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1 Electron-pinned Defect-dipoles for High-Performance Colossal Permittivity Materials Wanbiao Hu 1, Yun Liu 1,*, Ray L. Withers 1, Terry J. Frankcombe 1, Lasse Norén 1, Amanda Snashall 1, Melanie Kitchin 1, Paul Smith 1, Bill Gong 2, Hua Chen 3, Jason Schiemer 1, Frank Brink 3 and Jennifer Wong-Leung 3,4 1 Research School of Chemistry, The Australian National University, ACT 0200, Australia 2 Mark Wainwright Analytical Centre, The University of New South Wales, Kensington, Sydney, NSW 2052, Australia 3 Centre for Advanced Microscopy, The Australian National University, ACT 0200, Australia 4 Research School of Physics and Engineering, The Australian National University, Canberra, ACT 0200, Australia * Correspondence and request for materials should be addressed to Yun Liu via yliu@rsc.anu.edu.au NATURE MATERIALS 1

2 Figure S1 Room-temperature dielectric permittivity and dielectric loss tangent vs. frequency at a (Nb+In) doping level of 20%. Inset is the impedance spectrum, which contains a low-frequency tail corresponding to a grain boundary contribution to the interfacial polarization giving rise to a significantly enhanced low-frequency permittivity and a loss relaxation peak. The impedance spectrum cannot be fitted by using only one parallel RQ element, but requires r twoo connected in seriess i.e. (R g Q g )(R gb Q gb ). Here, R g and R g b represent the grain and grain boundary b resistances, respectivelyr y. Q i (i=g, gb) is the corresponding phase element 1. Fitting the spectrumm gives the grain parameters shown in the inset. 2 NATURE MATERIALS

3 SUPPLEMENTARY INFORMATION spectrum is dominatedd by grain boundary effects, quite different from the behaviour of the t (Nb+In) co- frequency doped samples. By contrast, In-only doping results in low permittivity and low losss in the higher range. Figure S2 Room-temperaturee dielectric properties for Nb/In-only doping. (a) Permittivity and loss tangent for Nb-only doping. (b) Impedance spectra for Nb-only doping. (c) Permittivity and dielectric loss tangentt for In-only doping. Although Nb-only doping can also lead to very high dielectric permittivity, the permittivity quickly falls with increasing frequency and is accompanie ed by relatively high dielectric loss. Note also that there exist dielectric relaxation peaks on the loss curves. Thesee observations are attributed to space charges accumulating at the grain boundaries, a typical interfacial polarization effect 2. That is, the grain boundary regions largely contribute to the high permittivity as well as the high loss for the Nb-only and In-only samples. Particularly apparent for the 10% Nb-only doped d sample is that the impedance NATURE MATERIALS 3

4 Figure S3I Temperature dependences of the dielectricc properties of 0.5% (Nb+In) co-doped rutile TiO 2 at a range of frequencies. Figure S3II Complex impedancee plots [Z (ω)-z (ω)] (solid dots) of 0.5% % (Nb+In) co-doped TiO 2 measured at selected temperatures. The number for marks of T-number-K denotes the measurement temperature [unit: K]. Dielectric relaxation is observed in two temperature ranges: one occurs in the high temperature range above 450 K, as discussed in the manuscript for 10% (Nb+In) co-doped TiOO 2 [as well as presented in Figure S3I for 0.5% (Nb+In) co-doped TiO 2 ] while the other occurs only at a temperature below 50 K. Below 30 K, the measured dielectric permittivity quickly falls two orders of magnitude, i.e. from m the 10 4 level down to the 10 2 level. In order to identify the nature of this relaxation, complex impedance measurements of 0.5% (Nb+In) co-doped TiO 2 were carried out at selected temperatures (see Figure S3II). Note that in the low 4 NATURE MATERIALS

