Formation of Fe-Fe Antiferromagnetic Dimers in Doped TiO2

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C: Physical Processes in Nanomaterials and Nanostructures 2

Formation of Fe-Fe Antiferromagnetic Dimers in Doped TiO:Fe Nanoparticles Anatoly Yegorovich Yermakov, Andrei Fedorovich Gubkin, Alexander Vasilyevich Korolev, Leonid S. Molochnikov, Mikhail A. Uimin, Eugene V Rosenfeld, Mikhail I. Kurkin, Artem S. Minin, Alexey S. Volegov, Danil W. Boukhvalov, and Sergey F. Konev J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b10553 • Publication Date (Web): 17 Dec 2018 Downloaded from http://pubs.acs.org on December 17, 2018

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The Journal of Physical Chemistry

Formation of Fe-Fe Antiferromagnetic Dimers in Doped TiO2:Fe Nanoparticles Anatoly Ye. Yermakov,∗,†,‡ Andrei F. Gubkin,†,‡ Alexander V. Korolev,†,‡ Leonid S. Molochnikov,¶ Mikhail A. Uimin,†,‡ Eugene V. Rosenfeld,† Mikhail I. Kurkin,† Artem S. Minin,†,‡ Alexey S. Volegov,†,‡ Danil W. Boukhvalov,§,‡ and Sergey F. Konev‡ †M. N. Mikheev Institute of Metal Physics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620137, Russia ‡Institute of Natural Sciences, Ural Federal University, named after the first President of Russia B. N. Yeltsin, Yekaterinburg, 620002, Russia ¶Ural State Forest Engineering University, Yekaterinburg, 620100, Russia §College of Science, Institute of Materials Physics and Chemistry, Nanjing Forestry University, Nanjing, 210037, P. R. China E-mail: [email protected]

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Abstract In this work, we report the results of comprehensive experimental and theoretical study of magnetic properties of TiO2 nanoparticles (20 nm) doped with Fe at various concentrations ranging from 0.1 at.% to 4.6 at.%. Our EPR and magnetic measurements data evidence the mixed magnetic state where paramagnetic Fe3+ ions coexist with short-range antiferromagnetic correlations caused by negative exchange interaction between neighboring Fe3+ ions. A quantum mechanical model of the Fe-based magnetic cluster represented as a set of dimers with strong ∼ (100-300) K and weak (∼1K) exchange interactions has been proposed. Our model was found to provide a good description of magnetic properties of TiO2 :Fe nanopowders. DFT calculations confirmed that two types of spin-pairs with weak and strong exchange interactions can be formed in the vicinity of an oxygen vacancy. Accumulation of magnetic moment carriers and formation of magnetic clusters in TiO2 nanoparticles with anatase structure was found to be a general tendency for all studied TiO2 :Fe nanopowders.

Introduction The study of magnetic states in the diluted magnetic semiconductors (DMS) doped with magnetoactive 3d-ions is of particular interest because of their possible technological applications. It is well known, for instance, that DMS on the base of TiO2 nanomaterials are promising materials for spintronics, catalyst and sensors applications. However, the underlying mechanisms which are responsible for the electronic structure and the magnetism in DMS is still a subjects of a hot debates. 4 For instance, the nanopowder samples based on the TiO2 nanocrystals doped with iron seem to exhibit a substantial role of the surface where accumulation of defects and 3d dopants may give rise to a certain type of magnetic states. 5–7 The strong influence of Fe in TiO2 on the catalytic and sensor properties was revealed. 1–3 There are a lot of controversial studies of magnetism in TiO2 :Fe evidencing emergence of ferromagnetic contribution in the paramagnetic matrix of TiO2 :Fe as well as unrecognized 2


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magnetic phases which were interpreted using a number of models. 4,8 It has been found in some works, e.g., 5,8 that the ferromagnetic contribution involves a very small part of the total magnetoactive 3d ions doped in the anatase structure of TiO2 while the rest of the magnetic moment carriers form a paramagnetic matrix. An attempt to describe magnetic properties of the paramagnetic matrix using a model of randomly distributed paramagnetic Fe3+ centers was found to be unsuccessful even for samples with a small content of magnetic dopant. Particularly, temperature dependence of magnetic susceptibility cannot be well approximated with the Curie law. Approximation of the magnetic measurements data using the Curie-Weiss law turns out to be not so rigorous, but it provides a negative value of the Weiss constant that underline the negative exchange interactions between magnetic Fe3+ ions. 9 However, the concentration of the Fe3+ ions having spin value S=5/2 estimated from the Curie-Weiss law fit was found to disagree with the real chemical content of the dopants. 5 So, it appears to be unclear which magnetic states apart from the pure paramagnetic one can be formed by the rest of the Fe3+ magnetic ions in the TiO2 :Fe system. The surface of nanoparticles is known to be a place where doped 3d ions as well as the crystal structure defects tend to localize and accumulate. Formation of the iron based complexes caused by the interaction of Fe3+ ions with defects, oxygen atoms or vacancies and, possibly, with Ti3+ ions seems to be thermodynamically favorable in the near surface layer. 6,8,10–13 It is obvious, we can not exclude the non-random accumulation of Fe ions in the core of particle due to specific sites in the TiO2 lattice with defects as well. In the simplest case, non-interacting magnetic complexes may be approximated with a set of dimers, trimers or other clusters. There are a plenty of examples in literature where magnetic properties of the nonmagnetic compounds doped with magnetoactive ions 14–16 were successfully approximated using a model of magnetic clusters composed of dimers and trimers coupled with AFM interaction. It should be emphasized that combination of magnetic measurements with electron paramagnetic resonance (EPR) spectroscopy may be a powerful probe for studying of a short-range magnetic order and the crystal field splitting in heterogeneous magnetic

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systems. 17–19 In the present work, magnetic states of the nanocrystalline TiO2 doped with iron at various concentrations ranging from 0.1 at.% to 4.6 at.% in as-prepared state and after etching was studied by the EPR spectroscopy and SQUID-magnetometry. A quantum mechanical approach 20 based on the model of spin pairs (dimers) located in the paramagnetic matrix of the randomly distributed uncoupled Fe3+ spins was tested for approximation of the magnetic measurements data. Additionally, DFT calculations were performed in order to estimate a magnitude of exchange interactions in antiferromagnetically coupled pairs of Fe3+ ions in the vicinity of oxygen vacancy.

