Strong out-of-plane magnetic anisotropy in ion irradiated anatase TiO2 thin films

The temperature and field dependence of the magnetization of epitaxial, undoped anatase TiO2 thin films on SrTiO3 substrates was investigated. Low-energy ion irradiation was used to modify the surface of the films within a few nanometers, yet with high enough energy to produce oxygen and titanium vacancies. The as-prepared thin film shows ferromagnetism which increases after irradiation with low-energy ions. An optimal and clear magnetic anisotropy was observed after the first irradiation, opposite to the expected form anisotropy. Taking into account the experimental parameters, titanium vacancies as di-Frenkel pairs appear to be responsible for the enhanced ferromagnetism and the strong anisotropy observed in our films. The magnetic impurities concentrations was measured by particle-induced X-ray emission with ppm resolution. They are ruled out as a source of the observed ferromagnetism before and after irradiation.


I. INTRODUCTION
3][4][5][6][7] The observed FM at such high temperatures is unusual because of the large spin polarization of the, mainly, valence (hole) bands (e.g., O-2p in oxides or the σ band in carbon-based materials) induced by a relatively low defect density of ∼ 5 %.The induced FM above room temperature in wide-band gap semiconductors has a large potential for applications in optoelectronics and magneto-optic devices. 8There is no general consensus, whether cations or anions vacancies are responsible for the magnetic ordering in oxides.For example, studies on HfO 2 or ZrO 2 suggest that the observed FM is due to O vacancies, [9][10][11][12] in disagreement with first principle theoretical studies which indicate that O vacancies do not show any magnetic moment in simple, binary oxides, but Hf vacancies do. 3 The observed FM in undoped oxide nanoparticles (Al 2 O 3 , In 2 O 3 , ZnO or SnO 2 ) was attributed to oxygen vacancies at the surface of the particles. 13Experimental and theoretical studies on the undoped oxide systems such as ZnO [14][15][16] or TiO 2 , 17 indicate that cation vacancies are responsible for stable magnetic moments, which can induce ferromagnetic order 3 when their concentration is around 5 %. 1,15,16here are several studies on DIM in TiO 2 , 7,[18][19][20][21][22] with ferromagnetic signals up to 880 K, 20,23 also for thin films of anatase and rutile prepared by pulsed laser deposition. 24Several mechanisms have been proposed to explain the source of FM in these materials.According to some band structure calculations, 20 the exchange interaction between Ti 3+ and Ti 4+ in anatase can cause FM.However, X-ray photoelectron spectroscopy results, on TiO 2−δ thin films grown on Si substrates under different oxygen pressures, do not find these ions. 24Results for annealed polycrystalline rutile and rutile/anatase TiO 2−δ powders suggest oxygen vacancies as source for FM.However, only Ti 4+ vacancies were detected and any exchange mechanism with Ti 3+ or Ti 2+ was excluded. 25In as-grown Ti 0.905 O 2 anatase thin films, Ti vacancies were found to cause ferromagnetism and p-type conductivity. 26In addition, for 4 MeV Ar 5+ irradiated polycrystalline rutile, Ti vacancies were suggested to be the main source of the room temperature FM 27 and a first principle study found a ferromagnetic moment of 3.5 µ B per Ti vacancy and 2.0 µ B per titanium divacancy, oxygen vacancies were excluded as source of a magnetic moment. 28pecial scientific research interest lies in materials showing perpendicular magnetic anisotropy, due to potential applications such as ultrahigh density magnetic recording, 29 where it is useful to extend the superparamagnetic limit to higher bit densities, 30 or tunnel magnetoresistance junctions. 31 pure magnetic patterning, without modification of the surface using additional ferromagnetic materials, is highly desirable for future applications.Thus, DIM with out-of-plane anisotropy can be a powerful tool to modify the magnetic properties of samples such as thin films or multilayered structures.Combined with lithography processes, it is possible to pattern ferromagnetic structures.Such magnetic patterns with out-of-plane magnetic anisotropy were produced with low-energy He + irradiation in CoPt, 32 SiC 33 and FePd. 34Increasing the ion fluence, the out-of-plane saturation field and the out-of-plane contribution to the magnetization decreased. 34,35Out-of-plane magnetic domain structures have also been found in La 0.67 Sr 0.33 MnO 3 on SrTiO 3 , where the anisotropy is due to in-plane tensile strain in LSMO film caused by the STO substrate. 36n this work, the influence of the irradiation of low-energy ions (maximum energy: ≈ 300 eV) on the magnetic properties of anatase TiO 2 thin films grown on SrTiO 3 (STO) was investigated.The low-energy used implies that defects are created only within a few nanometers from the surface of the thin film and to avoid any possible extra magnetic contribution due to modification of the substrate.In addition, low-energy irradiation is more accessible for industrial applications, due to the complication in producing ions with MeV energy, and costly devices.To verify that no magnetic dopants are introduced during growth and treatment with ions, laterally resolved particle-induced X-ray emission (PIXE) was used.The results show that FM is induced by ion irradiation with a Curie temperature above 300 K, and that the responsible defects are not oxygen vacancies but Ti-divacancies.One interesting outcome obtained in this work is the evident magnetic anisotropy observed after the first irradiation, indicating an easy axis parallel to the c-axis of the thin film, i.e. normal to the main surface.This magnetic anisotropy vanishes with increasing defect density.

