Using time-differential perturbed angular correlation of γ rays, we investigated the electric-field gradient of polycrystalline EuTiO3 and Eu2Ti2O7, with 181Hf(181Ta) as a probe, following different thermal treatments. The measurements were performed at ISOLDE-CERN following 80 keV implantation at the Bonn Radioisotope Separator. The experimental results indicated successful induction of different phases in the implantation recovery process at 1273 and 1373 K. These observations were combined with ab initio calculations and X-ray diffraction measurements. A comparison of ab initio calculated electric-field gradients with the measured values discriminates between different structures and defects and rules out many possible cases. The Ta probe at the Ti site in the Eu2Ti2O7 phase is found to be the most probable case of site occupation after annealing at 1373 K, while annealing at 1273 K keeps EuTiO3 in the vicinity of the Ta probe. A discussion of the hyperfine interactions that promote variation in the interaction strength at the 181Ta site is presented.

The time-differential perturbed angular correlation (TDPAC) technique1 has been recognized as an efficient local characterization technique in condensed matter research. In particular, TDPAC has been applied in investigations of hyperfine fields in perovskite-type titanates since the beginning of the 1970s,2 allowing scientists to obtain remarkable results. For instance, the technique has been used to characterize phase transitions in ceramic samples of PbTiO3 and BaTiO3 by measuring the temperature dependence of the Ti-site electric-field gradients (EFGs) at temperatures very close to the ferroelectric-to-paraelectric transition temperature, Tc. The samples were doped with small amounts of Hf that emitted radiation from the 181Hf(181Ta) probe. The results showed that high-frequency nuclear quadrupole interactions decreased as the temperature approached Tc, clearly reflecting tetragonal-to-cubic transitions in both materials.3 In addition, the polarization dependence of EFGs at different sites in PbTiO3, BaTiO3, and other oxides has been revealed by one ab initio study4 and Landau theory for the relation between electric field and electric polarization,5 which strongly support the usefulness of the TDPAC method.

In addition to the TDPAC method, the Mössbauer technique has also been used in the analysis of hyperfine parameters at Eu sites in EuTiO3. The phase purity in bulk EuTiO3 was investigated using 151Eu-Mössbauer spectroscopy, between 90 K and 325 K. The extracted isomer shift for the major component was −12.45 mm/s, an isomer shift indicative of Eu2+; thus, the sample contained purely divalent Eu.6 In thin EuTiO3 films, a similar result was found.7 The isomer shift has also been around −13 mm/s in other works.8–10 The area ratio of the Eu2+ absorption relative to the total absorption, AEu2+/AEu, was found to be 0.97, and the full width at half maximum of one component of the Lorentzian multiples was 2.92(4) mm/s.8 EuTiO3 is magnetically ordered below 5.5 K and shows a magnetic spectrum at 2.2 and 4.2 K. The extrapolated hyperfine field at 0 K is 325 ± 7 kOe. Oxygen-deficient perovskites, EuTiOx, with x between 2.68 and 3, showed Mössbauer parameters that were identical to those of EuTiO3. No indication of quadrupole splitting was noted.9 Mössbauer spectroscopy is very useful because it easily distinguishes between the valence states through their different isomer shifts. The relatively small linewidth of the europium-151 Mössbauer transition facilitates the observation of two hyperfine interactions, the isomer shift, and the magnetic hyperfine field. Observation of the third hyperfine interaction and the quadrupole interaction is more difficult.

