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Low temperature EPR investigation of Co2+ ion doped into rutile TiO2 single crystal: Experiments and simulations
Journal of Magnetism and Magnetic Materials 423 (2017) 145–151
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Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Low temperature EPR investigation of Co2+ ion doped into rutile TiO2 single crystal: Experiments and simulations
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A. Zerentürka, M. Açıkgözb, , S. Kazanc, F. Yıldızc, B. Aktaşc a b c
Department of Physics, Marmara University, 34722 Kadıköy, Istanbul, Turkey Bahcesehir University, Faculty of Engineering and Natural Sciences, Besiktas Campus, 34349 Besiktas, Istanbul, Turkey Department of Physics, Gebze Technical University, 41400 Gebze, Kocaeli, Turkey
A R T I C L E I N F O
A BS T RAC T
Keywords: Co2+ TiO2 Rutile EPR, low temperature
In this paper, we present the results of X-band EPR spectra of Co2+ ion doped rutile (TiO2) which is one of the most promising memristor material. We obtained the angular variation of spectra in three mutually perpendicular planes at liquid helium (7–13 K) temperatures. Since the impurity ions have ½ effective spin and 7/2 nuclear spin, a relatively simple spin Hamiltonian containing only electronic Zeeman and hyperfine terms was utilized. Two different methods were used in theoretical analysis. Firstly, a linear regression analysis of spectra based on perturbation theory was studied. However, this approach is not sufficient for analyzing Co+2 spectra and leads to complex eigenvectors for G and A tensors due to large anisotropy of eigenvalues. Therefore, all spectra were analyzed again with exact diagonalization of spin Hamiltonian and the high accuracy eigenvalues and eigenvectors of G and A tensors were obtained by taking into account the effect of small sample misalignment from the exact crystallographic planes due to experimental conditions. Our results show that eigen-axes of g and A tensors are parallel to crystallographic directions. Hence, our EPR experiments proves that Co2+ ions substitute for Ti4+ ions in lattice. The obtained principal values of g tensor are gx=2.110(6), gy=5.890(2), gz=3.725(7) and principal values of hyperfine tensor are Ax=42.4, Ay=152.7, Az=26 (in 10−4/cm).
1. Introduction
TiO2 (see, e.g. [7,8]) was reported after several experimental investigations. Particularly, the magnetic properties of the Co-implanted TiO2 thin films, on single-crystalline (100), (001) and (110) TiO2 substrates of rutile structure, by magneto-optical Kerr effect (MOKE) and superconducting quantum interference device (SQUID) techniques were studied by our group [9]. It was revealed strong room-temperature ferromagnetism, with magnetic parameters depending on the crystallographic orientation of the substrate. Also, the magnetic anisotropy of cobalt implanted single-crystalline rutile was studied by means of by the same techniques, MOKE and SQUID [10]. The defects (oxygen vacancy and/or impurities) of the paramagnetic ions (Fe3+, Cu2+, Co2+, Gd3+, Cr3+, Mn4+, Mn2+, Ni2+ and V4+ which can substitute for the cation in host lattice) doped rutile TiO2 have been examined in various studies. Previously, g-values of Co2+ doped rutile TiO2 at room temperature were investigated experimentally [11,12] and theoretically [13] using the second-order perturbation formulas on the basis of the cluster approach. It was suggested that divalent cation impurities i.e. Co2+ and Ni2+ in TiO2 may have an adjacent oxygen vacancy for charge compensation [14]. It is clear that there may be two possible positions to be located by a
It has been known that TiO2 crystals are one of the most promising oxide semiconductors with many attractive chemical, electronic, and optical properties, and thus are widely used for, e.g., air purification, solar cell, self-cleaning coating, as well as used as the material in the first memristor device by Picket et al. [1]. It was found that oxygen vacancy in TiO2 crystal move with the electric field applied for the electric current and become a conductor depending on the defect density of the perfectly stoichiometric TiO2 crystal which is basically an insulator. There exist three different forms of TiO2 crystals, namely, rutile, anatase, and brookite. The rutile phase is most useful for different applications, especially as a dilute magnetic semiconductor (DMS) with high Curie temperature TC [2] since rutile is thermodynamically most stable, see, e.g. [3]. Much attention has been devoted to the discovery of high-Curie temperature diluted magnetic oxides (e.g. transition metal doped TiO2, ZnO, SnO2 and others) to be potentially important for the development of the spintronic devices [4,5]. It is also worth to note that room-temperature ferromagnetism accomplished in iron doped rutile TiO2 (see, e.g. [6]) and cobalt doped
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Corresponding author. E-mail address: [email protected] (M. Açıkgöz).
http://dx.doi.org/10.1016/j.jmmm.2016.09.081 Received 2 August 2016; Received in revised form 2 September 2016; Accepted 16 September 2016 Available online 17 September 2016 0304-8853/ © 2016 Elsevier B.V. All rights reserved.
Journal of Magnetism and Magnetic Materials 423 (2017) 145–151
A. Zerentürk et al.
Fig. 3. EPR spectra of Co2+ paramagnetic centers in the first plane: (010) orientation when (a) the peaks are separated most from each other and (b) the peaks are very close to each other.
Fig. 1. The polyhedral model of rutile TiO2 crystal viewed along the c axis generated with VESTA visualization code. The red thick line shows the (110) plane. Red (shaded) spheres represent oxygen (titanium) atoms. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
transition ion doped into rutile TiO2 crystal: substitutional Ti4+ sites and interstitial positions. In the case that Ti4+ in TiO2 crystal is substituted by another positive ion with different ionicity, the difference in radii of the substitution and dopant ions may be decisive as well. The radius of Ti4+ ion in the octahedral configuration is 0.075 nm, whereas that of Co2+ is 0.079 nm [15]. In this study, rutile TiO2 single crystals doped with Co2+ ions using implantation technique have been investigated by EPR at low temperatures. Regression analyses of the spectrum as well as exact diagonalization (ED) analysis method have been carried out. The spin-Hamiltonian parameters, namely the anisotropic g-factors gx, gy, and gz and hyperfine interaction parameters Ax, Ay, and Az for Co2+ ions have been determined and the results been discussed in detail.