II. EXPERIMENTAL
Here, the experimental procedures are discussed.Section II A describes the thin film production, impurity analysis and magnetization measurements.The details of the used low-energy irradiation are discussed in Section II B, to show the reader how one can estimate the mean free path of different ions that are produced in the plasma and accelerated towards the sample surface.

A. Thin film preparation, impurity analysis and magnetization measurements
The thin films have been prepared using pulsed laser deposition (PLD).As substrate, STO (100) etched by hydrofluoric acid and annealed in oxygen atmosphere prior to the film deposition has been used, which has been shown to be suitable for growing epitaxial anatase thin films. 37The films have been grown at a temperature of 650 • C. The oxygen pressure during the PLD was kept at 0.003 mbar, and the resulting thickness of the film was ≈ 150 nm. 37A sketch of the substrate and sample is shown in FIG. 1.During the growth process, a mask was used to fix the substrates on the holder.As a consequence, the substrate is not completely covered with TiO 2 , as sketched in FIG. 1.In order to check for impurities, particle-induced X-ray emission measurements were performed on both sides, indicated by yellow areas.The inset shows a SRIM simulation of the penetration depth of the Ar ions (peak value is ≈1.5 nm).
The steps necessary to keep the sample in place, as well as its handling and the process of ion irradiation in the argon/hydrogen plasma chamber, are possible sources of contamination.To check the contribution of contaminants (in particular the magnetic ones) quantitatively, PIXE measurements were performed.This is a very sensitive (accurate) method to measure the main magnetic contaminants in the TiO 2 thin film samples investigated here, with a minimum detection limit of ≈ 6 µg/g.To check for possible contamination during the ion irradiation, 50 % of the sample was covered with Teflon in order to maintain the sample in the as-prepared conditions, see FIG. 1.After treatment, PIXE measurements in both regions (without the Teflon cover) were done as shown in FIG. 1, where the investigated areas are indicated as yellow, transparent squares.The areas were intentionally chosen so that a part of the substrate, a part of the edge of the thin film and the film itself were analyzed.In this way, one obtained information about the contamination of the substrate (due to the growth process and hydrofluoric etching), of the edge of the film (due to the mask used to fix the substrate during the growth process), and of the TiO 2 film as grown, and after the plasma treatment.To further rule out magnetic contamination due to handling or irradiation, a substrate was placed for 1.5 h into the plasma chamber; no measurable change of the magnetic moment was observed.To elucidate the crystallographic structure of the grown TiO 2 thin films, X-ray diffraction (XRD) was performed (Philips X'Pert Diffractometer with Bragg-Brentano goniometer).The field dependence of the magnetic moment at three different temperatures, the temperature dependence of the magnetization at constant applied fields (zero-field and field cooled curves) and the remanence of the sample were measured by a superconducting quantum interference device (SQUID) magnetometer from Quantum Design.

