Defect dipoles are significant point defects in perovskite oxides as a result of their impact on oxygen vacancy dynamics. Electron paramagnetic resonance (EPR) was used to investigate the local defect structure of single crystal BaTiO3 doped with manganese. These results, along with a re-analysis of literature data, do not support the conclusion that transition metal-oxygen vacancy nearest neighbor defect dipoles (MnTiVO)× in ferroelectric BaTiO3 are majority defect centers as previously reported. Local symmetry analysis of the zero-field splitting term of the spin Hamiltonian supports the assignment of fully coordinated defect centers as opposed to defect dipoles for resonance signals at geff ∼ 2. A newly discovered defect center with g ∼ 6 is observed in the manganese doped system, and it is argued that this defect center belongs to an associated defect complex or defect dipole. This newly reported strong axial defect center, however, is present in small, minor concentrations compared to the well-known Mn2+ center with zero-field splitting of D ∼ 645 MHz. In regard to relative concentration, it is concluded that the dominant point defect related to the Mn2+ ion doped in BaTiO3 corresponds to B-site substitution with six nearest neighbor anions in octahedral coordination.

Unless intentionally donor doped, the defect chemistry of oxide perovskite materials will typically be controlled by impurities or intrinsic defect centers that act as acceptors.1–5 Ferroelectric oxides are often intentionally doped with acceptor ions to take advantage of the “hard” properties produced by this type of substitution.6 In undoped materials, acceptor defects are still present in relatively large concentrations as a result of unintended impurities or intrinsic partial Schottky reactions.7 High temperature processing will result in acceptor doped materials that are charge compensated by oxygen vacancies. When these materials are cooled to room temperature, the oxygen vacancy concentrations are kinetically frozen-in, and the oxygen stoichiometry in the system is fixed at high concentrations on the order of the acceptor impurity concentrations.8–12 As a result, the concentrations of charged ionic point defects in the material are orders of magnitude larger than the concentration of electrons and holes at ambient temperature.13 Samples will have a defect chemistry dominated by oxygen vacancies and ionized acceptors rather than electronic carriers. This type of charge compensation is typically written as a charge neutrality equation using Kröger-Vink notation

[A]+2[A]=2[VO],
(1)

where the primary defects considered in an ABO3 perovskite are A, A, and VO which correspond to singly and doubly ionized acceptor dopants and oxygen vacancies, respectively.14 When an acceptor ion and oppositely charged oxygen vacancy sit on nearest neighbor sites in the lattice, they are referred to as a defect complex or defect dipole and are represented in Kröger-Vink notation as (AVO) and (AVO)×.

The dominant mobile defect in acceptor doped perovskite materials is the oxygen vacancy. Understanding the interaction of mobile oxygen vacancies and immobile acceptor defect centers is of particular importance to the study of ionic transport and ferroelectric reliability.15–18 If no interaction exists between these two types of defects, oxygen vacancy mobility is approximated to be independent of defect chemistry in the dilute limit, and the measurement of ionic transport phenomena should reflect this. Defect chemistry independent mobility, however, is not the precedent, as studies have shown oxygen vacancy mobility to be impacted by defect chemistry and thermal history.19–23 

The formation of defect complexes in the perovskite structure has been well documented in SrTiO3.24–26 Defect dipoles produce large crystal field anisotropy in the local vicinity of the associated transition metal ion. As shown in Figure 1 however, there are many types of local distortions that can result in zero-field splitting (ZFS) of the effective spin Hamiltonian measured by magnetic resonance techniques. The tendency to want to assign any large zero-field splitting found in perovskites to a defect complex has been prevalent in the literature. Because there are multiple reasons non-centrosymmetric crystal systems can have axial distortions at point defect center sites, some of these defect dipole assignments have been proven to be incorrect.27 As a cautionary tale, even the cubic, incipient ferroelectric KTaO3 system can accommodate multiple types of defect centers responsible for large axial zero-field splitting parameters.28 When properly characterized, however, these splittings have been shown to be the result of off-center displacements of a dopant sitting on the perovskite A-site rather than defect dipoles as previously reported.28,29 Similarly, the zero-field splitting found in the manganese doped BaTiO3 system has been assigned to defect dipoles in the literature.30 This work has been used in subsequent studies to develop models concerning the impact of defect dipoles on ferroelectric aging phenomena.31,32

FIG. 1.

Common oxygen vacancy related defects in perovskite dielectrics and the associated reliability mechanisms which can include ferroelectric aging and dielectric resistance degradation.12,15–18

FIG. 1.

