Investigation of the local environment of SnO 2 in an applied magnetic field

C T This paper presents the results of time-differential perturbed gamma – gamma angular correlation measurements of SnO 2 thin films carried out in an applied magnetic field. The measurements were performed upon the implantation of Fe at 80 keV and 111 In ( 111 Cd) at 160 keV. The samples were further characterized by energy- dispersive X-ray spectroscopy. The hyperfine parameters were studied at room temperature with and without an applied magnetic field. The results indicate the presence of two distinct local environments for the probe nuclei. Both occupy a paramagnetic state and correspond to a substitutional Sn site in the rutile phase of SnO 2 with different numbers of electrons added to SnO 2 :Cd 0 . In addition, the crystal homogeneity of the site 1 in- creases upon applying the


Introduction
Tin dioxide (SnO 2 ) is a wide-bandgap n-type semiconductor that has excellent optical transparency and native oxygen vacancies; it also features a high carrier density and high thermal stability. SnO 2 is used in numerous applications including dye-sensitized solar cells and gas sensors [1][2][3]. Some time ago, it was shown that SnO 2 can exhibit room-temperature ferromagnetism depending on the doping and consequently on the inner structure [4][5][6]. However, despite numerous studies, no sound explanation for this phenomenon has been found. In fact, it was later acknowledged that transition-metal doping reduces the magnetic moment, and the increase in magnetic ordering is tied to both oxygen vacancies and the confinement of defects [7]. No ferromagnetism is detected in similar systems such as TiO 2 , ZnO [8,9], and SnO 2 [10] in which hyperfine methods were used to implant a small quantity of probe material. Conversely, even with a negligible dopant concentration, online emission M€ ossbauer spectroscopy results in a plethora of defects due to online implantation measurements, making interpretation difficult. Thus, we present the results of time-differential perturbed gamma-gamma angular correlation (TDPAC) studies of SnO 2 in an applied magnetic field. This technique requires a smaller concentration of dopants and consequent annealing upon implantation may fully recover the structure.
The hyperfine properties of SnO 2 have been well studied, and various methods have been applied to probe the local environment. Generally, Sn conversion-electron M€ ossbauer spectroscopy applied to SnO 2 samples shows that Sn ions tend to occupy 2þ and 4þ states [11]. 57 Fe M€ ossbauer online studies show that SnO 2 features two charge states, Fe 3þ and Fe 2þ ; the former exhibits spin-lattice relaxation, and the latter is attributed to recoil-caused interstitials [10]. TDPAC studies are the most profound and can include several isotopes of interest along with several types of samples, dopants, and annealing conditions. Upon implanting 111 In-(Cd) and annealing at 1023 K, Renteria et al. discovered that implantation at 400 keV resulted in two phases, (2)] and SnO, which were later transformed into a single phase of SnO 2 [11]. Although the hyperfine parameters coincided with previous reports [12,13], there was no dynamic interaction.
Ramos et al. studied hyperfine interactions by implanting 111 In-(Cd) into SnO 2 thin films at 160 keV and investigating the system over a broad temperature range (up to 923 K). The results revealed two fractions; the substitutional site was characterized by ω Q ~16.7 Mrad/s and η ~0.1 [14]. Recently, Darriba et al. [15] reported the combined dynamic and static quadrupole interactions (the so-called on-off model) complemented by ab initio calculations. The combined interactions were induced by an increase in the hole concentration as the temperature decreased, which was attributed to a shortage of electrons caused by the reduced thermal ionization of defects. The ω Q and η values for the local environment 1 were ~17 Mrad/s and ~0.2, respectively, while those of second fraction were ~22.5 Mrad/s and ~0.5, respectively [15]. Only above 650 K and 923 K, respectively, these interactions become purely static. Table 1 lists most of the parameters from previous works involving TDPAC with In as a probe isotope.
Applying a magnetic field can be advantageous because it increases sample homogeneity during sample preparation. For instance, during the fabrication of homogenized SnO 2 nanowires, a temperature gradient was found to be very important, especially under an applied magnetic field [17]. Moreover, such magnetically enhanced nanowires are more responsive to gaseous sulfur compounds [17]. The study of local phenomenology is useful to better understand the atomistic effects of external magnetic fields. Therefore, in this study, we used TDPAC to investigate the local effects of an applied magnetic field on SnO 2 samples.