B. Low-energy ion irradiation
The ion irradiation was done in a DC argon/hydrogen plasma chamber with a parallel plate configuration at room temperature using a Ar/H gas mixture (90% Ar and 10% H, Air Liquide).The substrate was placed on a sample holder 12 cm away from the electric field region, produced by two capacitance plates, where the gas was ionized.The film was connected to ground and the current was measured in order to calculate the amount of irradiated ions.A bias voltage of 300 V is applied to accelerate the ions towards the sample.
The produced plasma consists of 10 different species: e , Ar atoms, fast and metastable Ar, ArH + , H + , H + 2 , H + 3 , H atoms and H 2 molecules. 38In our experiment, only the species, which are accelerated towards the sample are of significance.Neutral atoms and molecules are not accelerated by the electric field but exhibit diffusive motion across the chamber.When no electric field was applied, no effects on the magnetic properties and also no change in the impurity concentration were measured.Note that the sample was placed 12 cm away from the plasma center.The influence of sputtered Cu from the parallel plates was also ruled out by means of PIXE measurements, see Section III.Therefore, only the in-the-plasma produced ion species and their energy, to estimate the corresponding defect production, were taken into account.
Whether a vacancy can be produced or not, depends on the energy E PKA transferred from the incident ion to the primary knock-on atom (PKA) as follows: 39 where E i is the ion energy, m j and r j are the masses and radii of particle j (j = 1,2), respectively, and d is the impact parameter.From Eq. ( 1), it immediately follows that 300 eV H + , H + 2 or H + 3 in anatase cannot cause Ti defects and the oxygen defect production is ineffective.The main production process of Ar ions is due to electron impact ionization of Ar, 38 however, the amount of electrons is heavily quenched along the tube. 40,41The main ion species left are ArH + ions, 38,[40][41][42] which can produce Ti and O vacancies effectively.
In order to estimate the energy of the incident ions, the mean free path (λ 1 ) of ArH + in a gas mixture composed of (neutral) Ar/H/H 2 has to be calculated as follows: 43 with where σ 12 = (σ 1 + σ 2 )/2 (averaged radii), m i is the molecular mass of species i, P i is the partial pressure, N A is the Avogadro constant and R denotes the universal gas constant.The first term corresponds to the ArH + -ArH + interaction and can be neglected, because the scattering cross section of ions is very low (Coulomb repulsion) and thus do not cause loss processes. 38Using the aforementioned experimental parameters, a mean free path for ArH + in Ar/H/H 2 gas of λ 1 ≈ 2.41 cm was found, before the recombination to atomic Ar occurs, where it was assumed all hydrogen atoms are bounded as ArH + .Due to the large partial pressure, the main scattering occurs with Ar atoms.Considering the geometry of our experimental setup (parallel plate configuration) most ArH + ions will have an energy of 60.2 eV, which is high enough to produce vacancies.Upon impact, the molecule will split and the most energy remains with Ar ion.The impact energy will have a broad distribution with many ions below and and above the average value.Therefore, a normal energy distribution will be used to calculate the probability to have energy E i (λ i ), where the fraction of ions without suffering from a collision is ∝ exp(−x/λ 1 ). 44With this, and using Eq. ( 1), the probability to have a E PKA (d) can be calculated.The defect formation probability (DFP) can then be estimated: 45 DFP( where α and γ are free parameters taken from Ref. 46   .Further details regarding defect production will be given in Section III D. The penetration depth of the argon ions can be estimated using a Monte Carlo simulation program (SRIM 47 ).The amount and type of the produced vacancies were estimated with the application of recent molecular dynamic studies 46 done for low-energy incident particles.