Common oxygen vacancy related defects in perovskite dielectrics and the associated reliability mechanisms which can include ferroelectric aging and dielectric resistance degradation.12,15–18

Close modal

If defect dipoles do in fact form in the perovskite lattice, the formation and strength of association of oxygen vacancies with acceptor point defect centers may control vacancy mobility at low temperatures where oxygen vacancies form defect complexes with acceptor sites.22 These types of near neighbor defect pairs are of particular interest in ferroelectric materials as a result of the effects of defect dipole formation on the pinning of domain wall mobility or stabilization of spontaneous polarization as illustrated in Figure 1.6,15,17 Some EPR studies of perovskite materials have determined that nearly all of the oxygen vacancies in a ferroelectric system sit nearest neighbor to an acceptor ion forming defect dipoles that constitute the majority defect centers in the lattice.30,33,34 This type of defect dipole is predicted to orient itself with respect to the direction of spontaneous polarization in a ferroelectric domain simply by means of an oxygen vacancy hopping mechanism.18 Appropriate characterization of EPR resonance signals is fundamental to the exercise of being able to effectively explain the relationships between point defect chemistry and dielectric relaxation and ionic transport phenomena.

Single crystal samples of BaTiO3 with ⟨001⟩ orientation doped with 0.5 mol. % manganese were purchased from Ceracomp, Inc. Transparent crystals were grown using a solid state crystal growth technique.35 Samples were annealed at high temperature under various oxygen activities to equilibrate a range of manganese valence states. These samples were then quenched to room temperature in order to freeze-in the oxygen vacancy concentration and preserve the desired manganese valence state. EPR measurements were made on a Bruker ER 200D-SRC X-band spectrometer.

Dielectric measurements were made using a Hewlett Packard 4284A Precision LCR meter and Delta Design oven. Polarization and strain measurements were made using a homemade modified Sawyer-Tower circuit and linear variable differential transducer. Crystals with sample dimensions 3 × 5 mm and 0.5 mm in thickness were contacted with sputtered platinum electrodes.

The Zeeman (Z), hyperfine (HF), axial, and cubic ZFS components of the spin Hamiltonian for a paramagnetic ion in a strong axial field in the perovskite lattice are given in Equations (2)–(4), where μB, geff, S, B, A, I, D, and Si are the Bohr magneton, effective g-factor, spin angular momentum, hyperfine coupling constant, nuclear spin angular momentum, second order axial zero-field splitting term, and angular momentum along the i-axis, respectively

ĤZ,HF=μBgeffSB+ASI,
(2)
Ĥcubic=(a6)[Sx4+Sy4+Sz415S(S+1)(3S2+3S1)],
(3)
Ĥaxial=D[Sz213S(S+1)]+F180{35Sz4[30S(S+1)25]Sz26S(S+1)+3S2(S+1)2}.
(4)

For the purpose of the following discussion, the most important terms that will be considered in Equations (2)–(4) are A and D; however, to ensure completeness, the fourth order ZFS terms a and F are included. The magnitude of the hyperfine coupling constant, A, is dependent on the size of the paramagnetic species, so values of A can be used to help determine the valence state of a particular ion.36 The ZFS parameter D is related to dipole interactions between electrons in ions with more than one unpaired electron like the Mn2+ S = 5/2 system under consideration. Unpaired electrons in ions placed in high symmetry octahedral environments like the cubic perovskite SrTiO3 system have relatively isotropic electron distributions around the ion leading to small values of ZFS terms. Conversely, ions in anisotropic environments like a dopant in a ferroelectric lattice or an ion with a nearest neighbor oxygen vacancy have large values of D.

EPR has proven to be a successful tool used to evaluate local structural evolution and order-disorder transitions in SrTiO3, BaTiO3, and PbTiO3 systems.37–43 The manganese doped system used in this study was specifically chosen as a result of the wealth of EPR experimental data previously collected on manganese doped BaTiO3 and the isoelectronic S = 5/2 system of Fe3+ doped BaTiO3. The local structure of the paramagnetic ion in relation to its nearest neighbor oxygen ligands can be derived using Newman superposition model (NSM) analysis.44–47 Experimental measurement of the EPR parameters necessary to make structural calculations using methods like the Newman superposition model analysis, however, is not a trivial practice. Multiple microwave frequencies are often needed for the exact calculation of the second and fourth order ZFS parameters.24,48–50 The precise measurement of the most important EPR parameters for both iron and manganese doped crystals has been made by various research groups, and a comprehensive list of these parameters is given in Table I.