Preparation methods, refining and samples characterization The low temperature (T = 160 ◦ C) sol-gel method was used for synthesis of the TiO2 :Fe nanopowders in order to reduce the concentration of impurity phases and provide uniform distribution of the dopant atoms over the TiO2 matrix. A series of the nanocrystalline samples with iron content ranging from 0.14 at.% to 11.90 at.% have been synthesized (see Table 1). The acid treatment (HCl etching) was carried out for all samples immediately after synthesis. All tools and containers used in our experiments were made of non-ferromagnetic materials such as plastic, titanium and ceramics. Additionally all the tools were treated in bimolar solution of HCl (2 HCl) before use in order to eliminate any possible contaminations. 5-ml disposable plastic test-tubes were used for etching of as-synthesized samples. TiO2 :Fe powder in the amount of 50-100 mg was mixed with 5 ml of 2M HCl in the test-tubes and treated for 30 sec in a pool-type ultrasound disperser with a titanium activator. The obtained suspension was kept in container at normal conditions for 10 minutes. Then the TiO2 :Fe nanoparticles were separated from the suspension by centrifuging for 5 min at 12.000 4


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RPM. Supernatant liquid was separated carefully and then the same procedure was run over two more times. Upon the third cycle, ethanol substituted for water, and the resulted supernatant liquid was poured out and 95%-ethyl alcohol containing 0.1 M of hydrochloric acid was added to the sediment. A hydrochloric acid is needed at this stage in order to prevent formation of the stable suspension of nanoparticles which are difficult to separate by centrifuging. Titanium dioxide TiO2 in alcohol was treated with ultrasound and after that the sediment was centrifuged out. Then an alcohol was poured out, and the process was run over one more time. After being cleaned with ethanol, the sediment was transferred into a ceramic crucible and dried at 70 ◦ C. Table 1: The chemical compositions of the synthesized TiO2 :Fe samples before and after etching with HCl as it was estimated by inductively coupled plasma (ICP) mass spectrometry. Accuracy in determination of chemical composition by ICP is about ± 0.01%. Samples 1 2 3 4

Fe, at.% before etching 0.14 0.72 2.98 11.90

Fe, at.% after etching 0.12 0.67 2.41 4.63

The structural and magnetic states of the samples were carefully checked before and after acid etching using X-ray diffraction, EPR-spectroscopy, transmission electron microscopy (TEM). Magnetic state was controlled at each stage of etching by measuring the field dependence of magnetization at room temperature with the Faraday balance. The X-ray characterization was performed using a PANalytical Empyrean Series 2 X-ray diffractometer with Cu Kα radiation. The HighScore v.4.x. software was used to make a phase analysis, calculate the crystal structure parameters and estimate the size of the coherently scattering domains. Electron paramagnetic resonance measurements were performed on a Bruker ELEXSYS 580 pulse spectrometer in a stationary mode. The sample powder was placed in a special quartz tube of 4 mm in diameter. The sample volume ranged from 2 to 5 mm3 . The 5



spectra were registered at room temperature with Super High-Q rectangular resonator. The frequency of the microwave field was about 9.40 GHz. The interval of induction change of the constant magnetic field B ranged from 480 to 6000 Oe. The level of microwave power was 4.7 mW and modulation amplitude was 1 Oe. A transmission electron microscope (TEM) (JEM 2100 (JEOL)) was used to determine the morphology of the synthesized nanopowders before and after etching. The detailed magnetic measurements in a wide temperature range 2-350 K and in external magnetic fields up to 70 kOe were performed using MPMS-XL (Quantum Design, USA). The temperature dependencies of the magnetic susceptibility have been measured using zero field cooled (ZFC) and field cooled (FC) protocols. MathCad 14 and SciLab 6.2.0 software were applied in order to fit the magnetic measurements data.

Experimental results and discussion Characterization of iron-doped titanium dioxide samples X-ray diffraction patterns for the TiO2 :Fe sample 4 before and after etching and sample 3 before etching are shown in Figure 1. Both samples exhibit the crystal structure type of anatase described with the space group I41 /amd. A trace amount (∼2 w.%) of the impurity phase identified as Fe3 O4 was observed on the X-ray diffraction pattern for the as-prepared sample 4 doped with Fe up to 11.9 at.%. Contrary, we did not observe any extra reflections attributed to the Fe3 O4 phase or to the TiO2 brookite phase on the x-ray diffraction patterns for the as-prepared TiO2 :Fe samples 1, 2 and 3 with low concentration of Fe (see Figure 1, as an example sample 3 is shown). This result well agrees with Ref. 5 where doping of 3d ions into the TiO2 matrix with anatase structure above a certain concentration limit was shown to trigger a phase decomposition of the sample. The unit cell parameters for the as-prepared samples without etching (a=3.785 ˚ A, c=9.485 ˚ A for sample 3 and a=3.798 ˚ A, c=9.504 ˚ A for sample 4) were found to be slightly different in comparison with the unit cell parameters 6


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of the pure bulk TiO2 (#PDF84-1285: a=3.7848 ˚ A, c=9.5124 ˚ A). It has been found that etching of the sample 4 results in complete suppression of the Bragg peaks attributed to the impurity phase Fe3 O4 while the unit cell parameters were found to be almost unchanged (a

Intensity, a.u.

= 3.794 ˚ A, c = 9.504 ˚ A).

S4 as-prepared

S4 after Etching

S3 as-prepared

20

30

40

50

60

70

80

90

2q (degree)

Figure 1: X-ray diffraction patterns measured at room temperature for sample 4 in the as-prepared state and after etching in 2M HCl. X-ray diffraction pattern for sample 3 in the as-prepared state is shown at the bottom. Asterisks denote Bragg peaks of the Fe3 O4 impurity phase. Vertical bars denote Bragg angles of the TiO2 .

S4 as-prep

1.2

S4 after etching

300

0.9

s (emu/g)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


150 0

0.6 -150 -300

0.3

H (Oe) 0

2000

4000

6000

0.0 0

3

6

9

12

H (kOe)

Figure 2: Field dependences of magnetization and EPR spectra (in the inset) measured at room temperature for sample 4 in the as-prepared state and after etching. The field dependencies of magnetization for sample 4 measured at room temperature before and after etching are shown in Figure 2. It can be seen that the as-prepared sample 4 doped with Fe up to 11.9 at.% exhibits typical ferromagnetic behavior due to the ferromagnetic contribution of magnetite. The EPR signal for this sample is usual for the ferromagnetic state: the broad lines over 4 kOe with an effective g-factor over 2 (see inset 7



in Figure 2). The concentration of Fe in the sample was found to reduce down to 4.63 at.% after etching and magnetization curve transforms to the linear type that is typical for paramagnetic samples. The EPR spectrum changed its shape as well to the one that is characteristic of the systems containing paramagnetic centers and possibly the regions of short-range magnetic correlations of an antiferromagnetic type. Such transformations well agrees with the results of X-ray diffraction that revealed suppression of Bragg peaks of the Fe3 O4 impurity after etching. A chemically stable TiO2 :Fe matrix in the form of substitutional or interstitial solid solution containing impurity phases is known 21 to be resistant to etching while impurity phases which are not incorporated into the solid solution can be etched out. 22 Thus our synthesis method with the subsequent etching of the as-prepared samples in the 2M HCl solution produces TiO2 :Fe samples with the concentration of Fe up to 4.6 % which are free of magnetic impurity phases.