2. Experimental procedures Single crystalline (110) TiO2 rutile substrates have been implanted on the ILU-3 ion accelerator (Kazan Physical-Technical Institute) with 40 keV Co+ ions to a fluence of 1.50×1017 ions/cm2 at ion current density of about 8 µA/cm2. The sample holder was cooled by flowing water during the implantation to prevent the samples from overheating. The implanted samples have been annealed at T=950 °C in air
Fig. 4. The angular variation of the EPR spectra of Co2+ ions in the first plane. The angle of the recorded spectra is indicated to the right of each spectrum.
during 1 h. The annealed samples have been studied by electron paramagnetic
Fig. 2. Illustrations of the planes where the EPR spectra taken with respect to crystallographic axes. Blue thin rectangular prism represents the rutile sample, red vertical lines show the rotation axes, whereas green horizontal lines show the direction of static magnetic field. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
146
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Fig. 7. The angular variation of the EPR spectra of Co2+ ions recorded in the third plane. Fig. 5. (a) EPR spectra recorded in the second plane where the centers exactly superimpose. (b) Another sample EPR spectrum recorded in the second plane. Beginning with the third peak of the first center, the separation between the peaks belonging to two different centers is only a few Gauss. Similar situation was observed in almost all orientations in this plane.
Table 1 The results of regression analyses of Co2+ ions for both centers. The columns of G and A tensors are the eigenvectors. The eigenvalues of A are given in [in 10−4 cm−1] units. Some eigenvalues found as imaginary numbers showing that regression analysis is not sufficient for analyzing the experimental results. 1. Center G-eigenvalues 2.1472 0 0 G-eigenvectors 0.0403 0.7114 0.7017 A-eigenvalues 0+0.0036i 0 0 A-eigenvectors 0.9441 0.3265 0.0454
2. Center
0 3.7597 0
0 0 5.9101
0.9984 −0.0007 −0.0566
0.0398 −0.7028 0.7103
0 0.0097 0
0 0 0.0156
−0.2602 0.6535 0.7108
0.2024 −0.6829 0.7019
G-eigenvalues 2.0945 0 0 G-eigenvectors −0.0683 0.6999 −0.7110 A-eigenvalues 0+0.0040i 0 0 A-eigenvectors 0.9353 0.3231 −0.1441
0 3.7560 0
0 0 5.8869
0.9968 0.0782 −0.0187
−0.0425 0.7100 0.7029
0 0.0103 0
0 0 0.0154
−0.3284 0.6415 −0.6933
−0.1316 0.6958 0.7061
cell parameters. The most recent values [17] of the lattice parameters for rutile (a, c): experimental (0.4625, 0.2960) nm and theoretical DFT optimized (0.4540, 0.28602) nm were provided. The tetragonal (eigen) axes of two equivalent Ti4+ sites in the unit cell are perpendicular to each other and they are also perpendicular to the tetragonal axis of the crystal structure. The local point symmetry around Ti4+ sites in rutile structure is lowered from Oh to D2h due to the slight distortion of the coordinating oxygen octahedron with two different Ti–O bond lengths, which are 0.1944 nm for 4 O-ligands in (110) plane and 0.1988 nm [18] for the other two O-ligands. Thus, we can expect two equivalent sets of paramagnetic centers for the Co+2 ions in the crystal.. In the measurements, EPR spectra of Co2+ doped rutile TiO2 crystal have been recorded in three mutually perpendicular planes at low temperatures (7–13 K). These are: the first plane (010), the second plane (110), and the third plane (1 1̅ 0). The illustrations of the planes are shown in Fig. 2. The results for each plane are presented in the following sections..
Fig. 6. The angular variation of the EPR spectra of Co2+ ions between 0° and 105° with 15° intervals.
resonance (EPR) technique using Bruker EMX X-band spectrometer (9.8 GHz) at liquid helium (7–13 K) temperatures. Angular dependences of EPR spectra have been recorded with the static magnetic field rotated either in the plane of the plate-like samples (“in-plane” geometry) or in the two perpendicular planes (“out-of-plane” geometry) nearly coinciding with crystallographic planes of a substrate. Thus, there are three rotational planes in total for each sample to obtain the angular dependences of the EPR spectra. The temperature dependence of EPR spectra was studied using a continuous helium gas flow cryostat made by Oxford Instruments. The temperature stability was better than 0.5 K. 3. Results and discussion
3.1. Spectra obtained in the first plane: (010) At room temperature, the rutile TiO2 crystals (see Fig. 1) have the tetragonal space group P42/mnm [16]. The unit cell contains 6 atoms. There are six neighboring oxygen ions around each Ti4+ ion and two Ti4+ ions in the unit cell, whereas each O2− anion is coordinated to three Ti4+ cations. Several data are available in literature for the unit-
Fig. 3 shows the spectra of the peaks belonging to two different centers for Co2+ ions in the first plane when the peaks separated most from each other and are very close to each other, respectively. The marking of the peaks is also indicated. The peaks appearing on the left 147
Journal of Magnetism and Magnetic Materials 423 (2017) 145–151
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Fig. 8. (a–c) The comparison of the experimental gg values of Co2+ ions (black squares and red circles) in rutile TiO2 with theoretical simulation results (black and red lines) obtained from regression analyses in three planes respectively. Black (red) color was used for first (second) center. As seen the centers follow each other with a 90° difference in the first plane but they are parallel in the other planes. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
can be attributed to the first center while those on the right belong to the second center. As expected, 8 hyperfine splitting peaks of Co2+ ions are easily seen. The peak numbers on the peaks indicate nuclear spin states. As easily seen from Fig. 3(b), except for the outermost three peaks of each center (peaks 1, 2 and 3 for the first center, peaks 6, 7 and 8 for the second center), the other peaks have partially overlapped.. The angular variation of the EPR spectra for Co2+ ions are presented in Fig. 4. The presence of two different centers and the angle of 90° between these centers are seen. Also, it is clear that the EPR spectra of Co2+ yield basically two groups of eight peaks. Between these main peaks, secondary peaks with much smaller intensities also occur at many angles since the curve width of these main peaks are rather small. When the angle changes the peaks of these two main groups shift in different directions along the axis of the static magnetic field. Furthermore, the separation between these eight peaks of each group varies with angle. It is noticed that a 90° phase difference occurs between the resonance fields of the groups. Such behavior indicates the presence of two different Co2+ centers which are structurally equivalent but oriented with 90° difference relative to each other..