5 SUPPLEMENTARY INFORMATION temperature range (see Figure S3II a and the correspondingly enlarged b), only an essentially linear arc with a high-frequency near-zero intercept is observed from each complex impedance plot (more clearly seen from the enlarged Figure S3II b). This means that the complex impedance contains only one constituent intragrain contribution which can be considered to be the source of the colossal dielectric permittivity 3. For comparison purposes, plots of the high-temperature complex impedance are also given in the case of 0.5% (Nb+In) co-doped TiO 2 (Figure S3II c and the correspondingly enlarged d). As clearly seen from Figure S3II, where the solid lines correspond to the fitting results (solid lines) using a Cole-Cole model, the interfacial effect isn't observed at temperatures below 400 K but appears only at ~450 K. This is in good agreement with the (only high-temperature) Maxwell-Wagner type, interfacial polarization observed from dielectric spectroscopies in Figure S3I and Figure 2 in the manuscript. The very low temperature dielectric relaxation (< 50 K) is attributed to electron freezing in the defect clusters that can be described by the equation 4 : = exp( U/ kt) 0 where τ is the relaxation time, k B the Boltzmann constant, and U the activation energy. From the relaxation peaks in the dielectric loss spectra, the relaxation time (τ) associated with each frequency was measured. A linear fitting (seen the inset to Figure S3I) of ln τ vs. 1/T, then gives U = 15 mev. Such an activation energy is far smaller than the typical grain activation energy (~ 0.78 ev) and also cannot be attributed to the motion/hoping of oxygen vacancies at such a low temperature range since the activation energy for motion/hopping of oxygen vacancies is generally quite high no matter whether the vacancies are intrinsic or originate from ionic substitution. For instance, the activation energy of oxygen vacancies is 0.91 ev for BaTiO 5 3, ev for KNbO 6 3, and ev for cation substituted SrTiO 7 3. It can therefore only be attributed to the energy of activating/freezing electrons in the defect-dipoles. It has been reported that electrons are easily self-trapped in a defective (even defect-free) rutile structure at a Ti site and can also be thermally activated with a relatively lower low activation energy 8. Similar behavior has also been found in perovskite ceramics with an energy of mev for the low-temperature activation of polaron-like defects 9. B NATURE MATERIALS 5

6 Figure S3III Temperature-dependent dielectric permittivity and loss l tangent of 0.5% (Nb+In)( doped TiO 2 with different electrodes (dots: Au, Lines: L Ag). Unlike either CaCu 3 Ti 4 O 12 (CCTO) 10 or La 2-x Sr x NiO 4 (x = 1/3 or 1/8) 11 (LSNO), wheree the dielectric permittivity varies ~1900% (in the plateau region) when the Ag electrodes are replaced by Au, changingg the electrode material (Ag and Au, respectively), in our co-doped case, does not significantly alter the dielectric permittivity (only ~ 35%) in the case of co-doped TiO 2. This strongly suggests that the surface barrier layer capacitance (SBLC) contribution to the observedd high dielectric permittivity, in our case, is not dominant. Figure S3IV DC conductivity of 0.5% (Nb+In) doped TiO 2 as a function of temperature. The measured DC conductivity of the LSNO family is from ~10-7 Ω -1 1 cm -1 at loww temperature to ~ Ω -1 cm - 1 at 300 K 1 12 while that of CCTO also variess from ~10-7 Ω -1 cm -1 at a low temperature to ~10-1 Ω -1 cm -1 at 6 NATURE MATERIALS

7 SUPPLEMENTARY INFORMATION 300 K 10. The measured DC conductivity (Figure S3IV) of co-doped TiO 2 is 3-4 orders of magnitude lower than those of both LSNO and CCTO. It is therefore highly unlikely that there is a significant SBLC effect in co-doped TiO 2 by contrast with LSNO and CCTO. It is also clearly seen that neither a single Arrhenius nor a Mott-VRH model can fit the DC conductivity over the whole temperature range. Therefore, the lowtemperature DC conductivity has little relevance to the dielectric relaxation observed in this temperature range. NATURE MATERIALS 7