Perovskite-type-titanate materials exhibit a rich variety of unusual and interesting ferroelectric, magnetic, and structural properties, and europium titanate (Eu0.5Ba0.5TiO3) presents the specific functionalities required for a solid-state-based search for the permanent electric dipole moment of the electron.11 For pure europium titanate, the dielectric permittivity exhibits an unusually sharp decrease at the Néel temperature, TN = 5.5 K, below which a G-type antiferromagnetic phase develops.12 A high sensitivity of the permittivity to the magnetic order or to the magnetic field12 is the signature of an extremely strong spin–phonon coupling in EuTiO3, which allows ferroelectric and ferromagnetic phase transitions to be induced using epitaxial strain.13 Magnetoelectric coupling is exceptionally high in the antiferromagnetic phase, although the crystal symmetry of EuTiO3 forbids linear coupling, and only biquadratic magnetoelectric coupling has been observed.14 Above room temperature (RT), EuTiO3 crystallizes in the cubic Pm3¯m perovskite structure, but near 282 K, it undergoes an antiferrodistortive structural phase transition to the tetragonal I4/mcm phase.15–17 Defects such as oxygen vacancies and Eu3+ ions strongly influence the temperature of the phase transition from a cubic to a tetragonal structure.16 

Pyrochlore-phase Eu2Ti2O7 presents the Eu3+ configuration (EuTiO3 contains Eu2+), which is attractive due to its strong spin-orbit coupling and appreciable magnetic susceptibility;18 it is an n-type semiconductor with an energy bandgap of approximately 2.5 eV and can form in a nanocrystalline form in which case it possesses two inequivalent positions for the Eu3+ ions (core and surface).19 Additionally, titanium pentoxide (Ti3O5) is a functional material that has attracted much attention from researchers, finding use in several applications.20 

The potential applications of perovskite EuTiO3 and pyrochlore Eu2Ti2O7 motivated this paper in which we report the first TDPAC experiments on these compounds, supported by X-ray diffraction (XRD) and ab initio calculations.

The variety of unusual and interesting ferroelectric, magnetic, and structural properties in europium titanates requires such local characterization for a deeper understanding of the Eu3+/Eu2+ influence in applications.

Bulk polycrystalline ceramic samples were prepared from a mixture of Eu2O3 (68.778 wt. %) and TiO2 (anatase, 31.222 wt. %) powders, which were homogenized in a planetary ball mill for 30 min (ZrO2 milling balls and bowls). Disk-shaped green bodies (diameter 15 mm, thickness 5 mm) were formed by uniaxial pressing (40 MPa) followed by cold isostatic pressing (300 MPa). The samples were sintered in a pure (99.9%) hydrogen atmosphere with a gas flow of 5 l/min (pressure ∼1.05 bars); the sintering temperature was 1673 K, with a 2-h dwell time (the heating and cooling rates were 10 K/min). The resulting EuTiO3 ceramics contained no secondary phases prior to further annealing. More details of the samples’ processing are described elsewhere.21 

HfO2, with natural isotopic composition, was irradiated for 6 days by a thermal neutron flux of 1015 n cm−2 s−1 in the high-flux reactor of the Institut Laue-Langevin (ILL) in Grenoble, in order to produce 181Hf via the 180Hf(n, γ) reaction. The nuclear probe 181Hf was implanted in the samples at 80 keV at the Bonn Radioisotope Separator (BONIS).22,23

Following implantation, radiation damage was annealed in a vacuum in two steps: first, at 1273 K for 5 h and then at 1373 K for 5 h. TDPAC measurements were carried out at ISOLDE-CERN24,25 using conventional and digital setups.26,27 Theoretical perturbation functions were fitted to the spectra using Nightmare software28 to extract hyperfine parameters.

TDPAC measurements were performed at 10 and 295 K in order to investigate the static electric quadrupole interactions of 181Hf(181Ta) in EuTiO3 and Eu2Ti2O7. To the best of our knowledge, no TDPAC measurements had been done before in either system.

Following the TDPAC experiments, the samples were measured in Bragg-Brentano geometry on a PANalytical X’Pert PRO diffractometer equipped with a Co tube (λ = 0.178 901 nm).