TABLE I.

Experimentally measured EPR parameters for SrTiO3 and BaTiO3. Ferroelectric phase: cub = cubic, tet = tetragonal, and rh = rhombohedral.

Selected EPR parameters for Fe3+, Mn2+, and Mn4+ doped BaTiO3 and SrTiO3
Fully coordinated
gisocDdaFΔ/2Ax = AyAzReference
PbTiO3 tet Mn2+ … 2010 … … 2010 −246 … 43  
Mn4+ 1.987 gx=y 9498 … …  213.2 238.4 50  
 1.99 gz        
Fe3+ 2.010 gx=y 17 460 696 −522 18 910 34  
 2.009 gz        
BaTiO3 rh Mn4+ 1.997a 19 500b …  219b 202b 37 b 
        66 a 
tet Mn2+ 2.002 645 50 … 762 −246 −231 70  
Fe3+ 2.003 2769 306 −54 3465 48  
cub Mn2+ 2.002 36  −238 −238 70  
Fe3+ 2.003 306  48  
SrTiO3 cub Mn2+ 2.004 70e  248 248 25  
Mn4+ 1.994 …  −210 −210 41  
Fe3+ 2.004 595  39  
Oxygen vacancy nearest neighbor 
   giso  D″   Ax = Ay Az  
BaTiO3 rh Fe3+ 2.00  31 200   49  
tet Mn2+ 2.003  720   237 237 30  
SrTiO3 cub Mn2+ 2.003 gz  16 320   195 228 25  
 2.008 gx=y        
cub Fe3+ 2.010  42 750   24  
Superposition model intrinsic parameters (MgO reference, Ro = 2.101 Å) 
 b¯2 (GHz) t2 b¯4 (MHz)  t4  
Fe3+ −12.4 87.3  8.9 46  
Mn2+ −4.7 8.16  
Selected EPR parameters for Fe3+, Mn2+, and Mn4+ doped BaTiO3 and SrTiO3
Fully coordinated
gisocDdaFΔ/2Ax = AyAzReference
PbTiO3 tet Mn2+ … 2010 … … 2010 −246 … 43  
Mn4+ 1.987 gx=y 9498 … …  213.2 238.4 50  
 1.99 gz        
Fe3+ 2.010 gx=y 17 460 696 −522 18 910 34  
 2.009 gz        
BaTiO3 rh Mn4+ 1.997a 19 500b …  219b 202b 37 b 
        66 a 
tet Mn2+ 2.002 645 50 … 762 −246 −231 70  
Fe3+ 2.003 2769 306 −54 3465 48  
cub Mn2+ 2.002 36  −238 −238 70  
Fe3+ 2.003 306  48  
SrTiO3 cub Mn2+ 2.004 70e  248 248 25  
Mn4+ 1.994 …  −210 −210 41  
Fe3+ 2.004 595  39  
Oxygen vacancy nearest neighbor 
   giso  D″   Ax = Ay Az  
BaTiO3 rh Fe3+ 2.00  31 200   49  
tet Mn2+ 2.003  720   237 237 30  
SrTiO3 cub Mn2+ 2.003 gz  16 320   195 228 25  
 2.008 gx=y        
cub Fe3+ 2.010  42 750   24  
Superposition model intrinsic parameters (MgO reference, Ro = 2.101 Å) 
 b¯2 (GHz) t2 b¯4 (MHz)  t4  
Fe3+ −12.4 87.3  8.9 46  
Mn2+ −4.7 8.16  
a

Reference 66.

b

Reference 37.

c

g is unitless, all other values are in units of MHz unless otherwise noted.

d

All D parameters were measured at room temperature and are given as absolute values.

e

a = 70 MHz for Mn2+ was estimated from a(Fe3+)BaTiO3cub/a(Mn2+)BaTiO3cub.

Once precise measurements of the ZFS parameters have been made, these values can be used to model the paramagnetic ion's local structure consisting of the surrounding nearest neighbor oxygen ligands.51 The second order ZFS parameters, D and E, are typically sufficient to describe the local structure using Newman superposition model analysis.52,53 For systems with small second order ZFS parameters, higher order terms are necessary to describe the resonance response. For systems where the second order parameters are much larger than higher order parameters (these are systems with large axial or rhombic distortions, i.e., the tetragonal phases of BaTiO3 or PbTiO3 as opposed to lattices with cubic symmetry, i.e., SrTiO3), it may be difficult to separate the contribution of each parameter to the total ZFS; and as a result, the second order parameter is given as an effective value, D′′, in Table I.54 For completeness, data are included in Table I for single crystals in which it was possible to separate the ZFS parameters into the respective second and fourth order components.