the nature of the rutile crystal, it was expected that the lines of the centers superimpose for all orientations in this plane. However, as seen in the spectra below, the centers are slightly separated from each other. Taking the measurements at a misaligned plane intersecting at an angle of a few degrees with the exact crystallographic plane is the reason of this separation. As can be seen in Fig. 5(a), the centers almost exactly superimpose to give a set composed of 8 peaks for the orientations at the intersection of these two planes. On the other hand, as in Fig. 5(b), at the angles away from these orientations the third peak of the first center overlaps with the first peak of the second center.. The angular variation of the EPR spectra of Co2+ ions taken at intervals of 5° between 0° and 105°. A subset of these spectra with 15° intervals are given in Fig. 6 for the second plane. It is seen that the centers superimpose in the 105° orientation. In the other angles the presence of two identical centers which move parallel to each other and generally the overlapping of the third peak of the first center with the first peak of the second center are observed. The separation of peaks belonging to different centers is only about 10 G.. 3.3. Spectra obtained in the third plane: (1 1̅ 0)
3.2. Spectra obtained in the second plane: (110) The angular variation of EPR spectra of Co2+ ions observed in the third plane are seen in Fig. 7, where, just as in the second spectrum, we see two different centers which move parallel to each other and overlap in the other angles. The peaks belonging to two centers in many
2+
In this plane, the EPR peaks of Co ions can be clearly observed. The 90° phase difference between the centers in the first plane leads us to consider that the dopant ions substitute for Ti4+ ions. Thus, due to 148
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A. Zerentürk et al.
Fig. 9. (a–c) The comparison of the experimentally obtained A results of Co2+ ions in rutile TiO2 with theoretical ones obtained from regression analyses in three planes. Especially in first plane (Fig. 9a) there is a huge discrepancy between experiment and theoretical simulation.
spectroscopic splitting tensor, S is the spin operator, A is the hyperfine tensor, and I is the nuclear spin operator. This expression can be written in terms of eigen axes:
Table 2 Anisotropic g values and hfs constant A [in 10−4 cm−1] for the rutile TiO2 doped with Co2+.
Expt. [10] Expt. [11] Theo. [12] This study 1. Center 2. Center
gx
gy
gz
Ax
Ay
Az
2.190 (5) 5.885 (1) 6.20 (2)
5.88 (2) 2.079 (1) 2.051 (5)
3.75 (1) 3.735 (5) 4.04 (2)
40
150
26
2.110(6) 5.890(2)
5.890(2) 2.110(6)
3.725(7) 3.725(7)
42.4 152.7
/ = β (gxx Hx Sx + gyy Hy Sy + gzz Hz Sz ) + (Axx Sx Ix + Ayy Sy Iy + Azz Sz Iz )
If the magnetic field is in the z-axis, Eq. (2) becomes rather simple:
/ = βgzz Hz Sz + Axx Sx Ix + Ayy Sy Iy + Azz Sz Iz 152.7 42.4
(2)
(3)
Eq. (2) can be transformed into the form in Eq. (3) using an appropriate axis transformation. Also, if we accept off-diagonal elements to be very small, instead of Eq. (1) the following equation can be obtained:
26.0 26.0
orientations are observed..
/ = βgeff HSz + Aeff Sz Iz 4. Regression analysis of the spectrum
(4)
where geff and Aeff are defined in the following forms:
EPR spectrum can be highly complex depending on the structural properties of the investigated materials. Especially, for the cases where hyperfine structure, fine structure or quadrupole interactions seen together, a detailed description about the structural properties of the sample as well as some advanced statistical methods should be used for a proper analysis. EPR spectrum of the Co2+(3d7) ions can be described by the following general spin Hamiltonian [19], which consists of Zeeman and hyperfine interaction terms
⎡ ggxx ggxy ggxz ⎤ ⎡ nx ⎤ ⎢ ⎥ geff 2 = [nx n y nz ] ⎢ ggyx gg yy gg yz ⎥ ⎢ n y ⎥ ⎢ ⎥ ⎢⎣ ggzx ggzy ggzz ⎥⎦ ⎣ nz ⎦
(5)
⎡ AAxx AAxy AAxz ⎤ ⎡ n ⎤ ⎢ ⎥ x Aeff 2 = [nx n y nz ] ⎢ AAyx AAyy AAyz ⎥ ⎢ n y ⎥ ⎢⎣ AAzx AAzy AAzz ⎥⎦ ⎢⎣ nz ⎥⎦
(6)
→ → →→ → / = βH ⋅→ g ⋅ S + S ⋅A ⋅ I
where nˆ is the unit-vector in the direction of the magnetic field. AA and gg are the squares of the hyperfine interaction and g tensors, respectively.