The TDPAC technique is a powerful tool for studying hyperfine fields in solids, one of its advantages being the possibility of obtaining information on lattice defects and charge fluctuations. The charge distribution at the 181Hf(181Ta) lattice site induces an EFG. Due to suitable nuclear properties and the relatively long half-life of the probe, it is possible to follow the evolution of phase transitions as a function of temperature, with high sensitivity. The TDPAC technique measures the perturbation function R(t) ≈ A22G22(t) for different perturbation factors G22(t).29,30 Considering spin I = 5/2 and static electric quadrupole perturbations in the polycrystals, the theoretical expression (1) is valid for a nonaxially symmetric EFG,

G22t=s0+n=13snηcosωnηt.
(1)

The quantity t is the time spent in the intermediate state of gamma quantum emission. The transition frequencies, ωn, are given by ωn=EMEM/=3M2M2ωQ.29 The coefficients, sn, denote the amplitudes, which can be determined by diagonalization of the interaction Hamiltonian, as well as the transition frequencies.31,32 Since the EFG is represented by a symmetrical and traceless (3 × 3) tensor, it can be fully characterized by the magnitude Vzz and the asymmetry parameter η = (VxxVyy)/Vzz; η varies from 0 to 1, where 1 is for maximal asymmetry. The transition frequencies are functions of the nuclear quadrupole frequency, which is defined by

ωQ=eQVzz4I(2I1),
(2)

where Q is the nuclear quadrupole moment and I = 5/2. The fundamental observed frequency, ω0, is the main hyperfine parameter considered in this work for reporting the experimental nuclear quadrupole interaction. The parameter δ accounts for the normal distribution of relative width around ω0.

If there are probe atoms exposed to j different lattice environments, and each of them creates a characteristic EFG at fraction f of the probe atom sites the perturbation function becomes Rt=A22jfjG22jt. In our case, a two-site model for data analysis was considered.

The hyperfine interactions between the EFGs and nuclear quadrupole moment, Q, of the probe nuclei can be either dynamic or static. Dynamic interactions occur because of time-dependent oscillations in the anisotropic γ emission, which are caused by the random fluctuations of hyperfine fields with a short correlation time, τ. Such interactions have been observed in measurements performed with 111In33,34 or 181Hf35 and are particular to EFG changes in magnitude or orientation, resulting from a dynamic spin-relaxation during the lifetime of the intermediate state; the interactions have been quantified by the transition rate between two states.36 An increase in this rate results in increasing exponential damping of the modulation amplitudes in the time spectrum. In contrast with the static case, an increase causes identical line broadening or damping for different ωn frequencies in the Fourier transform,37 and the R(t) spectrum can also be damped to 0. However, in the limit of very high transition rates, nuclear spin does not occur. Furthermore, the strength and orientation of the EFG are constant in time for static interactions.

For our data analysis, static quadrupole interactions were considered. Attenuation of the oscillation amplitudes for static interactions can be caused by randomly distributed defects around the probe. Damping of the frequency oscillations in time can be approximated by the Lorentzian or Gaussian distribution38 of frequencies around a central value of ω0. The full width at half maximum is FWHM/2 = δω0/100, with δ in percent or FWHM=δω08 ln 2 for the Lorentzian and Gaussian distributions, respectively.39 The experimental perturbation factor can be found in Ref. 40. Additional details about the TDPAC technique can be found in Refs. 30 and 31.

We used the density functional theory PAW method41 as implemented in the VASP code,42 with the PBE functional,43 to calculate the EFG of Ta at different lattice sites. We also used GGA + U, U = 5.7, and J = 1 eV for the Eu f electrons, following the work of previous researchers44,45 who employed the approach of Dudarev et al.46 The atomic forces that appeared were minimized to values lower than 5–20 meV/Å (20 in some supercells). We used an energy cutoff of 520 eV (400 eV was used in some large supercells, which was sufficient for converged results according to several test calculations). Ferromagnetic ordering was considered [a few calculations with G-type antiferromagnetic (G-AFM) ordering showed very small differences in the EFG].