III. RESULTS AND DISCUSSION
The PIXE results, see Table I, show that the amount of ferromagnetic impurities does not exceed the minimum detection limit.A very small amount of copper was detected in the as-grown and treated parts of the TiO 2 film.Using the minimum detection limit one can estimate the maximal possible magnetic moment due to magnetic contaminants.Magnetic moments of ≈ 0.66 µemu due to Fe, ≈ 0.26 µemu due to Ni and ≈ 0.53 µemu due to Co were obtained, resulting in a maximum total magnetic moment due to magnetic impurities of ≈ 1.45 µemu.The PIXE results do not show any difference between the as-prepared thin film and the sample after ArH + irradiation.Therefore, it can be stated that the change of the magnetic properties is a consequence of the irradiation with argon ions.The contamination of the STO substrate is given in µg/g, whereas the impurity level of the TiO 2 thin film is given for the complete film with an area of 0.196 cm 2 .
Structure analysis was done using XRD.The result is shown in FIG. 3. Beside the peaks of the STO substrate, only anatase peaks of (001) planes are found, indicating a perfect (001) orientation and an epitaxial growth of our films. 37From the analysis of the peak positions, one finds a lattice constant c ≈ 9.61 Å, which is slightly larger than the literature value of 9.51 Å for bulk TiO 2 .After the irradiation with argon ions the X-ray diffraction was measured again and the position and width of the diffraction peaks showed no difference within experimental resolution.

A. Magnetic characteristics of the as-prepared thin films
The contribution of the (STO) substrate to the temperature dependence of magnetization has to be subtracted from the measurement including the thin film.For this aim, the temperature dependent magnetic moment of the STO (001) substrate alone, before deposition of the TiO 2 film, at a field of µ 0 H = 0.25 T applied parallel and perpendicular to the c-axis, were measured.An example is shown in FIG. 4. The data were fitted using two contributions, where m d accounts for the diamagnetic contribution, which one assumes to be temperature independent, and the second term is the paramagnetic Curie law, where C is the Curie constant.FIG. 4 shows that this model fits very well the obtained experimental results.The paramagnetic contribution is negligible at temperatures T ≥ 100 K.The (temperature independent) diamagnetic contribution was m d ≈ −17.2 µemu at µ 0 H = 0.25 T. The same field strength was used for the temperature dependent measurements with the TiO 2 film.The zero-field-cooled (ZFC) and field-cooled (FC) measurements of the TiO 2 thin film are shown in FIG. 5, where the contribution of the STO substrate has been subtracted.To calculate the magnetization of the as-prepared thin film, a thickness of 150 nm was used.To calculate the magnetization of the treated films, a thickness of 2.5 nm was assumed, according to the penetration depth of the low-energy argon ions obtained by SRIM, see inset in FIG. 1.
In FIG. 6 the field hysteresis for the TiO 2 thin film at three different temperatures is shown for the as-prepared state as well as after the first and second irradiation.The contribution of the STO substrate was subtracted from the data.For the as-prepared state, a small magnetic moment with ferromagnetic behavior, see Figs. 5(a) and 6(a), was found; the values are close to the resolution limit of our SQUID device.9][50][51] In our case such defects might have been introduced during the growth process, especially at the STO/TiO 2 interface as a consequence of the lattice mismatch FIG. 4. Magnetic moment of the STO (001) substrate with an external field of µ 0 H = 0.25 T applied parallel to the c-axis.The line was fitted using Eq. ( 5).C was found to be 1.3 × 10 −5 (emuK/T).(≈ 3.4% for STO/anatase).As a result of the lattice stress at the interface, defects can be produced and they might be the reason for the initial ferromagnetic behavior in our sample.In addition, the initial FM contribution could be also originated from small amounts of magnetic contaminants, which maximum possible magnetic moment was estimated before.The magnetic moment of the as-prepared sample at low temperatures (m 0,ap ≈ 0.32 µemu) will be subtracted from the data of the argon ion irradiated samples.
In order to estimate the FM Curie temperature, the mean field approximation 52 was used, where m 0 is the spontaneous magnetic moment at T = 0 K, T C is the Curie temperature and β a critical exponent, which is predicted to be 1/2.This approximation (Eq.( 6)) has been used to fit the high temperature dependence of the ZFC curves, see FIG. 5.For the asprepared measurement, a Curie temperature of T C ≈ 445 K and a critical exponent β = 0.5 were obtained, similar values have already been reported in the literature for both, T C and β in TiO 2 thin films. 20

