1. Materials-286K 15 th December, 2014 Correlations between structure and transport in BaTiO 3 Santosh Raghavan Materials Department, University of California, Santa Barbara

2. BaTiO 3 2 A. Von Hippel, Reviews of Modern Physics, 22, 221 (1950) B. Sarkar et al, J. Phys D: App Phys, 45, 505304 (2012) Ferroelectric perovskite at RT (T C = 120 °C) Used in capacitors and piezo applications d http://www.mdpi.com/sensors/sensors-10- 01935/article_deploy/html/images/sensors-10-01935f2-1024.png

3. Local Ti distortions toward octahedral faces 3 Q. Zhang, T. Cagin and W. A. Goddard, PNAS, 103, 14695 (2006) BaTiO 3

4. Local Ti distortions toward octahedral faces 4 Q. Zhang, T. Cagin and W. A. Goddard, PNAS, 103, 14695 (2006) Vacancy formation Carrier transport mechanism Metal – Insulator transition BaTiO 3

5. 1. Vacancy formation in Sr 1-x Ba x TiO 3 5 H.M. Chan, M.P. Harmer, D. M. Smyth, J. Am. Ceram. Soc., 69, 507 (1986) D. Makovec, Z. Samardzija, U. Delalut and D. Kolar, J. Am. Ceram. Soc., 78, 2193 (1995) L. Wang, Y. Sakka, Y. Shao, G.A. Botton, T. Kolodiazhnyi, J. Am. Ceram. Soc., 93, 2903 (2010) In SrTiO 3, La + SrTiO 3  La Sr + V Sr ’’ + Ti Ti + 3O O + 1e - In BaTiO 3, 4La + 4BaTiO 3  4La Ba + V Ti ’’’’ + 4Ba Ba + 3Ti Ti + 12O O A-site substitution  A-site vacancy formation! A-site substitution  B-site vacancy formation! But easier to dope the B-site with Nb instead… In Sr 1-x Ba x TiO 3, both A-site and B-site vacancies!

6. 1. Vacancy formation in Sr 1-x Ba x TiO 3 6 V Ti ’’’’ – Most unlikely, highly energetic, major perturbation to the lattice Why does it form instead of V Ba ’’ ? Reason  Ti displacement, Ti—O hybridisation Off-center Ti covalently bonds to Oxygen  Stabilises V Ti ’’’’ Excess charge can be transferred to nearby partial covalent Ti—O bonds L. Wang, Y. Sakka, Y. Shao, G.A. Botton, T. Kolodiazhnyi, J. Am. Ceram. Soc., 93, 2903 (2010) 28% La-doped Sr 1-x Ba x TiO 3

7. 2. BaTiO 3 – Polaron hopping or Band transport? 7 T. Holstein, Annals of Physics, 8, 325 (1959) J.P. Boyeaux and F.M. Michel-Calendini, J. Phys. C: Solid State Phys.,12, 545 (1979) In BaTiO 3, experimentally measured μ Hall and μ drift are comparable! Holstein’s small polaron (SP) model μ ho – SP hopping μ b – SP band transport μ H – SP Hall transport Measured μ Hall and μ drift are supposed to be different

8. 2. BaTiO 3 – Polaron hopping or Band transport? 8 T. Kolodiazhnyi, A. Pedric, N. Niewczas, C. Bridges, A. Safa-Sefat and J.E. Greedan, PRB. 68, 085205 (2003) D. Emin, PRL, 25, 1751 (1970) Temperature – dependant mobility values in BaTiO 3 from literature all over the map… Most recent Y-doped BaTiO 3 samples showed mobility as high as 12 cm 2 /Vs at 120K! – Large polarons? Measured μ Hall and μ drift are supposed to be different but are comparable Band transport with a very heavy mass and phonon scattering? Correlated small polaron hopping theory can account for comparable μ Hall and μ drift ? Ba 0.996 Y 0.004 TiO 3

9. 2. BaTiO 3 – Polaron hopping or Band transport? 9 No last word in transport mechanisms even in the easier SrTiO 3 system Debate on exact BaTiO 3 transport mechanisms expected to continue… A. Verma, A.P. Kajdos, T.A. Cain, S. Stemmer and D. Jena, PRL, 112, 216601 (2014)

10. 3. BaTiO 3 – Metal-Insulator-Transition 10 A. Spinelli, M. A. Torija, C. Liu, C. Jan, C. Leighton, PRB, 81, 155110 (2010) In SrTiO 3, La + SrTiO 3  La Sr + V Sr ’’ + Ti Ti + 3O O + 1e - SrTiO 3  Sr Sr + V O ’’ + Ti Ti + 2O O + ½O 2 + 2e - Mott criterion for MIT at n c ~ 4×10 10 cm -3 Compensated carriers Mott criterion for MIT at n c ~ 10 15 cm -3 For SrTiO 3 Mott criterion for MIT at n c ~ 1×10 20 cm -3 For BaTiO 3 n c 1/3 a H ~ 0.25 SrTiO 3-δ

11. 3. BaTiO 3 – Metal-Insulator-Transition 11 T. Kolodiazhnyi, PRB, 78, 045107 (2008) In BaTiO 3, BaTiO 3  Ba Ba + V O ’’ + Ti Ti + 2O O + ½O 2 + 2e - Mott criterion for MIT at n c ~ 4×10 10 cm -3 Compensated carriers Mott criterion for MIT at n c ~ 10 15 cm -3 For SrTiO 3 Mott criterion for MIT at n c ~ 1×10 20 cm -3 For BaTiO 3 BaTiO 3-δ n c 1/3 a H ~ 0.25