Figure 3: Transmission electron microscopy images of the TiO2 :Fe sample in the as-prepared state (a) and after etching (b). The average size of coherently scattering domains was estimated to be about 20 nm before and after etching for sample 4 that is in the reasonable agreement with the data obtained from the transmission electron microscopy (Figures 3(a) and 3(b)). Figure 3(b) shows a surface of the TiO2 :Fe nanoparticle that have disordered crystal structure (denoted by A) and could potentially serve as a sink of doped Fe ions, crystal structure defects and impurities.

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Magnetic measurements Field dependencies of magnetization for samples 1, 2, 3 and 4 measured at low temperatures are shown in Figures 4(a) and (b). All the curves exhibit paramagnetic-like behavior and cannot be approximated by the Brillouin function taking into account Fe3+ spin value S=5/2 and concentration of the doped Fe ions determined by ICP mass spectrometry for all samples after etching (see Table 1). It has been found that all the Brillouin modeled magnetization curves exhibit substantially higher magnetization values than it was observed experimentally (see Table 2 and Figure 4). Table 2: Comparative analysis of the magnetic measurements data for samples 1, 2, 3 and 4: high field magnetization represented as a ratio of the Brillouin function to the experimental value of magnetization taken at the same field MBr /Mexp , Weiss constant Θ, inverse Curie constant, temperature independent contribution to the magnetic susceptibility χ0 , xCW concentration of the paramagnetic Fe3+ ions (S=5/2) obtained from the CW law fit, concentration of Fe ions obtained from the ICP mass-spectrometry and their ratio xCW/xICP. Sample MBr /Mexp 1 2 3 4

Θ, K

1.9 3.0 2.3 2.8

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1/C, χ0 xCW xICP Ratio g*Oe/emu*K emu/g*Oe at.%Fe at.%Fe xCW/xICP % 24575 -3*10−8 0.074 0.1 74 −8 7200 -4.9*10 0.253 0.7 36 1360 -4.1*10−7 1.34 2.4 56 −6 772 -1.1*10 2.4 4.6 52

-2 -2 -6 -6

(a)

(b)

S4 experiment

T=3K

2.0

Brillouin fit S4

S2 experiment

S3 experiment

Brillouin fit S2 1.5

s (emu/g)

Brillouin fit S3

10

s (emu/g)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


S1 experiment

T=2K

1.0

5

Brillouin fit S1

0.5

T=2K 0

0.0 0

20

40

0

60

20

40

60

H (kOe)

H (kOe)

Figure 4: Field dependencies of magnetization measured for samples 1, 2, 3, 4 and their fits made by Brillouin function (see the text). Temperature dependence of the magnetic susceptibility for sample 4 after etching mea9



sured in a field of H = 50 Oe using ZFC protocol is shown in Figure 5(a). No magnetic anomalies which can be attributed to the magnetic phase transitions were found on this curve. The inverse susceptibility curve 1/χ(T) measured in a low magnetic field of 50 Oe as well as in a high magnetic field of 20 kOe exhibits nonlinear behavior deviating from the Curie-Weiss law in a wide temperature range 40-300 K. Such a behavior can originate from substantial contribution of the temperature independent component that includes diamagnetic contribution of the TiO2 matrix itself and Van-Vleck contribution. Another possible scenario is the contribution of the short-range antiferromagnetic correlations persisting in the sample up to high temperatures. In order to estimate concentration of the paramagnetic Fe3+ ions (S=5/2), the high temperature part (100-350 K) of the inverse susceptibility measured in a field of 20 kOe was fitted by the Curie-Weiss (CW) law χ=χ0 + C/(T-Θ) that includes a temperature independent component. Bearing in mind fixed Fe3+ ions spin value S = 5/2, three adjustable parameters, which are temperature independent component χ0 , Weiss constant Θ and concentration of the paramagnetic Fe3+ ions x in Fex Ti1−x O2 , were estimated to be χ0 = 1.06x10−6 emu/g*Oe, Θ=-5 K and x=0.024. The best fit result is shown in Figure 5(b). The estimated temperature independent component χ0 is two orders of magnitude higher than the value that was reported for pure TiO2 powder sample with anatase structure χ0 = 0.02*10−6 emu/g. 23 The negative value of the Weiss constant implies emergence of the antiferromagnetic exchange interactions in the sample. The concentration of the paramagnetic Fe3+ ions was found to be almost twice less than the real Fe content determined experimentally by ICP mass-spectrometry (see Table 2). Little negative Weiss constant and reduced concentration of the paramagnetic Fe3+ ions obtained from the CW fit in comparison with the one obtained from ICP mass-spectroscopy were observed for samples 1, 2 and 3 as well (see Table 2). Additionally, one can see that temperature independent component χ0 tends to reduce its value for the samples with low concentration of doped Fe. It was estimated to be χ0 = -3.0*10−8 emu/g*Oe for the sample 1 with 0.1 at.% of Fe that is close to the value reported for the pure TiO2 with anatase struc-

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Sample 4 after etching H = 50 Oe

20

20

H = 20 kOe

15

15

c- c 1\(

0.00 0

100

200

c c- c

1/( 5

10 0

CW fit

1\

1/

10

0

0.05

c *10

4

0.10

25

Sample 4 after etching

(g*Oe/emu)

) *10 (g*Oe/emu)

0.15

(b)

25

-3

(emu/g*Oe)

(a)

c *10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


4

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) 5

300

Temperature (K)

0

0 0

100

200

300

Temperature (K)

Figure 5: (a) ZFC-susceptibility curve measured in a field of H=50 Oe for sample 4 after etching. (b) Inverse susceptibility 1/χ and 1/(χ-χ0 ) as a function of temperature fitted by the Curie-Weiss law. ture. 23 Such behavior implies that doping of Fe into the TiO2 matrix results in emergence of the additional component of magnetic susceptibility that is not described by the CW law. Inaccuracy in fitting of the inverse susceptibility by the CW law due to this contribution is compensated by enhanced value of the temperature independent component χ0 . Thus one can suggest that substantial part of the Fe3+ ions doped in the TiO2 sample may be magnetically correlated on a short-range scale. Coexistence of the paramagnetic and antiferromagnetic contributions as dimers and other clusters were discussed yet for different diluted magnetic semiconductors in Refs. 9,24,25 However, authors of these works discussed the magnetic results in the framework of the mean-field approximation while quantum mechanical approach to the interpretation of magnetic properties of the assumed spin clusters was not involved.