Following the first thermal treatment, the Ta atoms are probably bound to random defects and interact with a very weak EFG, as can be observed in the spectra displayed in Fig. 1 (left), measured at 10 K and RT. As expected, randomly distributed defects around the probe did not lead to the measurement of a sharp frequency but rather to a distribution of frequencies.

FIG. 1.

Experimental R(t) functions measured at 10 K and RT after annealing at 1273 K (left) and 1373 K (right) using 181Hf(181Ta). The least-squares fits of the hyperfine parameters are represented by pink and blue solid curves.

FIG. 1.

Experimental R(t) functions measured at 10 K and RT after annealing at 1273 K (left) and 1373 K (right) using 181Hf(181Ta). The least-squares fits of the hyperfine parameters are represented by pink and blue solid curves.

Close modal

In order to fit the data shown in Fig. 1, we assumed a Lorentzian shape distribution for the EFG. For the EuTiO3 phase, the very weak EFG distribution resulted from the cubic-symmetry deviation of the electric-charge distribution around Ta. For the measurements following annealing at 1273 K, we assumed a nuclear quadrupole interaction characterized by a distribution of frequencies with ω0 = 1 Mrad/s and FWHM = 1.27(1)% at RT or FWHM = 6.82(3)4% for 10 K.

The XRD results are shown in Fig. 2. The diffraction patterns were processed by Rietveld refinement47 in the program TOPAS.48 The XRD measurements performed on the sample annealed at 1273 K related to approximately 70% (wt. %) of the EuTiO3 phase, with a lattice parameter a = 3.910 Å. A secondary phase, Ti3O5, precipitated in the sample structure, probably as a consequence of annealing in vacuum, where the oxygen partial pressure was not controlled. Around 30% of the Ti3O5 presented lattice parameters of a = 9.98 Å, b = 5.08 Å, c = 7.16 Å, and β = 109.91. It is important to emphasize that the Ti3O5 phase was not observed in the TDPAC experiments.

FIG. 2.

X-ray diffractogram of the samples performed following annealing at 1373 K (top) and 1273 K (bottom). For better visualization, the main peaks of the phases have been designated A, B, and C.

FIG. 2.

X-ray diffractogram of the samples performed following annealing at 1373 K (top) and 1273 K (bottom). For better visualization, the main peaks of the phases have been designated A, B, and C.

Close modal

For the samples annealed at 1373 K, the XRD measurements showed approximately 72% (wt. %) of the EuTiO3 phase with a lattice parameter a = 3.905 Å and around 28% of Eu2Ti2O7 with a = 10.212 Å. The lattice parameters of EuTiO3 were relatively high, being evidence of point defects.49 

Evidence for vacancy trapping associated with a change in the Eu charge-state (from 2+ to 3+) was found following annealing at 1373 K, as shown in Fig. 1 (right); a static Vzz of approximately 22 × 1021 V/m2 with η = 0 and a well-defined quadrupole frequency at 10 K and RT could be observed for site (local environment) 1. This static interaction arises from a specific Eu charge state and defect configuration to which the Ta probe attaches.

Europium is the most volatile metal of the lanthanide series. During all high-temperature treatments of the EuTiO3 samples (and mainly in a vacuum because of low partial pressures), small amounts of Eu were evaporated, disrupting the stoichiometry of the perovskite structure (Eu1−xTiO3−y) to a small degree. This metastable composition began to decompose during annealing in the vacuum.

Table I gives the corresponding experimental hyperfine parameters for the experiments following annealing at 1373 K with Gaussian distributions. The observed quadrupole interaction frequency for site 1 decreased with increasing temperature. This behavior can be assigned to the general increase in the bond lengths resulting from thermal expansion of the crystal lattice, thereby reducing the nuclear quadrupole interaction. To obtain the experimental Vzz value, the Q = 2.28(2) b value50,51 was considered, leading to a Vzz error of approximately 10%. In addition to the high Q value, the probe 181Hf has several properties, which make it a very convenient isotope for TDPAC experiments. It has a long half-life of 42.4 days, and it decays over β to an excited state of Ta.51 The TDPAC measurement is performed using the 133–482 keV cascade with the intermediate I = 5/2 state, which has a half-life of 10.6 ns and +3.29(3) μN.51 

TABLE I.