An effective ZFS parameter can be derived to describe systems with significant fourth order contributions. This effective parameter has been used by Hornig et al. to illustrate the relationship between the ZFS parameters and the magnitude of the spontaneous polarization in BaTiO3.48 The effective ZFS parameter containing second and fourth order terms is given as

Δ=2D+17a11b,
(5)

with the parameters D′, a′, and b′

D=DF180[30S(S+1)25],
(6)
a=a6+35180F,
(7)
b=a6,
(8)

where D, a, and F correspond to the second and fourth order ZFS parameters given in Equations (2)–(4).55 

The NSM can be used to determine the local positions of the six oxygen ligands surrounding a transition metal on the B-site of a perovskite lattice.52,53 For a paramagnetic ion placed at the center of an oxygen octahedron, a simplified expression of the ZFS parameters as a function of the tetragonal lattice constants c and a can be derived as

Dcoordinated=2b¯2(c2)[1(ca)t2],
(9)
acoordinated=7b¯4(c2)(ca)t4,
(10)
Fcoordinated=6b¯4(c2)[1(ca)t4],
(11)

where

b¯m(c2)=b¯m(Ro)[Roc/2]tm.
(12)

The function b¯m(R) is based on intrinsic parameters typically calculated from uniaxial strain data.53 The b¯m(Ro) and tm intrinsic values are given in Table I for the reference crystalline host MgO with Ro given as 2.101 Å.52 Equation (9) can be manipulated to account for an oxygen vacancy on one of the octahedral sites lying along the c-axis of the unit cell

Dvacancy=b¯2(c2)[12(ca)t2].
(13)

This type of analysis, for example, has effectively been used to determine the magnitude of local distortion around a B-site cation in the perovskite lattice produced by a paraelectric to ferroelectric phase transition.52,56 Newman superposition model analysis has also been used to determine the local structure of an acceptor ion with an oxygen vacancy in its nearest neighbor coordination shell.53 Examples of both of these types of defect centers will be given in the following discussion.

The effect of axial distortion on the magnitude of the effective ZFS parameter is given in Figure 2 as a function of the lattice parameters c/a. Allowing c to be a free parameter, Equations (9)–(13) were substituted into Equation (5) in order to derive an expression giving the effective ZFS parameter as a function of c/a in Figure 2. The experimentally obtained EPR response from this current work for an Mn2+ doped BaTiO3 crystal at room temperature with the c-axis aligned perpendicular to the z-axis of the applied magnetic field is given in the same plot. The EPR responses in Figure 2 were simulated using Easyspin software using the spin Hamiltonian parameters found by Ikushima in Table I.57 The experimental literature data points denoted by circles and stars in Figure 2 for the effective ZFS parameters for cubic SrTiO3 and tetragonal BaTiO3 and PbTiO3 are also given in Table I.

FIG. 2.

The effect of the perovskite unit cell tetragonality on the magnitude of the effective ZFS parameter is shown for a paramagnetic ion placed directly in the center of an oxygen octahedron. Experimental data points correspond to the values of the effective ZFS parameters measured on single crystal samples for fully coordinated Fe3+, Fe3+ with a nearest neighbor oxygen vacancy (FeVO), fully coordinated Mn2+, and Mn2+ with a nearest neighbor oxygen vacancy (MnVO)× for open circles, closed circles, open stars, and closed stars, respectively.52 Corresponding EPR resonance responses are plotted for the given effective ZFS parameter Δ. Included are experimental data of a crystal equilibrated at 900 °C and 3 × 10−12 atm denoted by *.

FIG. 2.

The effect of the perovskite unit cell tetragonality on the magnitude of the effective ZFS parameter is shown for a paramagnetic ion placed directly in the center of an oxygen octahedron. Experimental data points correspond to the values of the effective ZFS parameters measured on single crystal samples for fully coordinated Fe3+, Fe3+ with a nearest neighbor oxygen vacancy (FeVO), fully coordinated Mn2+, and Mn2+ with a nearest neighbor oxygen vacancy (MnVO)× for open circles, closed circles, open stars, and closed stars, respectively.52 Corresponding EPR resonance responses are plotted for the given effective ZFS parameter Δ. Included are experimental data of a crystal equilibrated at 900 °C and 3 × 10−12 atm denoted by *.