(1)
where β is the Bohr magneton, H is the magnetic field, g is the 149
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Fig. 10. (a–c) Experimental (blue stars) and theoretical results (black and red lines) of the angular dependence of the resonance fields for two centers of Co2+ ions in all three planes. The theoretical results obtained from exact diagonalization of spin Hamiltonian. Black (red) color was used for first (second) center. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Generally, in order to find g and A tensors in EPR experiments, angular dependence of the resonance fields are carried out in three different planes. In practice, since it provides a great convenience these planes are chosen being perpendicular to each other. In each of these planes the direction of magnetic field can be defined in terms of direction cosines. If the unit vector that is parallel to the magnetic field in each plane is as follows:
⎡ cos θ ⎤ ⎡ cos θ ⎤ ⎡ 0⎤ nˆ1 = ⎢ sin θ ⎥ , nˆ2 = ⎢ 0 ⎥ , nˆ3 = ⎢ cos θ ⎥ ⎢⎣ ⎥ ⎥ ⎢⎣ ⎥ ⎢⎣ 0⎦ sin θ ⎦ sin θ ⎦
taken, to relate these six parameters. When this method is used, the angles must be defined clearly. In addition to this, we must clearly determine the axis of rotation angle, that θ is the angle from which axis, and the direction of rotation. Similarly, we can do a solution for effective A2 values. It is known that in the analysis of the experimental results we aim to find n parameters and want to reduce the effect of random errors. For that, we do experiments as much as possible since it is impossible to do experiment with zero error. Thus, this causes us to get a large number of equations than n. Also, the experimental random errors contribute to make independent linear equations with each other. If we do not make a systematic error, by utilizing the randomness of the experimental errors, we can find the solution of the equations by drawing a graph that minimizes the experimental errors. This can be done by using a very useful statistical method that might be called the least squares method or a regression analysis. Typically, from EPR spectra the eigenvalues and eigenvectors of G and A tensors can be found with regression analysis. The results of regression analyses of Co2+ ion are given in Table 1 for both centers. It is seen that geigenvalues of two centers are real and close to each other, however one of the A-eigenvalues for each center is found as imaginary. Moreover, the eigenvectors of g tensors are parallel to crystal directions, whereas the eigenvectors of A tensors are questionable. The following Figs. 8 and 9 show the comparison of the theoretical results with the experimental results. It is clear in Fig. 8 that there is a quite good fit between theoretical and experimental results. However,
(7)
Then, Eq. (5) can be expressed for each plane as follows: 2 geff = ggxx cos2 θ + ggyy sin2 θ + ggxy cos θ sin θ + ggyx cos θ sin θ 1
2 geff = ggxx cos2 θ + ggzz sin2 θ + ggxz cos θ sin θ + ggzx cos θ sin θ 2
2 geff = ggyy cos2 θ + ggzz sin2 θ + ggyz cos θ sin θ + ggzy cos θ sin θ 3
(8)
Using ggxy = ggyx , ggxz = ggzx , ve ggyz = ggzy , since gg is a symmetric tensor, we obtain 2 geff = ggxx cos2 θ + ggyy sin2 θ + 2ggxy cos θ sin θ 1
2 geff = ggxx cos2 θ + ggzz sin2 θ + 2ggxz cos θ sin θ 2
2 geff = ggyy cos2 θ + ggzz sin2 θ + 2ggyz cos θ sin θ 3
(9)
where gg consists of six independent parameters. In our case there are 52 equations, as the number of angles at which the measurement is 150
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another by 90° difference whereas they move together in the other planes. Thus, it is concluded that impurity ions substitute for Ti4+ ion. The presence of two structurally equivalent paramagnetic centers for Co2+ ions has been observed since the same spin Hamiltonian parameters were obtained. The decomposition of the two different paramagnetic centers in the second (110) and third (1 1̅ 0 ) planes has been shown as a result of a small shift (~2°) of the rotation axis. Since the results show high anisotropy, we can say that oxygen vacancies in the structure of the samples do not occur randomly and only the oxygens in a given direction disappear.
in Fig. 9 it is seen a serious mismatch between the experimental and theoretical results in the first plane. This is because the second order perturbation theory approach is inadequate for Co atom showing very large amounts of anisotropy... 5. Exact diagonalization (ED) analysis of Co2+ spectra Exact diagonalization (ED) analysis is a powerful tool for calculating the spin-Hamiltonian parameters for 3dn ions in crystals. Since the ED method uses the contributions from all excited states, it can provide more accurate results for spin-Hamiltonian parameters [20]. The two Co2+ centers in rutile TiO2 crystal have been analyzed using ED method. The results are presented in Table 2 for both Co2+ centers. These results indicate that two centers follow one another by 90° of difference in the first plane and overlap in the other planes. The small amount of decomposition observed in the experimental spectrum is caused by small errors made in the plane of rotation. If we do not take into account these misalignments, we can’t fit the spectra of two centers with the same set of parameters. Since these misalignments are nonintentional, there was no measurements for them. However they must be small and the correct angle of misalignment should make the experimental errors smaller. Therefore, we wrote a MATLAB code for minimizing the experimental errors against the misalignments. The simulated misalignments that minimize the errors are 0 in the first plane and 2 ± 0.5 in the second and third plane. In this way, as seen from Table 2, two paramagnetic centers were fitted with the same set of values. Another point worthy of attention is the large anisotropy in the orthorhombic symmetry of Co2+ ions. The theoretical resonance fields obtained for each plane is seen in the following Fig. 10 with the experimental resonance fields. The results in Table 2 indicates that very comparable results we obtained here at low temperature for the all Spin Hamiltonian parameters to those at room temperature. The theoretical analyses of only g-factors was carried out in [12] using the secondorder perturbation formulas on the basis of the cluster approach for these Co2+ centers in rutile TiO2 and local structure parameters were predicted considering an orthorhombic local site symmetry around these Co2+ centers, which results in a rhombic distortion on the replaced Ti4+ sites with the following structural parameters R∥=0.19800 nm, R⊥ 0.19485 nm, and θ ≈ 81.21°..