Experimental hyperfine parameters for the different measuring temperatures following annealing at 1373 K.

T (K)Vzz (1021 V/m2)ηδ (%)Fraction (%)Fixed ω0 (Mrad/s)ηFWHM (%)Fraction (%)
10 22.4 0.12 (1) 6.7 (2) 75.0 (5) 6.82 (3) 25.0 (3) 
295 21.5 0.07 (1) 7.2 (5) 77.2 (6) 1.27 (1) 22.8 (2) 
 Site 1 Site 2 
T (K)Vzz (1021 V/m2)ηδ (%)Fraction (%)Fixed ω0 (Mrad/s)ηFWHM (%)Fraction (%)
10 22.4 0.12 (1) 6.7 (2) 75.0 (5) 6.82 (3) 25.0 (3) 
295 21.5 0.07 (1) 7.2 (5) 77.2 (6) 1.27 (1) 22.8 (2) 
 Site 1 Site 2 

The EFG distribution FWHM and fraction for site 2 decreased with increasing measurement temperature. In order to correlate the extracted hyperfine parameters with the location of the probe nuclei (181Ta5+) at ionic sites in EuTiO3, ab initio calculations were carried out as follows:

With a cubic Pm3¯m structure, Vzz was shown to be zero for Ta that was simply substitutional at the Eu or Ti sites, due to symmetry. We then considered the case of an oxygen vacancy (Ov) as nearest neighbor (nn) to Ta substitutional at Ti or Eu sites, starting with a 2 × 2 × 2 supercell. For Ta, substitutional at the Ti site with an nn Ov, we obtained Vzz = 31.80 × 1021 V/m2 for G-AFM order. Calculations with GGA + U (GGA) predicted Vzz = 34.4 × 1021 V/m2 (33.24 for GGA) and η = 0.16 (0.31 for GGA). We used GGA + U, as it was probably the better approximation, for the remaining calculations. (We tested the effect of different lattice parameters: using a = 3.85 and 3.95 Å resulted in Vzz = 37.4 × 1021 V/m2, η = 0.22, and Vzz = 32.2 × 1021 V/m2, η = 0.14, respectively.) However, this supercell was small, and we performed calculations with 3 × 3 × 3 and 4 × 4 × 4 supercells to remove any possible effects from interactions between the periodic defects (since the calculations were periodic, any defect would not have been disordered, as in a real sample, and may have interacted with its images if the supercell had not been large enough). The results, Vzz = 46.6 × 1021 V/m2 (3 × 3 × 3) and 45.9 × 1021 V/m2 (4 × 4 × 4), showed convergence with supercell size but were even higher and compared worse with the experimental low-temperature values. We also performed calculations with a next-nearest neighbor (nnn) Ov.

Ta that is substitutional at the Eu site with one nn Ov resulted in Vzz ∼ 71 × 1021 V/m2, η = 0.44, which is also far from the experimental value. The result with an nnn Ov decreased to a lower value of Vzz ∼ 56 × 1021 V/m2 but was still much higher than the experimental value, also with higher η, and was energetically unfavorable with respect to the nn case by 143 meV/fu. These results indicate that in the cubic phase, the experimental data cannot be explained by the Ta substitutional probe at the Ti or Eu sites, including cases with an Ov near the substitutional sites (Ta:Ti and Ta:Eu). The results are summarized in Table II.

TABLE II.

Simulated values for Pm-3m with oxygen vacancies (Ov).

