Mitglied der HelmholtzGemeinschaft Vacancyvacancy interaction in Sr Ti

Mitglied der Helmholtz-Gemeinschaft Vacancy-vacancy interaction in Sr. Ti. O 3 bulk and surfaces 02 Apr 2014 Ali Al-Zubi, Gustav Bihlmayer & Stefan Blügel Peter Grünberg Institut and Institute for Advanced Simulation Forschungszentrum Jülich and JARA, Jülich, Germany

Motivation Rutile Ti. O 2[1] Ø low Eform with high no. of ordered VO Ø [001] is energetically preferred Ø increased conductivity due to - e localization function - partial DOS - VO NN Ti band-decomposed charge density DFT (3 x 3 x 4 super cell GGA+U, U=7) 8 VO 6 VO [1] Blanka Magyari-Köpe , Seong Geon Park, Hyung-Dong Lee and Yoshio Nishi, J Mater Sci 47, 7498 (2012) 02 Apr 2014

Motivation VO clustering in Sr. Ti. O 3 [2] A F D B E G C Ø clustering of VO for LDA+U Ø strong e-localization at the apical Ti ion Ø linear clusters preferred but no energies provided! 2 VO 4 VO DFT (4 x 4 x 4 super cell LDA+U, U=5) [2] Cuong et al. , PRL 98, 15503 (2007) 02 Apr 2014

ab-initio defect modeling Sym. Film geometry 9 layers Super cell model (001) surface §DFT calculation 2 x 2 x 4 (80 atoms) §FLAPW-Method Ti Sr §Thin films and supercells §GGA, DFT+Ud single-vacancy formation Energy double-vacancy Interaction Energy Eform= E(0 Vo) – [E(1 Vo) + E(O)] Eint= E(2 Vo)+E(0 Vo) – 2*E(1 Vo) 02 Apr 2014

Bulk calculations single VO: ξ Sr |ε|=1. 1% Ti |ξ|=1. 2% δ ε |δ|=2. 2% Not Relaxed Eform[e. V] Relaxed GGA GGA+U 9. 68 10. 24 8. 45 10. 11 Ø Relaxation gains 1. 5 - 2. 0 e. V [3] Ø Absolute values depend on xc-potential Ø GGA (GGA+U) Eg = 1. 85 (2. 20) e. V single-vacancy formation Energy Eform= E(0 Vo) – [E(1 Vo) + E(O)] [3] Evarestov et al. , Int. J. Quant. Chem. 106, 2173 (2005) 02 Apr 2014

RP phase Sr 2 Ti. O 4 single VO: GGA Sr. O N NN NNN 02 Apr 2014

RP phase Sr 2 Ti. O 4 single VO: GGA Sr. O N NN NNN Relax. [%] (p 1 x 1) c(2 x 2) p(2 x 2) Sr +21. 2 +21. 7 +21. 8 Ti -8. 9 -8. 8 -12. 5 Ø formation energy is strongly affected by structural relaxations Ø repulsive single homogeneous vacancies 02 Apr 2014

RP phase Sr 2 Ti. O 4 single VO: GGA+U Sr. O N NN NNN Relax. [%] (p 1 x 1) c(2 x 2) p(2 x 2) Sr +21. 2 +21. 7 +21. 8 Sr +22. 4 +20. 7 +21. 2 Ti -8. 9 -8. 8 -12. 5 Ti -7. 7 -8. 5 -10. 3 Ø formation energy is strongly affected by structural relaxations Ø repulsive single homogeneous vacancies 02 Apr 2014

RP phase Sr 2 Ti. O 4 single VO: c(2 x 2) un relaxed p(2 x 2) un relaxed Ø formation energy is strongly affected by structural relaxations Ø repulsive single homogeneous vacancies 02 Apr 2014

RP phase Sr 2 Ti. O 4 single VO: c(2 x 2) un relaxed p(2 x 2) relaxed un relaxed Eform(r)-Eform (ur)= -4. 78 e. V -7. 94 e. V Ø formation energy is strongly affected by structural relaxations Ø repulsive single homogeneous vacancies Ø Charge localization on Ti dx 2 -y 2 lowers Eform 02 Apr 2014

Surface calculations single VO: GG A +U Bulk Eform A GG Ø Ti. O 2: increasing the vac-vac distance effectively decreases Eform 02 Apr 2014

Bulk calculations double VO: [2] 4 x 4 x 4 super cell B 2 x 2 x 4 super cell G Ø GGA and GGA+U both predict VO clustering Ø GGA (GGA+U) relaxations minimize the Eint by ~1. 4 e. V (0. 5 e. V) Ø How is the charge ordering? [2] Cuong et al. , PRL 98, 15503 (2007) C Eint= E(2 Vo)+E(0 Vo) – 2*E(1 Vo) 02 Apr 2014

Bulk calculations double VO: z VO-VO (Ti DOS): Ti 1 Ti 3 y x Ti 2 1 2 3 4 Ti 4 Ø the charge is homogeneously spread on neighboring Ti Eg= 2. 0 e. V 02 Apr 2014

Bulk calculations double VO: VO-VO (Ti orbitals): Ø the charge is localized on dx 2 -y 2 z y x Eg= 2. 0 e. V Øthe charge is delocalized dxy, dyz, dzx conductivity! 02 Apr 2014

Bulk calculations double VO: z VO-Ti-VO (Ti DOS): Ti 1 y x Ti 2 2 1 3 Ti 4 4 Eg= 2. 0 e. V Ø 2 e- are localized on Ti 1 Ø 2 e- are delocalized on the outer Ti Conductivity! 02 Apr 2014

Bulk calculations double VO: z VO-Ti-VO (Ti DOS): y x Ti 1 1 Eg= 2. 0 e. V Ø 2 e- are localized on Ti 1 dz 2 02 Apr 2014

Bulk calculations double VO: z VO-Ti-VO (Ti DOS): Ti 2, 3 y x 2 3 Eg= 2. 0 e. V Ø 1 e- is delocalized on Ti 2, 3 dz 2 and dyz 02 Apr 2014

Bulk calculations double VO: z VO-Ti-VO (Ti DOS): y x Ti 4 4 Eg= 2. 0 e. V Ø 1 e- is localized on Ti 4 dyz 02 Apr 2014

Summary o double-VO like to form linear clusters in bulk STO o Relaxations 0. 6 -1. 3 e. V energy gain o possible orthogonal conducting channels o MIT: consider also orbital- and charge ordered states Outlook Ø extend to surfaces and 1 D line defect states in STO Ø double-VO and 1 D line defect in RP Ø extend to Ti. O 2 rich phases Thanks to. . . § Kristof Szot, Wolfgang Speier and Rainer Waser § SFB 917 Nanoswitches TP A 4 02 Apr 2014