Time-differential perturbed gamma-gamma angular correlation method
Due to the suitable nuclear properties (i.e., spin 5/2) and relatively long half-life of the parent 111 In nuclei, the evolution of the local environment can be followed with high sensitivity by measuring the perturbation function RðtÞ � A 22 G 22 ðtÞ, where is the perturbation factor, with ω n being the transition frequencies between two M states. The mentioned perturbation factor is valid for nuclear spin I ¼ 5/2 of the intermediate state of the daughter 111 Cd probe nuclei. Moreover, if probe atoms are exposed to j different lattice environments (sites), and each of them creates a characteristic field gradient at a fraction f of the probe-atom sites, the perturbation function becomes ðtÞ. The observable ω n frequencies are given by ω n ¼ 6ω Q C n ðηÞ. The coefficient C n can be numerically calculated for a known η [18]. Additionally, the coefficients s n denote the amplitudes of the transition frequencies ω n and are summations of the Wigner 3j symbol products that run over the allowed magnetic-field-split hyperfine states. Besides, the axial asymmetry of the electric field gradient tensor or deviations from it are described using the asymmetry parameter η ¼ ðV xx V yy Þ=V zz . The primary component V ZZ of the electric field gradient tensor can be obtained from the nuclear quadrupole frequency ω Q as follows: ; (2) where Q is the nuclear quadrupole moment. Furthermore, the lowest transition frequency ω 0 is the hyperfine parameter considered in this work and describes the experimental nuclear quadrupole interactions. Additional details about the TDPAC technique can be found in Refs. [19,20].
In the presence of a magnetic field, the TDPAC technique is also suitable for measuring magnetic contributions to the hyperfine fields, and the perturbation function is given by [21].
Pure-magnetic-dipole interactions have frequencies ω 1 ¼ ω L and where μ N is the nuclear magneton, and I ¼ 5 The coefficient f is the amplitude of the modulation, which is related to the fraction of TDPAC probes occupying an environment that produces a nonzero B HF , and A 22 is the anisotropy coefficient of the γ-γ cascade. The argument of the exponential term contains Δω L , which reflects a distribution about the modulation frequencies caused by slight perturbations of the probe atom. For the experiments in this study, we assume a Lorentzian frequency distribution.
In the presence of both magnetic and electric hyperfine interactions, the analysis of the combined interaction in the TDPAC spectra is very complex. Its formalism is given by [22,23].
where a k1k2 nN is a weighting factor, and τ is the lifetime of the intermediate state (τ ¼ 84:5 ns for I ¼ 5/2). In particular, the perturbation function (4) cannot be solved analytically and must be computed numerically.
Furthermore, the angular correlation function depends strongly on η, β (the orientation of the magnetic field direction with V zz ), y ¼ ωL ωQ (the ratio of the Larmor frequency to the quadrupole interaction), and α (a second Euler angle), as shown by Alder et al. [22]. In this study, the TDPAC technique was used to measure the hyperfine parameters in SnO 2 thin films with and without an applied magnetic field.

Experiment
Thin films with thicknesses of ~100 nm were deposited on Si(100) substrates by magnetic sputtering. The 111 In probe nuclei were ionimplanted with an energy of 160 keV after the implantation of 1% Fe at 80 keV. The implantations were performed at the Bonn Isotope Separator (BONIS) ion implanter [24,25], as described in Ref. [26]. Ion implantation was followed by heating to 873 K in air for 10 min. Approximate full-cascade SRIM calculations [27] indicated an ion range of ~40 nm (38 and 42 nm for Fe and In ions, respectively) and approximately 18 nm of straggle (see Fig. 1a). Fig. 1b Thin films Implanted In [11] 16.7 0.1 Thin films Implanted In [14] The hyperfine parameters were measured at room temperature (RT). The measurements were taken with and without an applied magnetic field of 2.1 T [28]. Fig. 2 shows a schematic diagram of the magnet apparatus, which had a radius of 5 cm and lead housing. The two permanent magnets were separated by 2.4 mm and produced in this space a 2.1-T magnetic field. To reduce gamma-ray absorption and scattering, the cylindrical pot had 12 radial windows. The samples were positioned inside the pot facing down toward the detector plane.
Energy-dispersive X-ray spectroscopy (EDS) was performed on the SnO 2 thin films after the TDPAC experiments. The EDS measurements were conducted at 20 kV. Fig. 3 shows the RT perturbed angular correlation spectra of the thin films after maintaining the films in air at 873 K for 10 min (thermal treatment in air). The upper spectrum belongs to a sample with no field, while the bottom spectrum was obtained from a sample in an applied magnetic field of 2.1 T. The blue lines are fits that give the hyperfine parameters, which are presented in Table 2.