Close modal

There is close agreement between the calculated effective ZFS parameters using the NSM for an iron or manganese ion substituted on the perovskite B-site using Equations (9)–(13) in Figure 2 compared to the experimentally determined effective ZFS values. The derived effective ZFS parameter for manganese ions tends to deviate more from the experimental values compared to iron. According to Shannon and Prewitt, the difference in ionic radii between octahedrally coordinated Fe3+ and Ti4+ is 0.04 Å, while the Mn2+ ion is much larger than the B-site by 0.225 Å.58 This size discrepancy may force additional local distortion of the octahedral symmetry causing a deviation of the experimental ZFS terms from those predicted using the simplified model given by Equations (9)–(13).

The agreement between the model calculations in Figure 2 with the experimental data for coordinated Fe3+ and Mn2+ ions hosted in cubic lattices as well as unit cells with large ferroelectric distortions displays the power of the NSM and confirms the fully coordinated B-site substitution assignments made by the researchers listed in Table I. The agreement between the experimental data and model calculations for nearest neighbor defect complexes is not as strong as shown in Figure 2. As was first shown by Siegel and Muller, additional displacements of the nearest neighbor ions surrounding the paramagnetic ion must be accounted for to explain the ZFS parameter for defect complexes containing nearest neighbor oxygen vacancies.53 However, for the present discussion, the main point that should be taken from Figure 2 is the stark difference between the appearance of the resonance signals for ions doped in BaTiO3 with effective ZFS parameters less than 3 GHz and effective ZFS parameters greater than 3 GHz. Only large ZFS parameters much greater than 3 GHz have been reported for systems that are considered to contain defect dipoles.34,53,59–61 For systems with relatively small c/a ratios and small effective ZFS parameters, Figure 2 shows that the NSM model predicts the ion will be fully coordinated, not associated with an oxygen vacancy, and the corresponding resonance response will be centered around geff ∼ 2. Conversely, for defect dipoles, the NSM model predicts large ZFS parameters with the resonance signals centered near geff ∼ 6.

The dielectric response of the crystals exhibits the typical behavior of acceptor doped BaTiO3.62 The permittivity as a function of temperature measured at 1 kHz with a 1 V applied ac voltage for samples equilibrated under different oxygen activities is given in Figure 3. The cubic to tetragonal transition TC is shifted to lower temperature values with higher degrees of reduction in a manner similar to other reported transition metal doped BaTiO3 systems.62,63 The effect of transition metal defects on the position of the ferroelectric transition temperature has been attributed to the centering of the transition metal in the oxygen octahedron in opposition to the displaced intrinsic position of the Ti4+ ion in the tetragonal phase.52 

FIG. 3.

The dielectric permittivity measured as a function of temperature for 0.5 mol. % Mn doped BaTiO3 single crystals.

FIG. 3.

The dielectric permittivity measured as a function of temperature for 0.5 mol. % Mn doped BaTiO3 single crystals.

Close modal

The presence of defect dipoles in SrTiO3 crystals and the observation of ferroelectric aging in acceptor doped BaTiO3 have led to the natural assumption that similar nearest neighbor defect associates form in ferroelectrics and are responsible for ferroelectric aging. The single crystal samples tested in this study show the same ferroelectric aging behavior observed by other researchers.15,18,31,64,65 The effect of aging on the ferroelectric properties during the typical evolution of internal bias of a reduced manganese doped sample at room temperature in the tetragonal phase is shown in Figure 4.

FIG. 4.

The effect of aging on 0.5 mol. % Mn doped BaTiO3 single crystal that has been equilibrated at 950 °C under 2 × 10−5 atm PO2 before being quenched to room temperature. The samples were allowed to age at room temperature, and the effect of aging can be seen as a result of the changes to (a) the pinching of the polarization hysteresis loop and (b) the butterfly strain loop measured at 1 Hz. All electric fields were applied parallel to the c-axis.

FIG. 4.

The effect of aging on 0.5 mol. % Mn doped BaTiO3 single crystal that has been equilibrated at 950 °C under 2 × 10−5 atm PO2 before being quenched to room temperature. The samples were allowed to age at room temperature, and the effect of aging can be seen as a result of the changes to (a) the pinching of the polarization hysteresis loop and (b) the butterfly strain loop measured at 1 Hz. All electric fields were applied parallel to the c-axis.