B. Magnetic characteristics after the first irradiation
After the first ArH + irradiation (≈ 28.6 × 10 16 argon ions/cm 2 , flux: 1.59 × 10 14 cm −2 s −1 ), the magnetic moment increased to m 0 ≈ 3.5 µemu, which is one order of magnitude larger than the asprepared film and, after background subtraction, ∆m 1st ≈ 3.2 µemu, see Figs. 5 (b) and 6 (b).One observes not only an increase in the saturated magnetic moment but also in the coercive field, i.e.H c ≈ 100 Oe at all temperatures.
Applying the aforementioned MFT model to the results obtained after first ArH + irradiation, yields an effective critical exponent of β ≈ 0.17 and a rough estimation of the Curie temperature of T C 792 K. Similar values have been found in defected TiO 2 thin films grown in a reduced oxygen atmosphere 20 (T C = 880 K).It is evident that there is only a small temperature dependence of the magnetization at saturation (within the measured temperature range), indicating that the Curie temperature is larger than room temperature.In FIG. 7

C. Magnetic characteristics after the second irradiation
In the second treatment, the amount of irradiated ions is twice the amount implanted during the first treatment (i.e.≈ 57.3 × 10 16 argon ions/cm 2 ).The temperature dependent measurements can be seen in FIG. 5. Now a magnetic moment (at 0.25 T and T = 5 K) of m 0 ≈ 6.2 µemu is obtained, and ∆m 2nd−ap ≈ 5.9 µemu, with a reduced Curie temperature of T C 473 K. Considering the produced magnetic moment after the first irradiation of ∆m 1st ≈ 3.2 µemu, one would expect a magnetic moment of 9.6 µemu.Therefore, the observed increase is ≈ 0.6 times less than one would expect from the first treatment, if there was a linear relation with the amount of introduced ions.This indicates that, the amount of formed local magnetic moments scales not linearly with the argon ions fluence and that the magnetic defect formation probability is not only a function of crystallographic direction, PKA energy and temperature, but also depends on the defect concentration, until saturation occurs.Similar behavior was already observed for DIM. 34,35n FIG. 7 the temperature dependence of the remanence of the TiO 2 thin film after the second Ar ion irradiation is shown.The temperature dependence shows a stronger variation, as was already observed in ZFC -FC curves, with a remanence of m R ≈ 0.98 µemu at a temperature of T = 5 K. Considering the PIXE and the remanence results, one can discard the possibility that the ferromagnetic order originates from impurities.The coercive field increased to H c ≈ 180 Oe at T = 5 K but it decreases to H c ≈ 50 Oe at T = 300 K.These results are in agreement with the temperature dependence of the magnetic moment (ZFC-FC) and remanence measurements.The observed change between the first and second treatment cannot be attributed to aging effects because measurements were reproducible when the sample was investigated again after several weeks.After the second Ar ion irradiation one finds a maximum magnetization of M ≈ 40 emu/g.This value was calculated using the complete area of the film.However, assuming the formation of clusters rather than a uniform distribution, 46 would result in a higher magnetization.