Results and discussion
Observable changes in spectra measured with the sample in an applied magnetic field of 2.1 T are mainly due to the applied magnetic field, which gives rise to a Larmor frequency of ω L ¼ 32 Mrad/s. However, the hyperfine parameters show no evidence of magnetic interactions for the pure sample beyond those from the 2.1-T magnetic field.
The results show that the magnetic field affects site 1 more than site 2. Comparison with previous studies [14,29,30] carried out after thermal treatment in vacuum or under a nitrogen atmosphere shows that using 111 In as probe nuclei when annealing at 873 K in air is not sufficient to remove all defects caused by the implantation process. This means that a considerable amount of oxygen vacancies were created; therefore, we cannot disregard the influence of these vacancies on paramagnetism, which arises from interactions between the defects and the applied magnetic field. Moreover, the oxygen vacancies lead to high charge-hole mobility, which is important for applications. Since the presence of the 111 In 3þ probe results in a charge imbalance, it is possible that oxygen vacancies and In are near-neighbors [12].
Due to the type of magnet-pot housing used in these experiments and its size, samples with relatively high activity were required to obtain sufficient statistics. Note that increasing the implantation dose creates more defects; the process can damage the upper layers down to 40 nm and produce interstitials and vacancies. Additionally, the metal present in the housing causes significant gamma-ray scattering, which reduces the gamma anisotropy.
The TDPAC results indicate the presence of two sites for the probe nuclei. The substitutional Sn site in the well-known rutile phase of SnO 2 presents two different local environments, referred to as site 1 and site 2. Upon applying a magnetic field, paramagnetic hyperfine interactions were detected at both sites.
The dominant local environment, site 2, has an electric field gradient of 5.75 � 10 21 V/m 2 for Q ¼ 0.641(25) [31]     respectively, obtained by Darriba et al. [15] from powder samples in a neutral cell (SnO 2 :Cd 0 ) using the Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA). This local environment can be assigned to the metastable state of Cd 0 at a substitutional Sn site in SnO 2 . The SnO 2 :Cd 0 notation is used when a (neutral) Cd atom replaces a (neutral) Sn one in SnO 2 oxide, i. e., none electron is added to the system to compensate the smaller valence of impurity (Cd 2þ ) atom when substituting the host atom (Sn 4þ ). The value we chose for the nuclear quadrupole moment of the 245-keV 5/2 þ level of the 111 Cd probe, Q ¼ 0.765(15) b [32], is close to that reported by Errico et al. [33], Moreover, with a nonzero applied magnetic field, the nuclear quadrupole interaction frequency of site 2 increases strongly from 14(1) to 26(3) Mrad/s. This value is similar to that obtained for thin films at room temperature [28.8(1) Mrad/s] [16]. The magnetic field affects the metastable state of Cd 0 . Considering Q ¼ 0.765(15) b, our electric field of 9 � 10 21 V/m 2 is too strong and cannot be compared to any simulated values from the work of Darriba et al. [15].
Conversely, with no applied magnetic field, the electric field gradient at the site 1 is 6.5 � 10 21 V/m 2 for Q ¼ 0.765(15) b [32], and the asymmetry parameter is 0.32 (3). These results are comparable to simulation results based on the local density approximation for a charged impurity state with 1.8-2.0 electrons added to SnO 2 :Cd 0 [15]. By applying a magnetic field, the electric field gradient for Q ¼ 0.765 (15) b [32] is 5.85 � 10 21 V/m 2 . These results are consistent with the PBE-GGA result of 5.75 � 10 21 V/m 2 with an asymmetry parameter of 0.19 [15] for SnO 2 :Cd 2 with two electrons added to the system. We therefore associate this local environment with Cd at substitutional Sn sites with 1.8-2.0 electrons added to SnO 2 :Cd 0 . The curious point is that the applied magnetic field has somehow increased the number of electrons in the local environment.
Interestingly, the results indicate that upon applying the magnetic field, the width of the nuclear quadrupole interaction frequency decreases at both sites. This frequency distribution is a crucial parameter for measuring the homogeneity of the crystal; thus, this result indicates that the local environment is more homogeneous in an applied magnetic field than in its absence. A similar effect was detected in AlN using the TDPAC technique [34]. Note that a magnetic field affects structural defects even in their pre-existing metastable states [35].
Crystal lattice imperfections mainly affect the electric field gradient tensor [36] by distributing its tensor components around the values of a perfect crystal lattice [36]. The asymmetry parameter of site 1 decreases significantly from 0.32(3) to 0.17(3) upon applying a magnetic field, which is a second indication that the applied magnetic field improves the crystal homogeneity. However, the increase in the asymmetry parameter of site 2 from 0.37(1) to 0.45(2) cannot be easily explained. This increase means that the local point symmetry of this particular site is disturbed by the applied magnetic field. If this site is associated with oxygen vacancies, it may be possible that the interaction between the applied magnetic field and the vacancies promotes an imbalance near the probe nuclei, thereby increasing the asymmetry [37].