8 Figure S4 Grain conductivities (ln σ g ) for 10% Nb-only doped TiOO 2 versus temperature, fitted by the Arrhenius (bottom scale) and Mott (top scale) ) models, respectively.. It can clearly be seen that the plot of ln σ g vs. 1/TT deviates from the linear Arrhenius law but fits much better to the Mott variable-range-hopping (Mott-VRH) relation in the case of this Nb-only doped TiO 2 sample. This allows the delocalized charges (or electrons) to be easily transported towards,, and to accumulate within, interfaces (or grain boundaries) to form interfacial polarization. Such transport is intrinsically quite different from the co-doped case, in which defect-dipoles are highly localizedd and respond to an external field via reorientation. For Nb-only doped rutile TiO 2, both experimental and theoretical studies support the notion thatt small polarons (e.g. electrons) can form complexes with Nb impurities, acting as shallow donors with a migration barrier for delocalized electrons of 0.02~0.03 ev. The experimental value is 0..02~0.03 ev V 13,14 while the calculated value 15 is 0.03 ev, respectively. 8 NATURE MATERIALS

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10 Figure S5 XRD patterns of rutile TiO 2 with dopants of (a) Nb+In, (b) Nb and (c) In at different doping levels. The red and green bars at the bottom are the standardd rutile TiOO 2 pattern (JCPDS No ) and the In 2 TiO 5 pattern (JCPDS No ), respectively. The asteriskss denote the NaCl internal standard. Nb can be easily doped into the rutilee TiO 2 structure (Figure S5-b). When co-doped with Nb, In can also be doped into the rutile TiO 2 structuree (Figure S5-a). By contrast, In cannot be separately doped into the rutile TiO 2 structure on its own at In doping levels beyondd 1%. The XRD patterns beyond this nominal In dopant level therefore contain a new impurity phase of In 2 TiOT 5 as shown by the peaks within the blue rectangular regions (Figure S5-c). 10 NATURE MATERIALS

11 SUPPLEMENTARY INFORMATION Figure S6 Valence state and defect characterizations for (Nb+In) or Nb/In-only dopedd TiO 2. (a) Core level XPS of Nb 3d electrons and corresponding fitting results. (b) Core C level XPS of Ti 2p electrons. (c) EPR spectra of 0.5% Nb doped TiO 2 measured at 67.5 K. NATURE MATERIALS 11

12 Figure S7 Lattice parameters (volume (V), axis ratio (c/a), a and c) c of (Nb+In) or Nb doped TiO 2 as a function of the doping levels. Black squares and red circles correspond to the lattice parameters of (Nb+In) and Nb-only doping, respectively. Grey arrowss (Figure S7-a) with ovals direct to the ordinate axis. Both (Nb+In) co-doping and Nb-only doping lead to a linear increase for V, a and c. A great difference is thatt Nbonly doping leads to a decrease in c/a while the opposite is observed after a incorporating additional In. Note thatt the ionic radii for Nb 5+ and In 3+ in oxygen octahedral co-ordination are 78 pm and 94 pm respectively, slightly larger than that for Ti 4+ of 74 pm. A natural conclusion is that elongation of the a axis seems to correlate with the contribution from the dopant Nb ions, while the presence off In dopantt ions seems to preferentially contribute to the expansion of the c axis. When considering that In 3+ possesses much the largest ionic radius (by comparison with that of Nb 5+ and Ti 4+ ) in octahedron, the involved In 3+ must be located preferentially along the c-axiss direction relative to the Nb 5+ locations. 12 NATURE MATERIALS

13 SUPPLEMENTARY INFORMATION Figure S8 Electronic density of states for (Nb+In)-codoped (a) and Nb-doped (b) TiO 2. Spin up states are shown on the positive y axis and spin downn states are shown on the negativee y axis. The site-projected densities of states for the two Ti 3+ ions are shown as red and blue traces. These projected densities of states correspond to the excess spin up (unpaired) electronic states, indicating that the unpaired spin density is localized to the Ti 3+ centers in the case of (Nb+In) co-dopedd TiO 2 and delocalized d in Nb-only doped TiO2. NATURE MATERIALS 13