Acknowledgments The authors MA and SK acknowledge support from the Scientific and Technical Research Council of Turkey (TUBITAK) through the Project no. 115F472. References [1] [2] [3] [4] [5] [6]
[7] [8] [9] [10]
[11] [12] [13] [14] [15] [16] [17] [18] [19]
6. Conclusion EPR spectra of Co2+ ions doped into rutile TiO2 by ion implantation technique have been investigated at low temperatures (7–13 K). It is seen that G and A tensors of both ions have the same eigen-axes, which coincide with crystal axes. Also, the centers in the first plane follow one
[20]
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Low temperature EPR investigation of Co2+ ion doped into rutile TiO2 single crystal: Experiments and simulations
crossmark
⁎
A. Zerentürka, M. Açıkgözb, , S. Kazanc, F. Yıldızc, B. Aktaşc a b c
Department of Physics, Marmara University, 34722 Kadıköy, Istanbul, Turkey Bahcesehir University, Faculty of Engineering and Natural Sciences, Besiktas Campus, 34349 Besiktas, Istanbul, Turkey Department of Physics, Gebze Technical University, 41400 Gebze, Kocaeli, Turkey
A R T I C L E I N F O
A BS T RAC T
Keywords: Co2+ TiO2 Rutile EPR, low temperature
In this paper, we present the results of X-band EPR spectra of Co2+ ion doped rutile (TiO2) which is one of the most promising memristor material. We obtained the angular variation of spectra in three mutually perpendicular planes at liquid helium (7–13 K) temperatures. Since the impurity ions have ½ effective spin and 7/2 nuclear spin, a relatively simple spin Hamiltonian containing only electronic Zeeman and hyperfine terms was utilized. Two different methods were used in theoretical analysis. Firstly, a linear regression analysis of spectra based on perturbation theory was studied. However, this approach is not sufficient for analyzing Co+2 spectra and leads to complex eigenvectors for G and A tensors due to large anisotropy of eigenvalues. Therefore, all spectra were analyzed again with exact diagonalization of spin Hamiltonian and the high accuracy eigenvalues and eigenvectors of G and A tensors were obtained by taking into account the effect of small sample misalignment from the exact crystallographic planes due to experimental conditions. Our results show that eigen-axes of g and A tensors are parallel to crystallographic directions. Hence, our EPR experiments proves that Co2+ ions substitute for Ti4+ ions in lattice. The obtained principal values of g tensor are gx=2.110(6), gy=5.890(2), gz=3.725(7) and principal values of hyperfine tensor are Ax=42.4, Ay=152.7, Az=26 (in 10−4/cm).
1. Introduction
TiO2 (see, e.g. [7,8]) was reported after several experimental investigations. Particularly, the magnetic properties of the Co-implanted TiO2 thin films, on single-crystalline (100), (001) and (110) TiO2 substrates of rutile structure, by magneto-optical Kerr effect (MOKE) and superconducting quantum interference device (SQUID) techniques were studied by our group [9]. It was revealed strong room-temperature ferromagnetism, with magnetic parameters depending on the crystallographic orientation of the substrate. Also, the magnetic anisotropy of cobalt implanted single-crystalline rutile was studied by means of by the same techniques, MOKE and SQUID [10]. The defects (oxygen vacancy and/or impurities) of the paramagnetic ions (Fe3+, Cu2+, Co2+, Gd3+, Cr3+, Mn4+, Mn2+, Ni2+ and V4+ which can substitute for the cation in host lattice) doped rutile TiO2 have been examined in various studies. Previously, g-values of Co2+ doped rutile TiO2 at room temperature were investigated experimentally [11,12] and theoretically [13] using the second-order perturbation formulas on the basis of the cluster approach. It was suggested that divalent cation impurities i.e. Co2+ and Ni2+ in TiO2 may have an adjacent oxygen vacancy for charge compensation [14]. It is clear that there may be two possible positions to be located by a
It has been known that TiO2 crystals are one of the most promising oxide semiconductors with many attractive chemical, electronic, and optical properties, and thus are widely used for, e.g., air purification, solar cell, self-cleaning coating, as well as used as the material in the first memristor device by Picket et al. [1]. It was found that oxygen vacancy in TiO2 crystal move with the electric field applied for the electric current and become a conductor depending on the defect density of the perfectly stoichiometric TiO2 crystal which is basically an insulator. There exist three different forms of TiO2 crystals, namely, rutile, anatase, and brookite. The rutile phase is most useful for different applications, especially as a dilute magnetic semiconductor (DMS) with high Curie temperature TC [2] since rutile is thermodynamically most stable, see, e.g. [3]. Much attention has been devoted to the discovery of high-Curie temperature diluted magnetic oxides (e.g. transition metal doped TiO2, ZnO, SnO2 and others) to be potentially important for the development of the spintronic devices [4,5]. It is also worth to note that room-temperature ferromagnetism accomplished in iron doped rutile TiO2 (see, e.g. [6]) and cobalt doped
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Corresponding author. E-mail address: [email protected] (M. Açıkgöz).
http://dx.doi.org/10.1016/j.jmmm.2016.09.081 Received 2 August 2016; Received in revised form 2 September 2016; Accepted 16 September 2016 Available online 17 September 2016 0304-8853/ © 2016 Elsevier B.V. All rights reserved.
Journal of Magnetism and Magnetic Materials 423 (2017) 145–151
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Fig. 3. EPR spectra of Co2+ paramagnetic centers in the first plane: (010) orientation when (a) the peaks are separated most from each other and (b) the peaks are very close to each other.
Fig. 1. The polyhedral model of rutile TiO2 crystal viewed along the c axis generated with VESTA visualization code. The red thick line shows the (110) plane. Red (shaded) spheres represent oxygen (titanium) atoms. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
transition ion doped into rutile TiO2 crystal: substitutional Ti4+ sites and interstitial positions. In the case that Ti4+ in TiO2 crystal is substituted by another positive ion with different ionicity, the difference in radii of the substitution and dopant ions may be decisive as well. The radius of Ti4+ ion in the octahedral configuration is 0.075 nm, whereas that of Co2+ is 0.079 nm [15]. In this study, rutile TiO2 single crystals doped with Co2+ ions using implantation technique have been investigated by EPR at low temperatures. Regression analyses of the spectrum as well as exact diagonalization (ED) analysis method have been carried out. The spin-Hamiltonian parameters, namely the anisotropic g-factors gx, gy, and gz and hyperfine interaction parameters Ax, Ay, and Az for Co2+ ions have been determined and the results been discussed in detail.
