only in 2-dimensional configurations, particularly in films with nano-size (e.g. for whose thickness is ideally below 100 nm).While both bulk and nano-powders are diamagnetic, only ultra-thin films are strongly ferromagnetic, indicating that the surface and the nano-subsurface layer play a very important role in tailoring the magnetic properties in TiO 2 .The existence of defect-related magnetic states was also confirmed in our quantum-mechanical calculations of Ti and O vacancies in different positions with respect to the (001) surfaces of TiO 2 .The computed magnetic states stemming from Ti vacancies are rather complex with ferromagnetic features.Importantly, local magnetic moments of atoms were found very sensitive to local structural relaxations of atomic positions due to both surfaces and the vacant atomic positions.The dynamics of O and Ti atoms are very important in shaping the magnetic properties of TiO 2 films.Oxygen vacancies result in weakly spin-polarized states when compared with those due to Ti vacancies.O atoms cannot contribute much to magnetic moment when Ti vacancies are far from the surface.Ti vacancies in TiO 2 are only metastable.The formation energy of Ti interstitials is lower than for Ti vacancies since high-temperature annealing, especially with a lot of O 2 available that would fill up O-related defects, then eliminate most of Ti vacancies.Lower temperatures, less O 2 , and shorter exposure times to such conditions can enable not only partial elimination of Ti vacancies but also can facilitate their diffusion into different states.As for ferromagnetic films whose thickness is below 100 nm, it seems that the O atoms are located closer to the Ti vacancies.

Figure 1 .
Figure 1.X-ray diffraction patterns for a 100 nm thick TiO 2 film.

Figure 2 .
Figure 2. (a) Magnetic moment versus magnetic field for TiO 2 nano-powders; and (b) magnetization versus magnetic field for TiO 2 films with various thickness with field was applied parallel to the film plane, taken at 300 K.

Figure 3 .
Figure 3. Thickness dependence of saturated magnetization taken at 300 K for TiO 2 films.

Figure 4 .
Figure 4. High resolution XPS spectra of (a) Ti 2p and (b) O 1s for the 100 nm thick TiO 2 film.

Figure 5 .
Figure 5. Schematic visualizations of four 94-atom computational slab supercells with Ti vacancies in different positions with respect to the surface (see the Ti vacancies indicated by dashed circles).The oxygen and titanium atoms are shown as spheres (red/brown for O and blue for Ti) with the diameter reflecting the values of the local magnetic moment of atoms (a few actual values in Bohr magnetons are listed).Note that the vacuum layer is not shown in its full size in the direction perpendicular to the surface.

Figure 6 .
Figure 6.Computed positions of Ti atoms along the z direction, i.e. the direction perpendicular to the studied (001) surfaces, within the four 94-atom computational slabs with Ti vacancies in different positions.Labels (a)-(d) correspond to the slabs shown in subfigures (a)-(d) in figure F1.Each sub-figure contains z-coordinates of groups of either three or four Ti atoms within the same atomic plane, see black full circles, with the three values corresponding to atomic planes with a Ti vacancy.These positions are subsequently averaged for each of the groups and used to compute the inter-planar distances.The distances calculated as the difference between the averaged values are indicated by full red circles.The group-averaged z-coordinate determines the vertical position of the full red circles while the value of the inter-planar distance to the neighboring plane of Ti atoms in the direction to the nearest surface is indicated by the horizontal value of each red circle.The inter-planar distances within the slabs are compared with the value in the bulk as indicated by the black vertical dashed line.

Figure 7 .
Figure 7. Schematic visualizations of computational slab supercell with two O vacancies (see the dashed circles).The oxygen and titanium atoms are shown as spheres (red for O and blue for Ti) with the diameter reflecting the values of the local magnetic moment of atoms (one value in Bohr magnetons for the Ti atom next to the O vacancy is listed).Note that the vacuum layer is not shown in its full size in the direction perpendicular to the surface.