D. Origin of the defect induced magnetic moment
Heavy or high energy ions create dense collision subcascades with dynamic annealing with only few reordering. 53Furthermore, these regions may lose their chemical order resulting in amorphous pockets, 54,55 which are resistant to reordering.However, light or low-energy ions produce dilute vacancy-interstitial pairs -Frenkel pairs (FPs) -along the ion path and/or upon collision.Due to diffusing ions and mobile vacancies, recombination processes are very likely and chemical reordering takes places. 35,53Thus, TRIM results are usually poor at low incident ion energy. 46Besides, the displacement energy should be considered as a function of chemical composition, which results in different E d values for rutile, anatase and brookite, as experiments on the polymorphisms of TiO 2 demonstrate. 45,46ecause defects as the FP are not in general stable, 45,46,56,57 a way to estimate a stable defect concentration is done through the introduction of the defect formation probability (DFP). 56The DFP depends on the crystallographic direction, the energy E PKA and temperature.As soon as E PKA reaches the threshold displacement energy, the probability to produce defects increases with energy, resulting in a smooth, non-linear increment as a result of recombination of unstable Frenkel pairs.A piecewise power law can be used to describe the behavior, see Eq. ( 4).Temperature has a large influence on E d ; calculations indicate that E d increases for oxygen from 18 eV at 300 K to 53 eV at 750 K due to activated recombination. 56To our best knowledge, experimental studies of E d for anatase have not been reported yet.In the case of rutile, values between 45 eV and 50 eV for Ti and 33 eV for oxygen were reported using TEM. 58olecular dynamic studies have shown that for low PKA energies, ≈ 75 % of the produced defects are Ti vacancies, 46 and for anatase at room temperature, a Frenkel pair (Ti V + Ti I ) results in recombination and is stable only when a second FP is produced at the nearest neighbouring sites, indicating that stability is only possible due to the localization of two FPs (di-FP). 46,59Simulations 45 and time-resolved cathodoluminescence spectroscopy 60 show that at room temperature the recombination processes reduce the amount of stable oxygen defects.Furthermore, oxygen defected TiO 2 is known to interact with the ambient air 61 such that recombination occurs.However, the sample was measured several weeks after irradiation and no change of the magnetic moment was observed.In addition, theoretical work predicts that the density of states in an oxygen deficient system is not spin polarized and that there are no magnetic moments at the O vacancies. 28ollowing these experimental and theoretical results, one concludes that the magnetic moment generated at the titanium di-FPs.Ti vacancies as a origin of FM were already found for as-prepared Ti 0.905 O 2 25 and TiO 2 irradiated by 4 MeV Ar 5+ . 27Theoretical work predicts a magnetic moment per Ti vacancy of 3.5 µ B .When a Ti vacancy is created, holes are introduced into the O-2p π band.Exchange splitting due to spin polarization of the low energy majority-spin state and high energy minority-spin state, lowers the total energy in the presence of holes.When two Ti atoms are removed from the nearest neighbouring sites, an oxygen dimer is formed along the z-direction. 28The 2 π * electrons of the oxygen dimer will drop to the lower states and compensate the holes.In addition, two Ti-O bonds are broken.This leads to a further decrease of the magnetic moment of the di-FP down to 2 µ B per Ti divacancy. 28The probability to produce a Ti di-FP is ≈ 24.4 % per defect. 46Therefore, considering the effective DFP of 1.26 % (see Section II B), a magnetic moment of m = 2.01 µ B per Ti di-vacancy is obtained.This result (see Table II) agrees very well with that of Peng et al. 28 (2 µ B per diFP).Further experimental parameters are given in Table II.
After the second Ar ion irradiation, and using the same DFP, the magnetic moment per Ti divacancy reduces to m = 1.3 µ B .This implies that the transformation to the ferromagnetic state saturates and less magnetic defects are produced increasing the defect. 34,35The mechanism can be regarded as ferromagnetic super exchange mechanism, similar to the Hubbard model. 28,62The more pronounced temperature dependence can be attributed to reduced long-range magnetic coupling as the defect concentration, and the disorder, increases reducing hybridization and the Curie temperature.

E. Unusual magnetic anisotropy at low defect concentration
An unusual magnetic anisotropy was reported for defective HfO 2 9 and Cr doped TiO 2 63 thin films, i.e. the magnetization at applied fields normal to the surface of the film reaches its saturation at much smaller fields than for the parallel direction, in contrast to the expected magnetic form anisotropy.In order to verify the possibility of such an anisotropy in the TiO 2 films, measurements FIG. 8. Anisotropy of the saturated magnetization after first and second argon ion irradiation at a temperature of T = 100 K.After first treatment, an easy axis perpendicular to the film surface can be observed.
under an applied field normal to the c-axis of the thin film were performed.For comparison, FIG. 8 shows the results of the hysteresis curves at T = 100 K under an applied field parallel and perpendicular to the c-axis.A clear anisotropy of the saturated magnetic moment after the first Ar ion irradiation is observed, similar to what has been already observed in the literature for dilute semiconductor thin films. 9,34,63The results show that the magnetization caused by irradiation of argon ions has a defined easy axis parallel to the c-axis, i.e. normal to the film surface.After the second treatment this magnetic anisotropy practically vanished, indicating that a preserved atomic lattice with a not very large defect concentration is required to get this interesting anisotropy.This anisotropy and the way to produce it may have useful applications for memory devices.Future studies should consider the possibility to produce well defined magnetic moments pinned normal to the main surface by single Ar ion irradiation, using, for example, nano-implanters. 64