Close modal

These reduced manganese doped crystals have clearly aged in the unpoled state as shown in Figure 4 as evidenced by the asymmetrical shifts of the polarization and strain loops as a function of time. The doped crystals were observed to exhibit ferroelectric aging regardless of the thermal annealing history, but the aging rates and magnitude of the internal bias changed depending upon equilibration conditions.

The manganese doped single crystals required the samples to be annealed with N2/H2 mixtures at temperatures of 900 °C and above before any resonance line associated with manganese ions became visible using X-band EPR as a probe. Reliable characterization of Mn3+ in BaTiO3 acting as a B-site acceptor using X-band spectroscopy has not been reported in the literature; so even though Mn3+ may be present in large concentrations depending on the thermal annealing history, Mn3+ is unobservable using standard continuous wave EPR X-band techniques. It has been shown that unlike Mn2+, Fe3+, and Cr3+ to name a few, the isovalent Mn4+ ion on the Ti4+ site participates in ferroelectricity and follows the same displacements as Ti4+.37,38,66,67 These studies, as well as investigations made by additional research groups, are in agreement in determining that annealing samples in oxidizing conditions is required in order to resolve the Mn4+ valence state.68,69 These studies have also determined that Mn4+ can only be viewed with X-band EPR in the low temperature rhombohedral phase of BaTiO3. Mn4+ is not observable in the higher temperature phases as a result of the order-disorder nature of the ferroelectric phase transitions. Because Mn4+ acts like the Ti4+ ion, the frequency of the displacements of Mn4+ along the cube diagonals in the higher temperature phases becomes fast enough to sufficiently broaden the EPR signal of the defect center rendering it unobservable.37 

There is less agreement concerning the necessary processing conditions required to produce Mn2+ centers. The former studies discussed thus far have shown that reducing conditions at high temperatures are necessary to produce Mn2+ centers, and their results agree with other notable studies concerning the manganese valence state in BaTiO3.62 Other researchers have reported Mn2+ related defect centers in crystals with no history of reduction.30,70,71 It is not immediately clear why in certain cases Mn2+ is only seen in highly reduced systems and then in other cases seen in oxidized samples. However, the crystals where Mn2+ was observed in the oxidized state were grown from KF or BaCl2 fluxes, and F as well as Cl have been shown to substitute for O2− in small concentrations in BaTiO3.72–74 The incorporation of F and Cl impurities on the oxygen site would result in a donor doping mechanism in these systems and would force manganese to lower valance states for charge compensation. This type of charge compensation would also limit the concentration of oxygen vacancies introduced to the system which could explain why the signal at geff ∼ 6 related to a defect dipole found in this study was not seen in the instances where BaTiO3 was grown from an alkali-halide flux. The observation of Mn2+ valence states in the single crystal samples grown using a solid state crystal growth technique reported in this study required strong reducing conditions agreeing well with the results of EPR, magnetic susceptibility, and thermogravimetry studies in which crystals were either grown using the Verneuil process or sintered ceramic materials were investigated.25,62,68,75

For this study, the absolute value of the hyperfine splitting constant of a crystal heated above the tetragonal-to-cubic phase transition was calculated to be 240 ± 0.7 MHz. This hyperfine value agrees with the assignment of Mn2+ on the B-site made by other investigators.30,53,76 The absence of EPR signals corresponding to Mn2+ on the B-site in oxidized samples is characteristic of redox-active ions with ionization energy levels deep in the band gap.10 The Mn3+/Mn2+ ionization energy has been measured by multiple research groups to be greater than 1.8 eV above the valence band edge.69,75 Thus, unless the crystal is heavily reduced, there are not enough donors present to drive the electroneutrality expression given in Equation (1) towards higher concentrations of Mn2+ unless high concentrations of extrinsic donors are also introduced to the system as shown in the case of PbTiO3.77 Crystals with large acceptor dopant concentrations were specifically chosen for this study in order to ensure the intended dopant was the majority defect center.

EPR data for manganese doped BaTiO3 single crystals equilibrated under various oxygen activities before being quenched to room temperature are plotted in Figure 5. The resonance lines for the different annealing conditions are not normalized with respect to the EPR cavity Q-factor or the sample mass, so quantitative comparisons concerning relative defect concentrations should not be made based on signal intensities of samples reduced under different conditions. There appears to be some small amount of impurity in the manganese samples related to iron resonance signals observed in the oxidized samples. For samples annealed in mixtures of N2/H2 at high temperature, the Mn2+ valence state is achieved confirmed by the magnitude of the hyperfine splitting parameter.