SiteSupercellVzz (1021 V/m2)η
Ta:Ti with nn Ov 2 × 2 × 2 36.3 0.00 
Ta:Ti with nn Ov 3 × 3 × 3 46.6 0.00 
Ta:Ti with nn Ov 4 × 4 × 4 45.9 0.00 
Ta:Eu with nn Ov 2 × 2 × 2 70.7 0.44 
Ta:Eu with nnn Ov 2 × 2 × 2 56.5 0.75 
SiteSupercellVzz (1021 V/m2)η
Ta:Ti with nn Ov 2 × 2 × 2 36.3 0.00 
Ta:Ti with nn Ov 3 × 3 × 3 46.6 0.00 
Ta:Ti with nn Ov 4 × 4 × 4 45.9 0.00 
Ta:Eu with nn Ov 2 × 2 × 2 70.7 0.44 
Ta:Eu with nnn Ov 2 × 2 × 2 56.5 0.75 

Next, we explored several other structures that have been studied and proposed for this material,44 with I4/mcm, Imma, and R3¯c space groups, which exhibits rotations of oxygen octahedra. Starting with these initial structures, we then included defects, which produced an additional decrease in symmetry. With these structures, the EFG with Ta at substitutional sites is not zero but is small (except for high concentrations of Ta:Eu starting with the I4/mcm space group). The results for Ta in different supercells of the different phases are given in Tables III–V. For Ta at Ti sites, the variation is small between phases (0 in the cubic phase to −3.3 × 1021 V/m2 in the I4/mcm space group), which indicates that in all cases, a simple substitutional Ti situation was not measured. With Ta at Eu, it is notable that the EFG changes drastically from the 1 × 1 × 1 supercell to the 2 × 2 × 1 supercell in the I4/mcm phase, though none of these calculations are consistent with the experimental results. The low values obtained in simple substitutions with low Ta concentrations indicate that other defects must be considered. Oxygen vacancies may, of course, greatly change the results seen in the cubic phase, so we also considered Ov in the I4/mcm and Imma phases. Finally, Ta, substitutional at Eu and with an nn Ov, agrees with the experimental value (Vzz = 22 × 1021 V/m2). The value is also close to, but less than, the experimental one if we consider the same kind of defect from the I4/mcm phase, with Vzz = 17.9 × 1021 V/m2. To complete the set of proposed structures with octahedral rotations, we also considered the R3¯c space group (here, the oxygen octahedra have the same alternating rotation angles in all three directions, corresponding to the a-a-a- rotation pattern in Glazer’s notation).52 In addition, we considered 2 × 2 × 1 supercells with respect to the hexagonal unit cell (separations of 11.06 Å between Ta impurities; one calculation with a 1 × 1 × 1 supercell revealed a small difference in the electric field gradient, Vzz = 2.0 × 1021 V/m2), resulting in Vzz = 2.1 × 1021 V/m2 and 48.2 × 1021 V/m2 for Ti and Eu substitutions, respectively, neither of which is close to the experimental value. The results are summarized in Table III.

TABLE III.

Simulated values for different crystal symmetries in EuTiO3.