TiO2 :Fe EPR spectroscopy EPR spectroscopy is an effective probe for detection and characterization of the paramagnetic centers and short-range magnetic order as it has been illustrated remarkably in Ref. 19 Contrary to magnetic measurements, EPR is very sensitive for revealing of the vanishingly weak interactions of an order of 10−2 - 10−3 K at room temperature. The EPR spectra measured on sample 3 in the as-prepared state and after etching are shown in Figure 6(a). One 11



can see that the shape of EPR spectrum was not affected by etching while its intensity was decreased by factor ∼2 after etching. There is no sign of the preferential accumulation of Fe ions on the surface of nanoparticles since etching would substantially affect the shape of the EPR-spectrum in opposite case. So, the EPR-spectra of samples 1, 2, 3 and 4 after etching measured at room temperature are shown in Figure 6(b). A comparison of the EPR spectra for sample 1 (x=0.1 at.%) and undoped TiO2 nanopowder samples are shown in Figure 6(c). The EPR spectrum for undoped TiO2 represents nearly symmetrical line with a g-factor of 2.003 and a line width of ∆H = 21 Oe. In accordance with Refs., 26–28 this line corresponds to oxygen vacancies (F+ - centers and O2 - radical oxygen) in the anatase structure of TiO2 . Two more lines having g-factors about 1.966 and 1.946 which can be attributed to the presence of Ti3+ are distinctly visible on the spectrum of the undoped sample. 29 The EPR-spectrum for sample 1 with low concentration of doped Fe is substantially different from the spectrum of the undoped sample. This spectrum exhibits an extra set of lines which accompany the intense central peak at g=2.003. Intensity of the central line tends to increase for the samples with higher iron content (see samples 2, 3, and 4 on Figure 6(b)) due to overlapping with the signal at g∼2 that is originated from the contribution of Fe3+ ions. Additional broadening of the central line caused by increasing of the iron content in the sample seems to shadow the signal coming from Ti3+ that was observed on the spectrum of the undoped sample. Decomposition of the EPR-spectra for samples 1, 2, 3 and 4 revealed at least four signals with different linewidths in the region of g∼2 and a broad fifth signal at g∼4.3 exhibiting complex structure. The comparatively narrow lines localized near g∼2 can be attributed to the neighboring Fe3+ ions which are coupled by dipole-dipole interactions. 30–35 These narrow lines are overlapped with the broad lines upon increase of the iron content in the sample over 1 at.%. It should be emphasized that the EPR-spectra exhibit relatively broad intense lines for all the studied samples with iron content ranging from 0.1 to 4.6 at.%. The broad lines on the EPR-spectra of TiO2 samples doped with magnetic 3d ions were previously reported in Ref. 36–42 It was suggested that these lines may originate

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40

(b)

30

(a)

Sample 3

20

20

Intensity, a.u.

Intensity, a.u.

0

-20

g=4.3

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g~2.0

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As-prep state

S3 S4

After etching -30

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H (Oe) Undoped TiO 2

20

Intensity (a.u.)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(c)

S1

10

0

-10 g=1.93 g=1.96 -20 3450

3475

3500

3525

H (Oe)

Figure 6: (a) EPR spectra measured on sample 3 in the as-prepared state (multiplied by factor 1/2) and after etching. (b) EPR spectra of samples 1, 2, 3 and 4 measured after etching. (c) EPR spectrum of sample 1 (x=0.1 at.%) in comparison with the spectrum of the undoped TiO2 sample (intensity multiplied by factor 3) are shown. from the antiferromagnetic (AFM) clusters formed by 3d magnetic ions coupled by negative exchange interaction. Another possible origin of the broad lines on the EPR spectra of the Fe doped TiO2 is emergence of the hematite-based magnetic impurity phase as it was discussed in Ref. 43 In order to test this scenario a series of EPR spectra were measured in a wide temperature range 130-500 K. It has been found that intensity of the broad line increases on sample cooling that is in contradiction with what one can expect for a signal originated from hematite. 43 The effect of crystal electric field (zero-field splitting D) along with exchange interactions should be considered when one performs an analysis of the EPR-spectra. 44 Estimation of the zero-field splitting effect from the EPR-spectra measured at different temperatures (in the range 130-500 K) revealed no shift of the observed lines. This is in agreement with Ref. 45 where D contribution for TiO2 with Fe3+ ions substituting for Ti4+ ions in the crystal 13



structure of anatase (solid solution) was estimated to be 0.4 K at room temperature. Thus zero-field splitting contribution turns out to be quite small in comparison with exchange interaction in the AFM clusters formed by Fe3+ ions.

4500

Sample 4

T = 300 K

Fit Peak 1 Fit Peak 2 Fit Peak 3

Intensity, a.u.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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3000

Fit Peak 4 Fit Peak 5 Differ. curve

4 1500

3 2

0

1

5 1000

2000

3000

4000

5000

H(Oe)

Figure 7: Decomposition of EPR signal of TiO2 :Fe sample 4 into components upon double integration at 300 K. Decomposition of the integrated EPR spectrum measured on sample 4 at room temperature is shown on Figure 7. The best fit result was obtained for a model with five Gaussian peaks (see Refs. 46 for details) as it is reported in Table 3. It was suggested that the broad line (see line 4 on Figure 7) around g∼2 originates from the short-range AFM correlations. The narrow central lines (see lines 1,2,3 on Figure 7) observed in the same region around 3500 Oe (g∼2) can be attributed to the paramagnetic Fe3+ ions with dipole-dipole interactions and 47 as well. The weight fraction of the broad vacancies (F+ centers) and O− 2 oxygen radicals

Gaussian peak with ∆H1/2 =1867 Oe that roughly corresponds to a fraction of antiferromagnetically correlated Fe3+ ions was found to be 66%. This result implies that the substantial part of Fe3+ ions are magnetically coupled in AFM clusters. Thus the EPR data along with the results of the magnetic measurements allows one to suggest a mixed magnetic state where paramagnetic centers coexist with short-range antiferromagnetic correlations caused 14


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by negative exchange interaction between neighboring Fe3+ ions in the simplest case as a dimers. Table 3: Parameters of decomposition of the integrated EPR spectrum measured at room temperature for sample 4. H0 is the field corresponding to the maximum signal on the absorption curve; ∆H1/2 is the absorption linewidth at the halfheight.