2. Experimental procedures Single crystalline (110) TiO2 rutile substrates have been implanted on the ILU-3 ion accelerator (Kazan Physical-Technical Institute) with 40 keV Co+ ions to a fluence of 1.50×1017 ions/cm2 at ion current density of about 8 µA/cm2. The sample holder was cooled by flowing water during the implantation to prevent the samples from overheating. The implanted samples have been annealed at T=950 °C in air
Fig. 4. The angular variation of the EPR spectra of Co2+ ions in the first plane. The angle of the recorded spectra is indicated to the right of each spectrum.
during 1 h. The annealed samples have been studied by electron paramagnetic
Fig. 2. Illustrations of the planes where the EPR spectra taken with respect to crystallographic axes. Blue thin rectangular prism represents the rutile sample, red vertical lines show the rotation axes, whereas green horizontal lines show the direction of static magnetic field. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
146
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Fig. 7. The angular variation of the EPR spectra of Co2+ ions recorded in the third plane. Fig. 5. (a) EPR spectra recorded in the second plane where the centers exactly superimpose. (b) Another sample EPR spectrum recorded in the second plane. Beginning with the third peak of the first center, the separation between the peaks belonging to two different centers is only a few Gauss. Similar situation was observed in almost all orientations in this plane.
Table 1 The results of regression analyses of Co2+ ions for both centers. The columns of G and A tensors are the eigenvectors. The eigenvalues of A are given in [in 10−4 cm−1] units. Some eigenvalues found as imaginary numbers showing that regression analysis is not sufficient for analyzing the experimental results. 1. Center G-eigenvalues 2.1472 0 0 G-eigenvectors 0.0403 0.7114 0.7017 A-eigenvalues 0+0.0036i 0 0 A-eigenvectors 0.9441 0.3265 0.0454
2. Center
0 3.7597 0
0 0 5.9101
0.9984 −0.0007 −0.0566
0.0398 −0.7028 0.7103
0 0.0097 0
0 0 0.0156
−0.2602 0.6535 0.7108
0.2024 −0.6829 0.7019
G-eigenvalues 2.0945 0 0 G-eigenvectors −0.0683 0.6999 −0.7110 A-eigenvalues 0+0.0040i 0 0 A-eigenvectors 0.9353 0.3231 −0.1441
0 3.7560 0
0 0 5.8869
0.9968 0.0782 −0.0187
−0.0425 0.7100 0.7029
0 0.0103 0
0 0 0.0154
−0.3284 0.6415 −0.6933
−0.1316 0.6958 0.7061
cell parameters. The most recent values [17] of the lattice parameters for rutile (a, c): experimental (0.4625, 0.2960) nm and theoretical DFT optimized (0.4540, 0.28602) nm were provided. The tetragonal (eigen) axes of two equivalent Ti4+ sites in the unit cell are perpendicular to each other and they are also perpendicular to the tetragonal axis of the crystal structure. The local point symmetry around Ti4+ sites in rutile structure is lowered from Oh to D2h due to the slight distortion of the coordinating oxygen octahedron with two different Ti–O bond lengths, which are 0.1944 nm for 4 O-ligands in (110) plane and 0.1988 nm [18] for the other two O-ligands. Thus, we can expect two equivalent sets of paramagnetic centers for the Co+2 ions in the crystal.. In the measurements, EPR spectra of Co2+ doped rutile TiO2 crystal have been recorded in three mutually perpendicular planes at low temperatures (7–13 K). These are: the first plane (010), the second plane (110), and the third plane (1 1̅ 0). The illustrations of the planes are shown in Fig. 2. The results for each plane are presented in the following sections..
Fig. 6. The angular variation of the EPR spectra of Co2+ ions between 0° and 105° with 15° intervals.
resonance (EPR) technique using Bruker EMX X-band spectrometer (9.8 GHz) at liquid helium (7–13 K) temperatures. Angular dependences of EPR spectra have been recorded with the static magnetic field rotated either in the plane of the plate-like samples (“in-plane” geometry) or in the two perpendicular planes (“out-of-plane” geometry) nearly coinciding with crystallographic planes of a substrate. Thus, there are three rotational planes in total for each sample to obtain the angular dependences of the EPR spectra. The temperature dependence of EPR spectra was studied using a continuous helium gas flow cryostat made by Oxford Instruments. The temperature stability was better than 0.5 K. 3. Results and discussion
3.1. Spectra obtained in the first plane: (010) At room temperature, the rutile TiO2 crystals (see Fig. 1) have the tetragonal space group P42/mnm [16]. The unit cell contains 6 atoms. There are six neighboring oxygen ions around each Ti4+ ion and two Ti4+ ions in the unit cell, whereas each O2− anion is coordinated to three Ti4+ cations. Several data are available in literature for the unit-
Fig. 3 shows the spectra of the peaks belonging to two different centers for Co2+ ions in the first plane when the peaks separated most from each other and are very close to each other, respectively. The marking of the peaks is also indicated. The peaks appearing on the left 147
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Fig. 8. (a–c) The comparison of the experimental gg values of Co2+ ions (black squares and red circles) in rutile TiO2 with theoretical simulation results (black and red lines) obtained from regression analyses in three planes respectively. Black (red) color was used for first (second) center. As seen the centers follow each other with a 90° difference in the first plane but they are parallel in the other planes. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
can be attributed to the first center while those on the right belong to the second center. As expected, 8 hyperfine splitting peaks of Co2+ ions are easily seen. The peak numbers on the peaks indicate nuclear spin states. As easily seen from Fig. 3(b), except for the outermost three peaks of each center (peaks 1, 2 and 3 for the first center, peaks 6, 7 and 8 for the second center), the other peaks have partially overlapped.. The angular variation of the EPR spectra for Co2+ ions are presented in Fig. 4. The presence of two different centers and the angle of 90° between these centers are seen. Also, it is clear that the EPR spectra of Co2+ yield basically two groups of eight peaks. Between these main peaks, secondary peaks with much smaller intensities also occur at many angles since the curve width of these main peaks are rather small. When the angle changes the peaks of these two main groups shift in different directions along the axis of the static magnetic field. Furthermore, the separation between these eight peaks of each group varies with angle. It is noticed that a 90° phase difference occurs between the resonance fields of the groups. Such behavior indicates the presence of two different Co2+ centers which are structurally equivalent but oriented with 90° difference relative to each other..