SiteSupercellVzz (1021 V/m2)η
I4/mcm 
Ta:Ti 1 × 1 × 1 −3.3 0.05 
Ta:Ti 2 × 2 × 1 0.6 0.05 
Ta:Eu 1 × 1 × 1 −39.5 
Ta:Eu 2 × 2 × 1 −1.8 
Ta:Eu with nn Ov 2 × 2 × 1 17.9 0.68 
Imma 
Ta:Ti 1 × 1 × 1 −2.4 0.22 
Ta:Ti 2 × 1 × 2 −2.8 0.63 
Ta:Ti with nn Ov 2 × 1 × 2 41.1 0.05 
Ta:Eu 1 × 1 × 1 −7.5 0.63 
Ta:Eu 2 × 1 × 2 −7.6 0.90 
Ta:Eu with nn Ov 2 × 1 × 2 22.1 0.69 
R-3c 
Ta:Ti 1 × 1 × 1 2.0 0.00 
Ta:Ti 2 × 2 × 1 2.1 0.00 
Ta:Eu 2 × 2 × 1 48.2 0.00 
SiteSupercellVzz (1021 V/m2)η
I4/mcm 
Ta:Ti 1 × 1 × 1 −3.3 0.05 
Ta:Ti 2 × 2 × 1 0.6 0.05 
Ta:Eu 1 × 1 × 1 −39.5 
Ta:Eu 2 × 2 × 1 −1.8 
Ta:Eu with nn Ov 2 × 2 × 1 17.9 0.68 
Imma 
Ta:Ti 1 × 1 × 1 −2.4 0.22 
Ta:Ti 2 × 1 × 2 −2.8 0.63 
Ta:Ti with nn Ov 2 × 1 × 2 41.1 0.05 
Ta:Eu 1 × 1 × 1 −7.5 0.63 
Ta:Eu 2 × 1 × 2 −7.6 0.90 
Ta:Eu with nn Ov 2 × 1 × 2 22.1 0.69 
R-3c 
Ta:Ti 1 × 1 × 1 2.0 0.00 
Ta:Ti 2 × 2 × 1 2.1 0.00 
Ta:Eu 2 × 2 × 1 48.2 0.00 
TABLE IV.

Simulated values for Eu2Ti2O7.

SiteVzz (1021 V/m2)η
Ta:Ti 18.4 
Ta:Eu −57.3 
SiteVzz (1021 V/m2)η
Ta:Ti 18.4 
Ta:Eu −57.3 
TABLE V.

Simulated values for Ti3O5.

SiteVzz (1021 V/m2)η
Ta:Ti 8.4 0.76 
Ta:Ti with minus one electron 8.4 0.79 
SiteVzz (1021 V/m2)η
Ta:Ti 8.4 0.76 
Ta:Ti with minus one electron 8.4 0.79 

To check the possibility of a pyrochlore phase, (Fd-3m) Eu2Ti2O7, we performed calculations with Ta substitutional at Eu and Ti sites. Since one unit cell of Eu2Ti2O7 already contained eight formula units (one formula unit contained the same atoms as the chemical formula, Eu2Ti2O7), we did not increase cell size in this case. The results are presented in Table IV. The existence of this phase was confirmed by our XRD and TDPAC results, following annealing at 1373 K. The experimental parameters (Vzz ≈ 22 × 1021 V/m2 with η ≈ 0.1) were close to the simulated values. This is a more realistic result, in contrast with the calculation for EuTiO3 with Imma symmetry and Ta at the Eu site with an Ov (Vzz = 22.1 × 1021 V/m2 with η = 0.69). The reason, we expect, is that Ta occupies the Ti site and the configuration of its Eu site with an Ov is energetically unfavorable. Furthermore, the Eu2Ti2O7 phase was also observed in the XRD results, and the simulated asymmetry parameter agrees with the experimental one.

Regarding the Ti3O5 phase, the lattice parameters measured by XRD were considered, and for the calculation, we used a 1 × 2 × 2 supercell. The calculations used GGA + U (U = 5.7, J = 1 eV for Eu f electrons), a 4 × 3 × 3 k-points grid, an energy cutoff of 500 eV, and a spin-polarized ferromagnetic solution was considered [final moments at Ti were of the order of 0.2–0.4 μB, while Ta had a small moment of 0.05 μB; O atoms had very small negative moments (∼−0.01 μB)]. The results of the EFG contribution are presented in Table V where the calculation with and without minus one electron give very similar results. The Ti3O5 phase was not observed in the TDPAC experiments but was discovered in XRD. A possible explanation is that the Ti3O5 phase was not present in the neighborhood of the TDPAC probe. The local environment of the probes is subjected to the implantation range and thermal diffusion range during thermal annealing and high temperature experiments. In our case, implantation was performed in a 3 mm × 3 mm area and with a very low concentration of the 181Ta probe.