12. 3. BaTiO 3-δ – Ferroelectric metal? 12 T. Kolodiazhnyi, M. Tachibana, H. Kawaji, J. Hwang and E. Takayama-Muromachi, PRL, 104, 147602 (2010) Low symmetry phases seen even in metallic BaTiO 3-δ

13. 3. BaTiO 3-δ – Ferroelectric metal? 13 T. Kolodiazhnyi, M. Tachibana, H. Kawaji, J. Hwang and E. Takayama-Muromachi, PRL, 104, 147602 (2010) Low symmetry phases seen in metallic BaTiO 3-δ T c (C  T) reduces as [V O ’’] increases Change in slope of T c near the MIT Itinerant electrons seem to screen the destabilising effect of V O ’’ to preserve low symmetry phases? Slope says n > n c (1.9×10 21 cm -3 ) needed to destroy the lower symmetry states Not possible to achieve n c with V O ’’

14. 3. BaTiO 3-δ – Ferroelectric metal? 14 n ~ 2×10 21 cm -3 Sample retains long range cubic symmetry at all temperatures Local Ti displacements still persist in the sample at all temperatures!! Highly Nb doped BaTiO 3

15. 3. BaTiO 3-δ – Ferroelectric metal? 15 n ~ 2×10 21 cm -3 Sample retains long range cubic symmetry at all temperatures Local Ti displacements still persist in the sample at all temperatures!! Highly Nb doped BaTiO 3 K. Page, T. kolodiazhnyi, T. Proffen, A.K.Cheetham and R. Seshadri, PRL, 101, 205502 (2008)

16. 3. BaTiO 3-δ – Ferroelectric metal? 16 I-K. Jeong, S. Lee, S-Y Jeong, C. J. Won, N. Hur and A. Llobet, PRB, 84, 064125 (2011) PDF still shows 2 Ti-O distances, albeit reduced Mixture of 40% tetragonal FE phase and 60% metallic cubic phases  Claim no co-existence of metallicity and ferroelectricity?

17. 3. MIT due to e - doping or donor-lattice distortion? 17 Y. Iwazaki, T. Suzuki, Y. Mizuno and S. Tsuneyuki, PRB, 86, 214103 (2012) DFT says pure electron doping can cause C  T transition to vanish! Claim local Ti displacements vanish as well by pure electron doping Calculated n c ~ 1.36×10 21 cm -3 Donors like Nb or V O ’’ only accelerate the disappearance of the C  T transition

18. R +3 Ti +3 O -2 3 Ba +2 Ti +4 O -2 3 Integration of BaTiO 3 with RTiO 3 /SrTiO 3 interfaces 18 A. Ohtomo and H. Y. Hwang, Nature, 427, 423 (2004) R. Ohtsuka, M. Matvejeff, K. Nishio, R. Takahashi, and M. Lippmaa, Appl. Phys. Lett., 96,192111 (2010) P. Moetakef, T. A. Cain, D. G. Ouellette, J. Y. Zhang, D. O. Klenov, A. Janotti, C. G. Van de Walle, S. Rajan, S. J. Allen, and S. Stemmer, Appl. Phys. Lett. 99 (2011) 232116 LSAT 5 nm SmTiO 3 20 nm SrTiO 3 x nm BaTiO 3 ??? Ba 2+ O 2- Study of the BaTiO 3 – RTiO 3 interface Will there still be a 2DEG at the interface? What will happen to the insulating BaTiO 3 films? Similar interface between SrZrO 3 and SmTiO 3 has no 2DEG! Start by inserting thin BaTiO 3 layers in between SrTiO 3 and SmTiO 3

19. Integration of BaTiO 3 with RTiO 3 /SrTiO 3 19 SmTiO 3 SrTiO 3 BaTiO 3 [100][110] [100][110] [100][110]

20. Integration of BaTiO 3 with RTiO 3 /SrTiO 3 20 LSAT 5 nm SmTiO 3 20 nm SrTiO 3 x BaO layers 1 BaO 2 BaO 3 BaO 4 BaO 5 BaO 8 BaO 14 BaO Hall coefficient indicates presence of space charge layer with ~3×10 14 cm -2 of electrons similar to RTiO 3 /SrTiO 3 Increasing BaTiO 3 film thickness, the films switch from metallic to insulating behaviour at 5 BaO (or 4 u.c. BaTiO 3 ) 17 nm BaTiO 3 / 5 nm SmTiO 3

21. Integration of BaTiO 3 with RTiO 3 /SrTiO 3 21 LSAT 5 nm SmTiO 3 20 nm SrTiO 3 x BaO layers 1 BaO 2 BaO 3 BaO 4 BaO 5 BaO 8 BaO 14 BaO 17 nm BaTiO 3 / 5 nm SmTiO 3 If all the electrons are in the BaTiO 3, the critical carrier concentration (remote doping) for metallic BaTiO 3 is n 3D ~ 1.2×10 21 cm -3 (for 5 BaO) T. Kolodiazhnyi et al., PRL 104,147602 (2010) V. Fritsch et al., PRB 64, 045113 (2001)

22. Integration of BaTiO 3 with RTiO 3 /SrTiO 3 22 LSAT 5 nm SmTiO 3 20 nm SrTiO 3 x BaO layers 1 BaO 2 BaO 3 BaO 4 BaO 5 BaO 8 BaO 14 BaO Mobility of the space charge layer shows a sudden drop around 3 to 5 BaO layers Possible that BaTiO 3 switches from tetragonal to cubic around 4 u.c. due to pure electron doping?

23. Summary 23 Q. Zhang, T. Cagin and W. A. Goddard, PNAS, 103, 14695 (2006) Vacancy formation Carrier transport mechanism Metal – Insulator transition BaTiO 3