the nature of the rutile crystal, it was expected that the lines of the centers superimpose for all orientations in this plane. However, as seen in the spectra below, the centers are slightly separated from each other. Taking the measurements at a misaligned plane intersecting at an angle of a few degrees with the exact crystallographic plane is the reason of this separation. As can be seen in Fig. 5(a), the centers almost exactly superimpose to give a set composed of 8 peaks for the orientations at the intersection of these two planes. On the other hand, as in Fig. 5(b), at the angles away from these orientations the third peak of the first center overlaps with the first peak of the second center.. The angular variation of the EPR spectra of Co2+ ions taken at intervals of 5° between 0° and 105°. A subset of these spectra with 15° intervals are given in Fig. 6 for the second plane. It is seen that the centers superimpose in the 105° orientation. In the other angles the presence of two identical centers which move parallel to each other and generally the overlapping of the third peak of the first center with the first peak of the second center are observed. The separation of peaks belonging to different centers is only about 10 G.. 3.3. Spectra obtained in the third plane: (1 1̅ 0)
3.2. Spectra obtained in the second plane: (110) The angular variation of EPR spectra of Co2+ ions observed in the third plane are seen in Fig. 7, where, just as in the second spectrum, we see two different centers which move parallel to each other and overlap in the other angles. The peaks belonging to two centers in many
2+
In this plane, the EPR peaks of Co ions can be clearly observed. The 90° phase difference between the centers in the first plane leads us to consider that the dopant ions substitute for Ti4+ ions. Thus, due to 148
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Fig. 9. (a–c) The comparison of the experimentally obtained A results of Co2+ ions in rutile TiO2 with theoretical ones obtained from regression analyses in three planes. Especially in first plane (Fig. 9a) there is a huge discrepancy between experiment and theoretical simulation.
spectroscopic splitting tensor, S is the spin operator, A is the hyperfine tensor, and I is the nuclear spin operator. This expression can be written in terms of eigen axes:
Table 2 Anisotropic g values and hfs constant A [in 10−4 cm−1] for the rutile TiO2 doped with Co2+.
Expt. [10] Expt. [11] Theo. [12] This study 1. Center 2. Center
gx
gy
gz
Ax
Ay
Az
2.190 (5) 5.885 (1) 6.20 (2)
5.88 (2) 2.079 (1) 2.051 (5)
3.75 (1) 3.735 (5) 4.04 (2)
40
150
26
2.110(6) 5.890(2)
5.890(2) 2.110(6)
3.725(7) 3.725(7)
42.4 152.7
/ = β (gxx Hx Sx + gyy Hy Sy + gzz Hz Sz ) + (Axx Sx Ix + Ayy Sy Iy + Azz Sz Iz )
If the magnetic field is in the z-axis, Eq. (2) becomes rather simple:
/ = βgzz Hz Sz + Axx Sx Ix + Ayy Sy Iy + Azz Sz Iz 152.7 42.4
(2)
(3)
Eq. (2) can be transformed into the form in Eq. (3) using an appropriate axis transformation. Also, if we accept off-diagonal elements to be very small, instead of Eq. (1) the following equation can be obtained:
26.0 26.0
orientations are observed..
/ = βgeff HSz + Aeff Sz Iz 4. Regression analysis of the spectrum
(4)
where geff and Aeff are defined in the following forms:
EPR spectrum can be highly complex depending on the structural properties of the investigated materials. Especially, for the cases where hyperfine structure, fine structure or quadrupole interactions seen together, a detailed description about the structural properties of the sample as well as some advanced statistical methods should be used for a proper analysis. EPR spectrum of the Co2+(3d7) ions can be described by the following general spin Hamiltonian [19], which consists of Zeeman and hyperfine interaction terms
⎡ ggxx ggxy ggxz ⎤ ⎡ nx ⎤ ⎢ ⎥ geff 2 = [nx n y nz ] ⎢ ggyx gg yy gg yz ⎥ ⎢ n y ⎥ ⎢ ⎥ ⎢⎣ ggzx ggzy ggzz ⎥⎦ ⎣ nz ⎦
(5)
⎡ AAxx AAxy AAxz ⎤ ⎡ n ⎤ ⎢ ⎥ x Aeff 2 = [nx n y nz ] ⎢ AAyx AAyy AAyz ⎥ ⎢ n y ⎥ ⎢⎣ AAzx AAzy AAzz ⎥⎦ ⎢⎣ nz ⎥⎦
(6)
→ → →→ → / = βH ⋅→ g ⋅ S + S ⋅A ⋅ I
where nˆ is the unit-vector in the direction of the magnetic field. AA and gg are the squares of the hyperfine interaction and g tensors, respectively.