The application of an external magnetic field reveals the paramagnetic nature of SnO 2 , which is consistent with the results of all previous TDPAC experiments, including recent results obtained for thin films using 117 In and 111 Cd as probe nuclei [38]. Garcia et al. [39] argued that the observed ferromagnetism, which has quite frequently been reported in the literature, is due to sources other than intrinsic ferromagnetism. Ferromagnetism in semiconductor oxides remains debatable because the essential issues of uniformity and reproducibility have yet to be unraveled [40]. Fig. 4 presents the EDS spectrum, which show the signals of tin, iron, and oxygen from the sample, a pronounced peak of silicon from the substrate, and a signal corresponding to a small concentration of Cu impurity, which was contributed by the target holder during thin film deposition. The samples were coated with platinum before EDS analysis to improve conductivity. The target holder used during sputtering was composed of cupper; however, an electrostatic shield in the target was used to reduce the plasma and consequent sputtering of the target. Nevertheless, Cu contamination occurs under certain process conditions, as confirmed by EDS analysis in this study. We understand that Cu contamination, even at very low quantities, may affect the hyperfine parameters. Therefore, new experiments without Cu contamination will be performed for comparison with the results of this work. Moreover, additional experiments with 111m Cd are required to better understand how electron capture nuclear transmutation affects the 111 In probe in the samples, and if this effect can be observed under an applied external magnetic field. In this case, the measurements are subject to the electron conversion process of the 111m Cd probe. The influence of Fe and Cu in possible charge recombination process can be further investigated by comparing the results obtained with 111m Cd and 111 In probes. Future research along these lines was proposed at ISOLDE-CERN [41] within the solid-state physics program [42,43] as experiment LOI144 [44]. After these investigations, we intend to simultaneously implant 111 In and 111m Cd [45] for comparison.
The abovementioned TDPAC experiments should be complemented with self-diffusion experiments [46]. The diffusion of Cd into SnO 2 thin films strongly depends on the conditions of the heat treatment. Napo et al. deposited SnO 2 thin films with a thin Cd layer and annealed them Table 2 Hyperfine parameters obtained from measurements made using 111 In as probe nuclei. The frequencies ω Q and ω L are given in Mrad/s. The inset shows a zoomed-in view of the interval from 6.5 to 10 keV for a better view of the Cu peak.
at 850 K for 30 min under argon flow [47]. Depth profiles obtained using X-ray photoelectron spectroscopy show that Cd diffuses along the grain boundaries. Due to the improvement of the grain boundary quality, the conductivity could be increased by approximately a factor of two. After annealing at the same temperature for the same duration but under air instead of Ar, CdO was formed at the surface, prohibiting the diffusion of Cd into the SnO 2 layer. In-diffusion was investigated by Ray et al. to obtain SnO 2 /ITO bilayer films with good electrical and optical properties for the transparent electrodes of amorphous silicon solar cells [48]. In this work, the diffusion of indium through the SnO 2 layer into the p and i layers was observed by secondary-ion mass spectroscopy. The thickness of the SnO 2 layer was increased, allowing the deposition of the p layer at temperatures up to 180 � C without enhancing indium diffusion. To our knowledge, no previous studies have investigated Fe diffusion in SnO 2 .
In undoped SnO 2 the electrical conductivity depends on electrons resulting of a stoichiometry deviation in the material composition. As mentioned above, under atomistical view, these deviations are caused by lattice defects (vacancies or interstitials) [49,50]. Here, the vacancies correspond to oxygen and the interstitials to tin. In single-crystalline material, a resistivity dependency of 1/6 power was observed for double ionized oxygen vacancies [50]. Advani et al. investigated the diffusion kinetics of the oxygen vacancies by introducing a controlled amount of oxygen in SnO 2 thin-films annealed under a high-vacuum at 200 � C for 360 h [51]. During the heat treatment under vacuum, a large amount of oxygen vacancies are incorporated in relaxing to the equilibrium conductivity value. Introducing subsequently oxygen into the thin-film a net-motion of the vacancies from the bulk to the surface was caused (diffusion of Oxygen into the bulk). Therefore, the resistance increased following a squareroot of time behaviour and a diffusion coefficient of D O ¼ 1.4 � 10 17 m 2 s 1 was obtained [51].

Conclusions
Measurements of SnO 2 thin films in an applied magnetic field suggest the presence of two different local environments with distinct paramagnetic hyperfine interactions at room temperature. The effect of the applied magnetic field on the film reveals the paramagnetic nature of SnO 2 thin film and increases crystal homogeinity of site 1. Implantationinduced defects cause small changes in the hyperfine parameters of the second site, which has a slightly lower Larmor frequency. Both local environments can be associated with Cd at substitutional Sn sites with 1.8-2.0 electrons added to SnO 2 :Cd 0 . In future work, we intend to measure the samples after different thermal treatments to better understand how an applied magnetic field affects the crystal lattice defects. Measurements using 111m Cd as a probe are also foreseen.

Author contributions
J. Schell wrote the manuscript with contributions from T. T. Dang, D. V. Zyabkin and D. Gaertner. R. Mansano was responsible for sample preparation. A. W. Carbonari supervised the work and contributed to the writing of the manuscript.

Declaration of competing interest
The authors declare no conflict of interest.