IV. SUMMARY
Epitaxial anatase TiO 2 thin films were grown by PLD on STO substrates.Their phase and the crystallographic orientation were confirmed using X-ray diffraction measurements.The impurities concentration of the samples were examined using PIXE.Their concentration was too low to be the origin of the measured ferromagnetic signals.The as-grown sample shows a small ferromagnetic signal without magnetic anisotropy and with a Curie temperature of T C ≈ 445 K.The origin of this magnetic signal is probably related to lattice mismatch induced defects or defects generated during the growth process.The experimental studies presented in this work show a simple way to induce magnetism in anatase TiO 2 thin films, via irradiation of low energy ions.After the first irradiation, the magnetic moment at saturation increased by one order of magnitude, showing a very high Curie temperature of T C ≈ 792 K.A considerable out-of-plane magnetic anisotropy in the magnetization has been found.After the second irradiation, the magnetic moment increased again, but not linearly with the ion fluence, whereas T C was reduced and the anisotropy vanished.Experimental [24][25][26][27] and theoretical 28,45,46,56,57 results show that oxygen vacancies are not the source of magnetic moments, but Ti vacancies.The used ion energy to produce the defects triggers the formation of Ti di-vacancies or di-vacancy clusters. 45,46The obtained magnetic moment per Ti di-FP of m ≈ 2 µ B agrees with literature reports. 28The triggered magnetization at low ion energies and fluences shows an interesting anisotropy with an easy axis perpendicular to the film surface.The above mentioned experimental results offer new possibilities for future applications of DIM in TiO 2 thin films, using low-energy ion irradiation which can be easily included in industrial processes.

FIG. 1 .
FIG. 1. Sketch of the anatase thin film on the SrTiO 3 substrate.During ion irradiation the right side was covered with Teflon.In order to check for impurities, particle-induced X-ray emission measurements were performed on both sides, indicated by yellow areas.The inset shows a SRIM simulation of the penetration depth of the Ar ions (peak value is ≈1.5 nm).

FIG. 2 .
FIG.2.The Ti defect formation probability (DFP) as a function of incident ion energy and impact parameter d.The red line indicates the mean ion energy E i = 59.2 eV.The fraction of ions having a probability to produce defects of less than 0 %, is not shown.

FIG. 5 .
FIG. 5. Magnetic moment m (left y-axis) and magnetization M vs. temperature for the TiO 2 thin film in the (a) as-prepared state, (b) after the first and (c) after the second ion irradiation.The background signal of the substrate has been subtracted.The applied field was 0.25 T normal to the surface of the film.

FIG. 6 .
FIG. 6. Hysteresis measurements for (a) the as-prepared TiO 2 thin film, (b) the film after the first and (c) after the second ion irradiation.The paramagnetic contribution has been subtracted.
FIG. 7. Results of remanence measurements for TiO 2 thin film after the first and second Ar ion irradiation.
for anatase.The resulting DFP for Ti atoms in anatase can be seen in FIG.2.The red line indicates the mean energy of 59.2 eV of the incident Ar ions.A larger energy transfer E PKA is less probable, but results in a higher probability to produce defects and thus, one finds a DFP of 1.26 % per ion.The largest amount of the incident particles do not cause any Ti vacancy and can be neglected -only ions with a feasible DFP are shown in the figure

TABLE I .
Results of PIXE measurement of the STO substrate and TiO 2 thin film.The total mass of TiO 2 film is ≈ 11.2 µg.
FIG. 3. The X-ray diffraction ω − 2Θ scan of the as-grown TiO 2 thin film.Beside the anatase peaks in (001) direction, only the peaks of the STO substrate are visible.

TABLE II .
46mmary of different parameters and results of the TiO 2 thin film after first and second argon ion irradiation.Employing the results of molecular dynamic simulations46yields a magnetic moment per Ti divacancy m diFP (µ B ).