(1)
where β is the Bohr magneton, H is the magnetic field, g is the 149
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Fig. 10. (a–c) Experimental (blue stars) and theoretical results (black and red lines) of the angular dependence of the resonance fields for two centers of Co2+ ions in all three planes. The theoretical results obtained from exact diagonalization of spin Hamiltonian. Black (red) color was used for first (second) center. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Generally, in order to find g and A tensors in EPR experiments, angular dependence of the resonance fields are carried out in three different planes. In practice, since it provides a great convenience these planes are chosen being perpendicular to each other. In each of these planes the direction of magnetic field can be defined in terms of direction cosines. If the unit vector that is parallel to the magnetic field in each plane is as follows:
⎡ cos θ ⎤ ⎡ cos θ ⎤ ⎡ 0⎤ nˆ1 = ⎢ sin θ ⎥ , nˆ2 = ⎢ 0 ⎥ , nˆ3 = ⎢ cos θ ⎥ ⎢⎣ ⎥ ⎥ ⎢⎣ ⎥ ⎢⎣ 0⎦ sin θ ⎦ sin θ ⎦
taken, to relate these six parameters. When this method is used, the angles must be defined clearly. In addition to this, we must clearly determine the axis of rotation angle, that θ is the angle from which axis, and the direction of rotation. Similarly, we can do a solution for effective A2 values. It is known that in the analysis of the experimental results we aim to find n parameters and want to reduce the effect of random errors. For that, we do experiments as much as possible since it is impossible to do experiment with zero error. Thus, this causes us to get a large number of equations than n. Also, the experimental random errors contribute to make independent linear equations with each other. If we do not make a systematic error, by utilizing the randomness of the experimental errors, we can find the solution of the equations by drawing a graph that minimizes the experimental errors. This can be done by using a very useful statistical method that might be called the least squares method or a regression analysis. Typically, from EPR spectra the eigenvalues and eigenvectors of G and A tensors can be found with regression analysis. The results of regression analyses of Co2+ ion are given in Table 1 for both centers. It is seen that geigenvalues of two centers are real and close to each other, however one of the A-eigenvalues for each center is found as imaginary. Moreover, the eigenvectors of g tensors are parallel to crystal directions, whereas the eigenvectors of A tensors are questionable. The following Figs. 8 and 9 show the comparison of the theoretical results with the experimental results. It is clear in Fig. 8 that there is a quite good fit between theoretical and experimental results. However,
(7)
Then, Eq. (5) can be expressed for each plane as follows: 2 geff = ggxx cos2 θ + ggyy sin2 θ + ggxy cos θ sin θ + ggyx cos θ sin θ 1
2 geff = ggxx cos2 θ + ggzz sin2 θ + ggxz cos θ sin θ + ggzx cos θ sin θ 2
2 geff = ggyy cos2 θ + ggzz sin2 θ + ggyz cos θ sin θ + ggzy cos θ sin θ 3
(8)
Using ggxy = ggyx , ggxz = ggzx , ve ggyz = ggzy , since gg is a symmetric tensor, we obtain 2 geff = ggxx cos2 θ + ggyy sin2 θ + 2ggxy cos θ sin θ 1
2 geff = ggxx cos2 θ + ggzz sin2 θ + 2ggxz cos θ sin θ 2
2 geff = ggyy cos2 θ + ggzz sin2 θ + 2ggyz cos θ sin θ 3
(9)
where gg consists of six independent parameters. In our case there are 52 equations, as the number of angles at which the measurement is 150
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another by 90° difference whereas they move together in the other planes. Thus, it is concluded that impurity ions substitute for Ti4+ ion. The presence of two structurally equivalent paramagnetic centers for Co2+ ions has been observed since the same spin Hamiltonian parameters were obtained. The decomposition of the two different paramagnetic centers in the second (110) and third (1 1̅ 0 ) planes has been shown as a result of a small shift (~2°) of the rotation axis. Since the results show high anisotropy, we can say that oxygen vacancies in the structure of the samples do not occur randomly and only the oxygens in a given direction disappear.
in Fig. 9 it is seen a serious mismatch between the experimental and theoretical results in the first plane. This is because the second order perturbation theory approach is inadequate for Co atom showing very large amounts of anisotropy... 5. Exact diagonalization (ED) analysis of Co2+ spectra Exact diagonalization (ED) analysis is a powerful tool for calculating the spin-Hamiltonian parameters for 3dn ions in crystals. Since the ED method uses the contributions from all excited states, it can provide more accurate results for spin-Hamiltonian parameters [20]. The two Co2+ centers in rutile TiO2 crystal have been analyzed using ED method. The results are presented in Table 2 for both Co2+ centers. These results indicate that two centers follow one another by 90° of difference in the first plane and overlap in the other planes. The small amount of decomposition observed in the experimental spectrum is caused by small errors made in the plane of rotation. If we do not take into account these misalignments, we can’t fit the spectra of two centers with the same set of parameters. Since these misalignments are nonintentional, there was no measurements for them. However they must be small and the correct angle of misalignment should make the experimental errors smaller. Therefore, we wrote a MATLAB code for minimizing the experimental errors against the misalignments. The simulated misalignments that minimize the errors are 0 in the first plane and 2 ± 0.5 in the second and third plane. In this way, as seen from Table 2, two paramagnetic centers were fitted with the same set of values. Another point worthy of attention is the large anisotropy in the orthorhombic symmetry of Co2+ ions. The theoretical resonance fields obtained for each plane is seen in the following Fig. 10 with the experimental resonance fields. The results in Table 2 indicates that very comparable results we obtained here at low temperature for the all Spin Hamiltonian parameters to those at room temperature. The theoretical analyses of only g-factors was carried out in [12] using the secondorder perturbation formulas on the basis of the cluster approach for these Co2+ centers in rutile TiO2 and local structure parameters were predicted considering an orthorhombic local site symmetry around these Co2+ centers, which results in a rhombic distortion on the replaced Ti4+ sites with the following structural parameters R∥=0.19800 nm, R⊥ 0.19485 nm, and θ ≈ 81.21°..
Acknowledgments The authors MA and SK acknowledge support from the Scientific and Technical Research Council of Turkey (TUBITAK) through the Project no. 115F472. References [1] [2] [3] [4] [5] [6]
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6. Conclusion EPR spectra of Co2+ ions doped into rutile TiO2 by ion implantation technique have been investigated at low temperatures (7–13 K). It is seen that G and A tensors of both ions have the same eigen-axes, which coincide with crystal axes. Also, the centers in the first plane follow one
[20]
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