FIG. 5.

Development of defect resonance signals for manganese doped BaTiO3 crystals annealed under various oxygen activities. All measurements were made on crystals oriented with the c-axis aligned perpendicular to the applied magnetic field.

FIG. 5.

Development of defect resonance signals for manganese doped BaTiO3 crystals annealed under various oxygen activities. All measurements were made on crystals oriented with the c-axis aligned perpendicular to the applied magnetic field.

Close modal

For samples reduced enough to produce EPR signals related to Mn2+, a new defect resonance signal previously unreported in the literature is also found. The angular dependence of a poled manganese doped BaTiO3 single crystal reduced in a N2/H2 mixture at high temperature is shown in Figure 6. The angle of zero corresponds to the magnetic field directed perpendicular to the electrode surface of the crystal.

FIG. 6.

The orientational dependence of the resonance signals of a poled manganese doped BaTiO3 single crystal is given at room temperature. The angle of 0° corresponds to the direction of poling along the c-axis aligned perpendicular to the applied magnetic field direction.

FIG. 6.

The orientational dependence of the resonance signals of a poled manganese doped BaTiO3 single crystal is given at room temperature. The angle of 0° corresponds to the direction of poling along the c-axis aligned perpendicular to the applied magnetic field direction.

Close modal

The spin Hamiltonian parameters necessary to describe the resonance signals centered around geff ∼ 2 can be found in Table I for the fully coordinated Mn2+ center in tetragonal BaTiO3.

The second resonance signal centered around geff ∼ 6 when the poled direction is aligned perpendicular to the applied magnetic field is a new feature previously unreported for this system. It should be noted that reference to this EPR signal with large ZFS was made by Lambeck and Jonker in a paper published on ferroelectric aging of BaTiO3.64 Reference was made to the future publication of their EPR data, but these data remain unpublished.

The lineshape of an EPR resonance signal is a complex function of temperature, polarization, and local structure.78 It is not necessary for the present discussion to be able to fully describe the linewidth and signal intensity of the given spectra. For this discussion, the important structural parameter is the magnitude of the ZFS. Based on the previous discussion of Figure 2, the two signals in Figure 6 appear to correspond to a defect with a small ZFS parameter centered around geff ∼ 2 typical of fully coordinated Mn2+ and a defect dipole with a large ZFS parameter centered around geff ∼ 6.

The resonance signal at geff ∼ 2 is assigned to a fully coordinated Mn2+ center as it has been characterized in the past rather than the (MnVO)× defect dipole center characterized more recently by Zhang et al.25,30,68,70,76 A new defect resonance signal observed in Figure 6 at geff ∼ 6 can be assigned to the (MnVO)× defect center. This resonance signal is similar to the (FeVO) defect dipole in cubic SrTiO3 also centered at geff ∼ 6.24 The best experimental evidence to support assignment of the geff ∼ 2 EPR resonance signal to a fully coordinated center and the geff ∼ 6 signal in Figure 6 to a defect dipole is the temperature dependence of the EPR signals. The resonance signals for a reduced crystal in each phase of BaTiO3 are shown in Figure 7.

FIG. 7.

EPR signals of a reduced manganese doped BaTiO3 single crystal over a range of temperatures covering all four BaTiO3 phases. The samples were measured at 140 °C, 40 °C, −20 °C, and −110 °C for the cubic, tetragonal, orthorhombic, and rhombohedral phases, respectively, with the crystal oriented with the c-axis in the tetragonal phase aligned perpendicular to the applied magnetic field.

FIG. 7.

EPR signals of a reduced manganese doped BaTiO3 single crystal over a range of temperatures covering all four BaTiO3 phases. The samples were measured at 140 °C, 40 °C, −20 °C, and −110 °C for the cubic, tetragonal, orthorhombic, and rhombohedral phases, respectively, with the crystal oriented with the c-axis in the tetragonal phase aligned perpendicular to the applied magnetic field.

Close modal

Changes to the local oxygen octahedron symmetry around both of the paramagnetic defect centers in each phase of BaTiO3 are shown in Figure 7. The relative magnitude and direction of the axial ZFS vectors in each phase of BaTiO3 for three different local symmetry cases including a defect dipole, paramagnetic ion centered in the oxygen octahedron, and paramagnetic center displaced along the direction of spontaneous polarization are pictured in Figure 8.