An actual measurement of the limit for the electron electric dipole moment (EDM) with Eu0.5Ba0.5TiO3 was reported by Eckel et al.53 This type of measurement has not been further pursued because other measurement methods today show greater promise. The principal advantage of this solid-state method resides in the fact that one can easily upscale sample production and gain immediately EDM, thanks to statistical analysis, which is not so easy with neutron or radium EDM measurements. To date, the TDPAC technique has not been used to determine the EDM.

Our results demonstrate the feasibility of using the TDPAC technique to study hyperfine interactions in EuTiO3, complemented by ab initio calculations and XRD experiments. The comparison with ab initio calculations allows one to assign the Ti site in the Eu2Ti2O7 phase, the most probable site for Ta probes. The calculations further show that using the EFG is one way to discriminate between different possible structures, sites, and point defects in EuTiO3 using TDPAC with Ta probes.

The variety of unusual and interesting ferroelectric, magnetic, and structural properties in europium titanates requires such local characterization for a deeper understanding of the Eu3+/Eu2+ influence. The observed static interaction arises from a specific Eu charge state and defect configuration to which the Ta probe attaches. Point defects combined with Eu ions strongly influence the temperature of the phase transitions, and a proper configuration can achieve considerable magnetic susceptibility and strong spin-orbit and/or spin-phonon coupling. The TDPAC technique is well known in the investigation of point defects. Depending on the preparation method used for incorporating the radioactive probe atoms, it is possible to study the material without changing its properties. In this case, interference of the probe atoms with the properties of the sample and doping levels can be excluded.54 Additional TDPAC measurements with EuTiO3 are foreseen and are part of the ISOLDE-CERN project IS647 “Local Probing of Ferroic and Multiferroic Compounds.”55–57 

The main intention of this work was to study the electric-field gradient at the Ti and Eu sites in europium titanates by means of perturbed angular correlations, XRD diffraction, and ab initio calculations. We conclude that annealing at 1373 K changes the charge state of Eu, being related to the partial phase transition to the Eu2Ti2O7 phase. Moreover, the Eu2Ti2O7 phase was also observed in the XRD experiments, and the simulated parameters for Ta at the Ti site (Vzz = 18.4 × 1021 V/m2 with η = 0) are close to the experimental ones (Vzz ≈ 22 × 1021 V/m2 with η ≈ 0.1). Such annealing effects in EuTiO3 and Eu2Ti2O7 have not been studied, to the best of our knowledge, until now by means of perturbed angular correlations. The TDPAC results are in agreement with those of ab initio calculations and XRD diffraction, confirming the existence of the EuTiO3 and Eu2Ti2O7 phases. However, the Ti3O5 phase, present in XRD diffraction results, was not observed in the TDPAC experiments. The structural phase transition from cubic to tetragonal, which should occur between 282 and 300 K, was not observed, since measurements were carried out at temperatures of up to 295 K only. The induction of additional phases, Eu2Ti2O7 and Ti3O5, during the annealing process was complementary to the study of pure EuTiO3.

This research has received funding from the Federal Ministry of Education and Research (BMBF) through Grant No. 05K16PGA. The authors also acknowledge the support of the Czech Science Foundation (Project Nos. 18-09265S and 17-05620S) and support from the Ministry of Education, Youth and Sports of the Czech Republic under Project Nos. CEITEC 2020 (LQ1601) and SOLID21 (CZ.02.1.01/0.0/0.0/16_019/0000760). We also acknowledge support from the Portuguese Foundation for Science and Technology (FCT) under Project No. CERN-FIS-NUC-0004-2015. The Danish Ministry of Higher Education and Science is thanked for financial support via the NICE grant. We thank J. G. M. Correia for technical assistance during these experiments and U. Koester for the irradiation at the Institut Laue-Langevin. We also thank V. V. Shvartsman for fruitful discussions.

The authors declare no competing interests.

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