H0 , Oe g-factor ∆H1/2 , Oe Peak square, %

1 Peak 2 Peak 3 Peak PM PM PM 3385 3390 3371 1.994 1.996 2.002 82 220 661 2 6 22

4 Peak 5 Peak AFM SRO PM 3166 1565 2.13 4.3 1867 839 66 4

A quantum mechanical approach based on the model of spin pairs and singles As far as the Fe-based antiferromagnetic clusters in the anatase structure of TiO2 is considered, it appears natural to approximate these clusters with a set of antiferromagnetically coupled Fe3+ -Fe3+ pairs (dimers) as a simplest approach. In order to build a simple model that is able to quantitatively describe our magnetic measurements data, it is sufficient to take into account two types of Fe-Fe pairs with different exchange interactions. This assumption was justified by DFT calculations (see below). Most likely, there should be more of these pair types, and the probability of finding a dimer with a certain value of the exchange parameter should be described by the distribution function. Evidently, the introduction of a large number of adjustable parameters, allow to describe any experimental curves. On the contrary, we wanted to limit ourselves to a few most reasonable physical parameters as possible. TiO2 lattice it is not favor to continuous Fe atom distribution. Below, in the section of theoretical estimations of exchange interactions within Fe-pairs near defect on DFT-based modeling, the type of Fe atom distribution will be discussed more detail. Shortly, it should

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be say that in the lattice due to discrete set of atom sites and very strong dependence of exchange interaction from Fe-Fe distance in the nearest surrounding is unlikely to get unbroken distribution. Besides, the reason to simplify the situation is that one can clearly see a two fundamentally important experimental facts: (i) already at low temperatures, the Curie constant increases significantly, (ii) even at high temperatures it is much less than the value that would correspond to the set of individual Fe ions with a given concentration. Therefore, the simplest and minimum-making arbitrary assumptions model is reduced to the supposition that there are two groups of dimers. The model is, of course, relatively rough but quite physically clear and understandable. Let us assume that N is a concentration of Fe3+ ions per unit volume of sample. Let ns to be a concentration of Fe3+ ions which do not have nearby Fe-neighbors or, par abus de langage, they are singles (paramagnetic). Then let 2nd1 to be a concentration of Fe3+ ions which are coupled in pairs by exchange integral J1 and 2nd2 to be a concentration of Fe3+ ions which are coupled in pairs with an exchange integral J2 , where J2 > J1 and

ns + 2nd1 + 2nd2 = N

(1)

A simple model that is able to describe diversity of magnetic properties of the Fe-based magnetic clusters can be constructed by suggesting two types of Fe-dimers with different exchange interactions which seems to occur in TiO2 :Fe. Two atoms with spins s (s = 5/2 for Fe3+ ), g-factors g=2 and exchange interaction J between them make a pair having the full spin S and its projection m. The energy of this pair in external magnetic field B can be expressed as

1 E(J, S, m) = ES (J) − gµB Bm, ES (J) = −J S(S + 1) − s(s + 1) 2

(2)

(the negative sign of J corresponds to the antiferromagnetic coupling). The average magnetic 16


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moment of such pair at a temperature T is gµB Bm−Es (J) mexp kB T S=0 m=−S , M2 (J, B, T ) = gµB 2s S P P gµB Bm−Es (J) exp kB T 2s S P P

(3)

S=0 m=−S

And the full magnetic moment of the unit volume is

M (B, T ) = ns M1 (B, T ) + nd1 M2 (J1 , B, T ) + nd2 M2 (J2 , B, T ),

(4)

where M1 is the Brillouin function. The first component describes paramagnetic contribution of the single spins. The second and third components describe contributions from spin pairs with different exchange interactions J1 and J2 , respectively.

gµB B(2s + 1) 1 gµB B 2s + 1 coth − coth M1 (B, T ) = gµB s . 2s 2kB T 2s 2kB T

(5)

Since all the magnetization curves measured for samples 1, 2, 3 and 4 in a wide temperature range 20-350 K exhibit linear behavior up to high magnetic fields (B = 5T), it is convenient to use following expression for initial magnetic susceptibility instead of eq. 4:  2s X  ∂ 1  χ(T ) = M (B, T ) = ns C s + nd1 Cs (J1 , T ) + nd2 Cs (J2 , T ) , ∂B T B→0 S=1

(6)

where the following notations are used: S(S + 1)(2S + 1) (gµB )2 s(s + 1) , Cs (J, T ) = Cs Cs = 2s P 3kB s(s + 1)

exp − Es (J)/kB T (2λ + 1)exp − Eλ (J)/kB T

(7)

λ=1

At low temperatures kB T J1 < J2 the probability exp(-Es (J)/kB T ) to find a dimer in the state with spin S > 0 is small, and so the magnetic moments of the dimers are small as well. In this case contribution of dimers to magnetic susceptibility is proportional to Cs (J1,2 , T )

17



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and turns out to be small. Then it can be suggested that ns coincides with the number of spins obtained from the approximation of the low-temperature magnetic susceptibility with the expression ns Cs T −1 . The energies Es (J) represented as functions of S in eq.2 are described with a parabola so that the energy of a dimer in the state with the spin S = 2s or S = 2s − 1 may turn out to be much greater than kB T , even if J ≤ kB T . Therefore, dimers with different values of J may provide comparable contributions into susceptibility at intermediate values of temperature |J1 | < kB T < |J2 | . At very high temperatures kB T |J|s(2s + 1) in (7) a power expansion can be carried out for J/kB T : S(S + 1) − 2s(s + 1) (gµB )2 S(S + 1)(2S + 1) 1+J Cs (J, T ) ≈ 3kB (2s + 1)2 2kB T

(8)

and, substituting the result into Eq. 6, summing up over S as: 2s X

2(gµB )2 s(s + 1) Js(s + 1) Cs (J, T ) ≈ 1+ 3k 3kB B S=0

(9)

To this approximation, with J1 s(s+1) kB T J2 magnetic susceptibility can be expressed nd1 J Cs s(s + 1) . 1+2 χ(T ) ≈ (ns + 2nd1 ) T ns + 2nd1 3kB T

(10)

Following the procedure in Ref. 48 and carrying out the transformation 1 + a → (1 − a)−1 , we can obtain the magnetic susceptibility in the form of the Curie-W eiss law as

χ(T ) ≈ (ns + 2nd1 )

Cs nd1 J1 , Θ = −2 s(s + 1) < 0 T −Θ ns + 2nd1 3kB

18


(11)

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Similarly, at J2 s(s + 1) kB T the following expressions are obtained: Cs nd1 J1 + nd2 J2 Cs χ(T ) ≈ N 1+2 s(s + 1) ≈ N , T 3N kB T T −Θ nd1 J1 + nd2 J2 Θ = −2 s(s + 1) < 0. 2N kB

(12)

At very high temperatures kB T J2 s(2s + 1) all the pairs have to ”breakdown” so that the slope of the magnetization curve has to be nearly the same as the slope of the Brillouin function with the number N of spins. Nevertheless, exchange interaction manifests itself (similarly to the case of an antiferromagnetic phase) so that the curve χ−1 (T ) at low temperatures is steeper than it is usually observed for purely paramagnetic state. It means that the linear approximation of the χ−1 (T ) curve made at high temperatures would provide nonzero Weiss constant Θ and reminiscent the Curie-Weiss law. If one approximate the experimental data by the model curves one should assume that all the parameters – J1 , J2 , ns , nd1 , nd2 – do not depend on temperature. Nevertheless these parameters may exhibit weak dependence on the Fe content x in the sample due to the tendency of Fe ions to form magnetic clusters in TiO2 nanoparticles.