FIG. 8.

Effect of local symmetry on the ZFS parameter in BaTiO3 for the case of a defect dipole, fully coordinated and centered acceptor ion, and fully coordinated acceptor ion with average displacements along the directions of spontaneous polarization.

FIG. 8.

Effect of local symmetry on the ZFS parameter in BaTiO3 for the case of a defect dipole, fully coordinated and centered acceptor ion, and fully coordinated acceptor ion with average displacements along the directions of spontaneous polarization.

Close modal

The direction of the ZFS vector is highly sensitive to the symmetry of the local oxygen octahedron. If the paramagnetic defect center is surrounded by six oxygen ions, the ion will either be centered in the octahedron or it will have an average displacement along the direction of spontaneous polarization similar to the Ti4+ ion. As shown in Figure 8, if the paramagnetic ion has six oxygen ligands and is centered, rather than displaced, in the oxygen octahedron, the local field produced by the oxygen ligands that is responsible for the ZFS term will have axial or lower symmetry in all but the cubic phase. Because the γ angle in the rhombohedral phase of BaTiO3 is nearly 90°, this phase will have a nearly negligible second order ZFS constant. The octahedral symmetry of the rhombohedral and paraelectric phases should then have a second order axial ZFS term nearly equal to zero. For a centered ion, the E and D terms should be large and non-zero for the orthorhombic and tetragonal phases.55 It is shown in Figure 7 that the high field resonance responses centered at geff ∼ 2 in the rhombohedral and cubic phase do in fact exhibit cubic symmetry based on the observation that only six lines resulting from the hyperfine splitting term are observable. Negligible ZFS is observed for these phases for the geff ∼ 2 signal. Any deviation towards larger axial or rhombic distortions will split the Zeeman energy at zero magnetic field and produce additional resonance signals in multiples of six. These additional splittings can be viewed in the geff ∼ 2 signals of the orthorhombic and tetragonal phases shown in Figure 7. Referring to Figure 8, this local symmetry suggests the geff ∼ 2 signal is the result of the Mn2+ ion fully coordinated and centered with six oxygen ligands.

For a paramagnetic ion surrounded by only five oxygen ligands and an oxygen vacancy, the local symmetry at the defect center will always be less than cubic; and as a result, there will be a large ZFS term in the spin Hamiltonian. For the case of a nearest neighbor defect complex, unlike the direction of the ZFS vector in the case of an ion placed in the center of the oxygen octahedron, the ZFS term will be directed along a vector between the defect center and oxygen vacancy instead of along the direction of spontaneous polarization. As shown in Figure 8, for the case of BaTiO3, because the angles β and γ are small, the direction of the ZFS vector changes little in each phase of the material. It would appear then that the low field resonance signal at geff ∼ 6 shown in Figure 7 again meets the criteria of a nearest neighbor defect dipole.

It has been shown that the Mn2+ ion in the BaTiO3 lattice, when substituted on the B-site, forms both MnTi and (MnTiVO)× type defects. For the first time, experimental evidence of the (MnTiVO)× defect dipole in a doped BaTiO3 single crystal has been given. While quantitative calculations were not made to determine the concentration of each type of defect center due to the nature of the line broadening in the (MnTiVO)× signal, comparisons between the relative intensities of both types of defect resonance signals qualitatively suggest the (MnTiVO)× defect dipole species is the minority defect. For Mn2+ doping, according to Equation (1), an equal number of oxygen vacancies should be introduced to the system to allow for proper charge compensation [MnTi]=[VO]. The presence of the fully coordinated Mn2+ signal in this study proves that this charge compensation mechanism has not been met. Because EPR is only sensitive to nearest neighbor oxygen vacancy defects, the existence of defect dipoles consisting of acceptor impurities with oxygen vacancies in next nearest, next-next nearest neighbor shells, etc., cannot be discredited. The preference for oxygen vacancies to form defect dipoles with Mn3+ over Mn2+ cannot be discounted as well due to the inability to observe the Mn3+ defect center using X-band EPR spectroscopy. To account for proper ionic charge compensation, additional oxygen vacancies must be present on non-nearest neighbor lattice sites, or large concentrations of Mn3+ must coexist with Mn2+.

This material is based upon work supported by the National Science Foundation, as part of the Center for Dielectric Studies under Grant No. 0628817 and by the Air Force under Grant No. FA9550-14-1-0067.

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