14 Table S1: Projection of the singly occupied band (SOB) wave functions onto atom-centred s, p and d spherical harmonics centered on the two Ti 3+ ions. (Nb+In) co-doped TiO 2 Nb-only doped TiO 2 SOB1 SOB2 Ion1 Ion Ion1 Ion Table S1 shows the coefficients of components of the wave functions of the two singly occupied bands projected onto the Ti 3+ atomic sites. For these bands the projection coefficients on to all other atomic sites are an order of magnitude smaller, corroborating the density of states evidence that the unpaired spin density is localized on Ti 3+. However, this table shows that a critical difference between the Nb-doped and (Nb+In)- co-doped cases is that in the case of co-doping the unpaired spins on each Ti 3+ site are independent, whereas for Nb-only doping the electronic states are delocalized between Ti 3+ ions. 14 NATURE MATERIALS

15 SUPPLEMENTARY INFORMATION References 1 Haile, S. M., West, D. L. & Campbell, J. The role of microstructure and processing on the proton conducting properties of gadolinium-doped barium cerate. J. Mater. Res. 13, (1998). 2 Sarkar, S., Jana, P. K. & Chaudhuri, B. K. Colossal internal barrier layer capacitance effect in polycrystalline copper (II) oxide. Appl. Phys. Lett. 92, (2008). 3 Yang, J. et al. Small polaron migration associated multiple dielectric responses of multiferroic DyMnO 3 polycrystal in low temperature region. Appl. Phys. Lett. 101, (2012). 4 Homes, C. C., Vogt, T., Shapiro, S. M., Wakimoto, S. & Ramirez, A. P. Optical response of highdielectric-constant perovskite-related oxide. Science 293, (2001). 5 Warren, W. L., Vanheusden, K., Dimos, D., Pike, G. E. & Tuttle, B. A. Oxygen vacancy motion in perovskite oxides. J. Am. Ceram. Soc. 79, (1996). 6 Singh, G., Tiwari, V. S. & Gupta, P. K. Role of oxygen vacancies on relaxation and conduction behavior of KNbO 3 ceramic. J. Appl. Phys. 107, (2010). 7 Yu, Z., Ang, C. & Cross, L. E. Oxygen-vacancy-related dielectric anomalies in La: SrTiO 3. Appl. Phys. Lett. 74, (1999). 8 Deak, P., Aradi, B. & Frauenheim, T. Quantitative theory of the oxygen vacancy and carrier selftrapping in bulk TiO 2. Phys. Rev. B 86, (2012). 9 Lemanov, V. V., Sotnikov, A. V., Smirnova, E. P. & Weihnacht, M. Giant dielectric relaxation in SrTiO 3 -SrMg 1/3 Nb 2/3 O 3 and SrTiO 3 -SrSc 1/2 Ta 1/2 O 3 solid solutions. Phys. Solid State 44, (2002). 10 Krohns, S., Lunkenheimer, P., Ebbinghaus, S. G. & Loidl, A. Colossal dielectric constants in singlecrystalline and ceramic CaCu 3 Ti 4 O 12 investigated by broadband dielectric spectroscopy. J. Appl. Phys. 103, (2008). 11 Krohns, S. et al. Colossal dielectric constant up to gigahertz at room temperature. Appl. Phys. Lett. 94, (2009). 12 Sippel, P. et al. Dielectric signature of charge order in lanthanum nickelates. European Physical Journal B 85, 235 (2012). 13 Morris, D. et al. Photoemission and STM study of the electronic structure of Nb-doped TiO 2. Phys. Rev. B 61, (2000). 14 Deford, J. W. & Johnson, O. W. Electron transport properties in rutile from 6 to 40 K. J. Appl. Phys. 54, (1983). 15 Janotti, A., Franchini, C., Varley, J. B., Kresse, G. & Van de Walle, C. G. Dual behavior of excess electrons in rutile TiO 2. Phys. Status Solidi RRL 7, (2013). NATURE MATERIALS 15