Model description of magnetic data Firstly, it was an attempt to describe our experimental data by assuming the different variants of spin states in the frame of Brillouin function without the AFM dimers. We examine a three variants of spin states — S = 5/2, 2 and 1/2. In principle, the change of spin state could be connected with high or low spin state for Fe3+ or to be as a result of decrease of single Fe magnetic moment due to charge transfer processes, e.g., as it was shown in paper. 49–51 In fact, it can lead to decrease of magnetic Fe moment due to charge transfer down to 2.8 µB /Fe, however, as we demonstrate in the research at any Fe spin state it’s impossible to explain the experimental data for all samples in the frame of Brillouin function for the non-interacting of Fe spins. As well, in principle Fe3+ can be in the low spin configuration, 19



but both experiment and theory shows that this is rather unlikely situation in oxides at normal conditions. It is known that in Fe based oxides the low spin state can be stabilized only at rather large pressure, e.g. Fe3+ ions transform to the low spin state at 46 GPa in FeBO3 , 52 and at 50 GPa in Fe2 O3 . 53 Theoretical calculations demonstrate that spin-state transition in NaFeSi2 O6 is expected to occur at ∼60 GPa. 54 Thus, we do not expect that Fe3+ in TiO2 adopts the low spin configuration. Finally, we demonstrate that the only Brillouin function is absolutely incapable to explain and describe the experimental data of the all investigated samples in wide temperature range (2-300 K) at any value of spin states. Below we demonstrate the validity of quantum mechanical model for the Fe-based magnetic cluster represented as a set of two dimers with strong and weak exchange interactions and paramagnetic contribution. Our model was found to provide a good description of magnetic properties of TiO2 :Fe nanopowders with reasonable physical approximations. Magnetization curves measured for sample 4 (4.6 at.%Fe) at temperatures 3 K and 300 K as well as their fits by our model of mixed magnetic state with ns single non-coupled spins and two types of AFM dimers nd1 , nd2 with different exchange interactions J1 , J2 between spins are shown in Figures 8(a) and 8(b).

Good agreement between model curves and

2.0

r

2

(a)

= 0.998

0.08

r

2

(b)

= 0.999

T = 300K

T=3K mFe(mb/Fe)

1.5

mFe(mb/Fe)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 39

1.0

0.5

M(B) exp

0.06

0.04

M(B) exp

0.02

Model curve

Model curve 0.00

0.0 0

1

2

3

4

5

6

0

1

B (T)

2

3

4

5

6

B (T)

Figure 8: Model (solid line) and experimental (dots) magnetization curves for sample 4 at 3 (a) and 300K (b). experimental data was obtained for both temperatures with five adjusted parameters which are reported in Table 4 for samples 1, 2, 3 and 4. The total content of Fe in the samples 20


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Table 4: Values of the model parameters (singles content-ns , content of dimers with small exchange-nd1 , content of dimers with high exchange nd2 , exchange in pairs J1 ∼ 1K, exchange in pairs J2 ∼ 100-300 K) as they were obtained from approximation of the experimental magnetization curves measured for samples 1, 2, 3 and 4 at low temperature (2 K) and room temperature (300 K). Spin value of the Fe3+ ion was fixed to be S=5/2 and g-factor to g=2. Samples T,K ns , % 1 2 44 2 2 35 3 2 28 4 3 20 1 300 44 2 300 35 3 300 28 4 300 20

nd1 /J1 10/1 10/1 18/1 16/1 4/1 10/1 18/1 16/1

nd2 /J2 46/150 55/200 56/100 64/100 52/150 55/(200-300) 54/100 64/(100-150)

was manually fixed to the values which were obtained from ICP mass-spectrometry. It can be seen that two types of spin-pairs formed by weak J1 ∼1 K and strong J2 ∼ 100-300 K exchange interactions were found by this approximation for all samples. The values of the adjusted parameters at low and at room temperature were obtained from approximation of the respective magnetization curves and represented in Table 4. The concentration of Fe3+ ions strongly coupled with J2 was estimated to be 64% of the total Fe content in the sample while the concentration of Fe3+ ions weakly coupled with J1 was estimated be 16%. The rest 20% of magnetic Fe3+ ions with a spin of S=5/2 were found to be in a paramagnetic state. It should be emphasized that changing J2 value from 100 K up to higher values (∼ 300 K) doesn’t substantially affect the quality of fit while reduction of the J2 value below 100 K results in considerable discrepancy between the model curve and experimental data. Thus the estimated J2 values were reported in Table 4 as a range of values that provides good quality of fit. The model curve of the temperature dependence of magnetization for sample 4 was plotted using fixed values of the model parameters ns = 20%, nd1 = 16%, nd2 = 64%, J1 = 1K, J2 = 100K obtained from the fit of magnetization curves. Then the model curve was compared with the experimental data as well as with the Curie law curve plotted using 21



spin value s=5/2 for Fe3+ ions and a concentration of the paramagnetic centers x= 4.6 at.%, as it is shown in Figure 9. It can be seen that the Curie law curve exhibits poor agreement with the experimental data as well as with the theoretical curve obtained using our model. Contrary, the model curve exhibits good agreement (R2 = 0.9884) for sample 4 as well as for samples 1, 2 and 3 possessing low Fe content. M(T) exp Model

0.8

mFe (mb/Fe)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Curie law 0.6

Sample 4

0.4

H = 20 kOe 0.2

0.0 0

100

200

300

Temperature (K)

Figure 9: Magnetization as a function of temperature M(T) for sample 4 (empty symbols), Curie law curve (dashed line) and approximation made using our model of the mixed magnetic state where noncoupled paramagnetic spins coexist with two types of spin-pairs (solid line). If one suggest the random distribution of Fe ions over TiO2 matrix for sample 4 (4.6 at.%) then concentration of dimers do not exceed 5 % for coordination number Z=6. 55 The concentration of dimers estimated from statistical approach turns out to be substantially less than the value obtained from fit of the experimental data by our model. It is approximately ten-fold higher concentration (sum of nd1 & nd2) as compared to the statistical model (see Table 4). The similar discrepancy between statistical approach and our model was found for the samples 1,2,3 having lower content of doped Fe. Thus, the main conclusion is that the accumulation of magnetic moment carriers and formation of magnetic clusters modeled by Fe-Fe pairs seems to be a fundamental tendency for all studied TiO2:Fe nanopowders. This tendency can be understood in terms of thermodynamics of nanocrystalline materials having a lot of defects both in the core and surface area.

22


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Theoretical estimations of exchange interactions within Fe-pairs near defect on DFT-based modeling Density-functional theory (DFT) calculations were performed using the SIESTA pseudopotential code 56 as had been used successfully for related studies of impurities in the bulk and thin-f ilm morphologies of TiO2 . 57 All calculations had been made employing the PerdewBurke-Ernzerhof variant of the generalized gradient approximation (GGA-PBE) 58 for the exchange-correlation potential. After that, the calculated atomic positions were completely optimized. The ground electronic state was consistently found during optimization using norm-conserving pseudopotentials 59 for the cores, and a double-ξ plus polarization basis of localized orbitals for Fe, Ti, and O. The forces and total energies were optimized with an accuracy of 0.04 eV/˚ A and 1.0 meV, respectively. All calculations were carried out with an energy mesh cut-off of 300 Ry and a k-point mesh of 6×6×4 in the Monkhorst-Pack scheme. 60 For our calculations, we used TiO2 supercell of 96 atoms (see Figure 10(a-c)). For the modeling of single impurity, we substitute one titanium atom in octahedral site by iron, and for the modeling of pairs formation we substitute two Ti atoms at different interatomic distances in anatase structure. The calculations of the formation energies (Ef orm ) were based on the following formula:

Ef orm = [Etotal − (Ematrix − mET i + mEF e )]/m,

(13)

where Etotal is the total energy of TiO2 supercell with m atoms of iron, Ematrix is the total energy of pure supercell, and EF e and ET i are the total energies per atom of α-Fe and α-Ti respectively. The value of exchange interactions are obtained within the Heisenberg model:

EF M − EAF M = −S 2 J,

23


(14)


where EF M and EAF M is the total energy of the same system with parallel and antiparallel orientation of spins on iron impurities and S is the value of the spin.

Figure 10: Optimized atomic structure of single substitutional iron impurity (a) and the most energetically favorable Fe-Fe pairs at short distance (b) and the remoted (c) pair of Fe-impurities with large Fe-Fe distance in the vicinity of oxygen vacancy (b). The difference between formation energy per iron atom of the pair (red line) and single impurity and the value of exchange integral (blue line) as a function of the distance between iron centers (d). Fe atom indicate by blue color, Ti is grey color and O oxygen is red color. The first step of our calculations is the check of the oxidation state and magnetic moments on iron in perfect TiO2 and vicinity of the oxygen vacancy. In the first case the occupancies of the orbitals and the value of magnetic moment (3.72 µB ) evidence that the substitution of Ti4+ provides formation of Fe4+ center that contradicts to the reported above experimental results. Formation of Fe4+ centers leads to appearance of the states on Fermi level for single and the pair of the impurities (see Figure 11(a,b)). It is necessary to underline that the both states have the semiconducting behavior. These results are in agreement with the calculations for iron impurities in rutile. 61,62 In the vicinity of oxygen, magnetic moment on

24


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iron center is about 4.26 µB that is close to S=5/2 and d5 -configuration. The role of oxygen vacancy in the formation of Fe3+ centers can be expressed by the further formula: 2(TiO2 ) - O + 2Fe → Fe2 O3 . Note that this scenario is working only for the pairs but electronic structure is different in the case of single impurity (see Figure 11(b)). The deviation of magnetic moment from integer number can be caused by charge transfer (intratomic and interatomic) and AFM spin-polarization of Fe-ligands with respect to their parent-Fe. 46–48 Therefore the spin ground state and the value of calculated magnetic moment depend from the size of the supercell.

Figure 11: Total densities of states for the nearest pair (a) and single (b) of substitutional iron impurities with (blue dashed line) and without (solid red line) oxygen vacancy in vicinity. Based on this result we will further consider only the case of Fe-impurities in the vicinity of the oxygen vacancy. At the first step of our modeling, we compare the formation energies per iron impurity for the pairs and single impurity in the supercell. This single impurity is considered as a noninteracting. Results of the calculations (Figure 10b) demonstrate that at the distances of ∼1 nanometer iron impurities can be considered as separate and independent. 25



Further decreasing the distance between iron impurities provides an insignificant deviation of the formation energy from the single impurity. Only the two possible pairs of nearest iron impurities in anatase TiO2 that connected through an oxygen bridge (see Figure 10(b,c)) is extremely energetically favorable. Thus based on the calculated energies, we can prove a robust tendency for the formation of the pairs of iron impurities in the TiO2 matrix. To justify the proposed model (coexistence of two types dimers and singles) it should be underline at least two the most key factors. The first one is that in the TiO2 :Fe lattice with a strongly definite Fe atom site position it is difficult to wait some continuous distribution. It will be a discrete set of sites which are corresponded to well-defined atom position and distances between them in the nearest surrounding, in particular, confirmed by our DFT calculations (Figure 10 (d)). The second one, there is another important parameter this is very critical dependence of the exchange energy versus distance. One can observe a strong influence of distance between Fe-Fe-atoms (cut off) on the value of exchange interaction and very fast decaying at increasing atom-atom distance towards to the next atom (see Figure 10 (d)). So, it means one can limit ourselves to consideration just only by two groups of dimers with high exchange interactions (∼200-300 K) at short distances (on Figure 10 (d) — 3.3 ˚ A and 4.1 ˚ A respectively) and very weak (∼1 K) at the distances nearest to this site (∼5 ˚ A and more) in accordance with the DFT calculation (Figure 10(d)). There is no Fe-atoms at the distances between 4.1 ˚ A and ∼5 ˚ A. Another words one can say that there is not only intermediate short distances except — 3.3 ˚ A and 4.1 ˚ A between Fe atoms but also evidently intermediate value of exchange interactions are absent as well. Therefore, there are no continuous distribution of exchange interactions and, experimentally we have dealt with just only two groups of dimers having very large (100-350 K) and very small negative exchange interactions (∼1-2 K). Based on results of the calculation of exchange interactions and energy of the Fe-defects formation we can interpret exchange interaction of the large magnitude as an exchange within Fe-O-Fe pair of impurities while the second exchange of smaller magnitude as interactions at

26


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higher distances. Note that in the modeling we consider only the bulk-case. In the vicinity of the surface, some lattice distortions and imperfectness on the surface could influence the magnitude of the exchange and be the cause of the difference in the values calculated in DFT-based models and obtained in the fitting of experimental results. Another source of increasing of the value of antiferromagnetic exchange in dimers is manipulation by hosts and dopants. For example, in Mn-doped GaN systems was observed concentration-independent antiferromagnetic exchange of the order -1.624 K. 63 Moreover, one can expect in the imperfect areas, the appearance of dimers with positive exchange that, perhaps, some authors observe even at as-prepared state without undesirable phases. 16,64

Summary and conclusion In summary, a series of TiO2 :Fe-type samples with different Fe content has been synthesized by low-temperature sol-gel method and subsequently subjected to the etching in 2M HCl. It has been shown that etching of the samples in hydrochloric acid completely removes impurity phases as well as their ferromagnetic contribution. Then four samples possessing Fe content x = 0.1, 0.7, 2.4 and 4.6 at.% have been studied by magnetic measurements and EPR-spectroscopy. It has been found that the field dependencies of magnetization can’t be well described by the Brillouin functions if one to fix the spin value of Fe3+ ion as s=5/2 and the concentration of paramagnetic centers to the chemical content of Fe in the sample that was determined by ICP mass-spectrometry. Similar result has been obtained by approximation of the temperature dependencies of magnetic susceptibility by the Curie-Weiss law which cannot be capable to describe temperature dependence of the magnetic susceptibility correctly. In order to describe the magnetic properties of the TiO2 :Fe system (samples 1, 2, 3 and 4), a mixed magnetic state consisting of non-coupled paramagnetic Fe3+ ions and magnetically coupled iron complexes was proposed. In the simplest case such magnetic clusters can be approximated with a set of dimers having different exchange values in the two

27



pairs. A quantum mechanical model of the mixed magnetic state has been developed and applied to describe the magnetic measurements data. We found that the model describes both the magnetization curves and the temperature dependence of magnetic susceptibility with a sufficient accuracy. The fraction of the paramagnetic Fe3+ ions estimated from the magnetization curves at low temperature using our model was found to be 20% for sample 4 (4.6 at.% of Fe — Table 4). Decrease of the Fe content in the sample by factor 40 results in increase of the fraction of paramagnetic ions by factor 2 for sample 1 (0.1 at.% of Fe). This result implies a tendency and basic feature of Fe ions to form iron-based clusters rather than a random distribution over TiO2 matrix in the as-prepared state. In fact, the estimation of the Fe pairs formation probability for coordination number Z=6 (typical for TiO2 anatase) is less than 5% for sample 4. The fraction of the Fe ions involved in formation of the spin-pairs with large exchange (J ∼ 100-300 K) was estimated to be more than 50% for all samples. Similar distribution of Fe3+ ions between the paramagnetic matrix and magnetic clusters modeled by a combination of two types of dimers formed strong and weak exchange interactions was observed for all samples possessing different content of doped Fe. It seems to reflect a general tendency of TiO2 nanopowders to accumulate of magnetic Fe3+ ions around specific sites or defects in the crystal structure and form magnetic clusters that was confirmed by DFT calculations. The DFT calculations revealed that two types of spin-pairs with weak and strong exchange interactions can be formed in the vicinity of an oxygen vacancy and are extremely energetically favorable. Exchange interaction of the large magnitude can be interpreted as an exchange within Fe-O-Fe pair while the second exchange of smaller magnitude as interactions at longer distances. Moreover we can not exclude the appearance of FM coupling in the dimers due to large distance and to the Goodenough-Kanamori model. The results of approximation of magnetic measurements data are in good agreement with the EPR-spectroscopy. The paramagnetic contribution obtained from processing of the integrated EPR-spectrum for sample 4 was decomposed into the sum of four EPR signals (1, 2, 3 and 5 on Figure 7) accounting for about 34% of the total EPR signal (see Table

28


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2). The fifth broad EPR-signal (4 on Figure 7) overlapping with narrow paramagnetic lines around g ∼ 2 accounts for the rest 66% of the EPR spectrum and was ascribed to the antiferromagnetically correlated Fe3+ ions. Thus our model of the mixed magnetic state consisting of non-coupled paramagnetic Fe3+ ions and magnetically coupled Fe3+ ions forming iron-based clusters is evidenced by the EPR data. The ratio of the antiferromagnetically correlated to the paramagnetic Fe3+ ions (2:1) is close to the distribution that was determined by approximation of the magnetization curves using our model (3.5:1). The little excess of the paramagnetic contribution derived from the EPR spectrum over the can be attributed to the contribution of F+ centers and O− 2 radicals which were reported to exist in TiO2 -based nanopowders. 26,27 In conclusion, magnetic state of the as-prepared nanocrystalline TiO2 samples doped with Fe at various concentrations ranging from 0.1 at.% to 4.6 at.% immediately upon synthesis and after etching was studied by the EPR spectroscopy and SQUID-magnetometry. A quantum-mechanical model of the mixed magnetic state consisting of non-coupled paramagnetic Fe3+ ions and magnetically coupled Fe3+ ions forming iron-based clusters has been developed and successfully applied to describe magnetic measurements data. A direct evidence of the substantial contribution provided by short-range AFM order has been obtained by EPR-spectroscopy. The DFT calculations confirmed that two types of spin-pairs with weak and strong exchange interactions can be formed in the vicinity of an oxygen vacancy. The estimated exchange values was found to be in reasonable agreement with the J1 and J2 parameters obtained from the approximation of magnetic measurements data by our model. The selective spatial accumulation of the magnetic moment carriers and formation of magnetic clusters in the TiO2 matrix was found to be almost independent on the actual iron content in the samples within the studied concentration range. Such an effect seems to be a general tendency for all TiO2 :Fe nanopowders. Future studies are necessary in order to obtain direct experimental evidence for the existence of magnetic clusters in the TiO2 matrix and to clarify fundamental origin of the selective accumulation of the magnetic complexes.

29



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Acknowledgement The research was supported by the Russian Science Foundation (project 16-12-10004). The authors are grateful for the contributions made by our colleagues G.S. Zakharova, A.S. Konev, K.I. Borodin, Z.A. Phatakhova, A.M. Murzakaev, V.S. Gaviko. The X-ray investigation and magnetic measurements have been performed in the Collaborative Access Center of M.N. Mikheev Institute of Metal Physics of the Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia.

References (1) Sui, Y.; Liu, Q.; Jiang, T.; Guo, Y. Synthesis of Nano-TiO2 Photocatalysts with Tunable Fe Doping Concentration From Ti-Bearing Tailings. Appl. Surf. Sci. 2018, 428, 1149–1158. (2) Chen, B.; Haring, A. J.; Beach, J. A.; Li, M.; Doucette, G. S.; Morris, A. J.; Moore, R. B.; Priya, S. Visible Light Induced Photocatalytic Activity of Fe3+ /Ti3+ co-Doped TiO2 Nanostructures. RSC Adv. 2014, 4, 18033–18037. (3) Kaleji, B. K.; Mirzaee, S.; Ghahramani, S.; Rezaie, S.; Hosseinabadi, N.; Fujishima, A. Sol-Gel Synthesis of Sn/Fe co-Doped TiO2 Nanoparticles: Study of Structural, Optical and Photocatalytic Properties. J. Mater. Sci.: Mater. Electron. 2018, 29, 12351–12359. (4) Pereira, L. M. C. Experimentally Evaluating the Origin of Dilute Magnetism in Nanomaterials. Phys. D: Appl. Phys. 2017, 50, 393002. (5) Yermakov, A. Y.;

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Molochnikov, L. S.; Konev, S. F.; Konev, A. S.; Minin, A. S.; Mesilov, V. V.; Galakhov, V. R. et al. Surface Magnetism of Cobalt-Doped Anatase TiO2 Nanopowders. J. Phys. Chem. C 2016, 120, 28857–28866.

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Graphical TOC Entry

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Formation of Fe-Fe Antiferromagnetic Dimers in Doped TiO2

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