LaMnO 3 Revisited Outline (Re)classifying Cooperative Jahn-Teller - PowerPoint PPT Presentation

A Comprehensive First-Principles Study of the Interplay Between Strain, Lattice mode, and Electronic Degrees of Freedom Michael-Marcus Schmitt,Yajun Zhang, Alain Mercy, Eric Bousquet, & Philippe Ghosez XXIVth International Symposium on the Jahn-Teller Efgect 24th-29th June 2018 - Santander Physique Théorique des Matériaux, Q-MAT, CESAM, Université de Liège 1 LaMnO 3 Revisited

Outline (Re)classifying Cooperative Jahn-Teller Distortions in Perovskites LaMnO 3 Bulk Epitaxial Thin Films An Approach to a Ferromagnetic/Ferroelectric Multiferroic RMnO 3 Compound 2

(Re)classifying Cooperative Jahn-Teller Distortions in Perovskites

Q i e iqx 1 Q 2 Q 2 M JT R JT Q x Q z Q x R Q z Q 4 Q 5 Q 6 Q q R He, Z. & Millis, A. J. Phys. Rev. B, 2015, 91 , 195138 Varignon, J.; Bristowe, N. C. et al. ; Sci. Rep., 2015, 5 , 15364 Varignon, J.; Bristowe, N. C. & Ghosez, P. E Phys. Rev. Lett., 2016, 116 , 057602 Ederer, C.; Lin, C. & Millis, A. J. Phys. Rev. B, 2007, 76 , 155105 Perovskite Structure Same Individual Distortion Through Difgerent Cooperative Arrangements A Revised Notation! i = Vlecks Numbering q = q-vector in Cubic BZ Van Vleck: The octahedral Complex MX 6 Q R 1 2 3 4 0 0 0 Strain X 0 0 M 0 R He, Z. & Millis, A. J. Phys. Rev. B, 2015, 91 , 195138 Kanamori, J. J. Appl. Phys., 1960, 31 , 14-23 Van Vleck, J. H. The Journal of Chemical Physics 7.1 (1939): 72-84. i 1 John Hasbrouck Van Vleck a 1g e g e g a 1g e g Q 1 a 1g Q 2 Q 3 e g Q M t 2g t 2g e g O’Brien, M. C. & Chancey, C. Am. J. Phys., 1993, 61 , 688-697 Solid State Physicists Carpenter, M. A. & Howard, C. J. Acta Crystallogr. B., 2009, 65 , 134-146 t 2g Labels of Irreducible Representation M2+, M3+, R3-, R3+, R4-... Q Q Chemists Many difgerent Notations for this in the literature! t 2g 3 Oh M X Crystal Field Splitting

Q i e iqx 1 Q 2 Q 2 M JT R JT Q x Q z Q x R Q z Q 4 Q 5 Q 6 R He, Z. & Millis, A. J. Phys. Rev. B, 2015, 91 , 195138 Varignon, J.; Bristowe, N. C. et al. ; Sci. Rep., 2015, 5 , 15364 Varignon, J.; Bristowe, N. C. & Ghosez, P. E Phys. Rev. Lett., 2016, 116 , 057602 Ederer, C.; Lin, C. & Millis, A. J. Phys. Rev. B, 2007, 76 , 155105 Perovskite Structure Same Individual Distortion Through Difgerent Cooperative Arrangements A Revised Notation! i = Vlecks Numbering q = q-vector in Cubic BZ Q q Van Vleck: The octahedral Complex MX 6 1 2 3 4 0 0 0 Strain X 0 0 M 0 R He, Z. & Millis, A. J. Phys. Rev. B, 2015, 91 , 195138 Kanamori, J. J. Appl. Phys., 1960, 31 , 14-23 Van Vleck, J. H. The Journal of Chemical Physics 7.1 (1939): 72-84. i Q R John Hasbrouck Van Vleck t 2g Q 1 a 1g Q 2 Q 3 e g t 2g t 2g 1 e g a 1g t 2g M2+, M3+, R3-, R3+, R4-... Q M Many difgerent Notations for this in the literature! Carpenter, M. A. & Howard, C. J. Acta Crystallogr. B., 2009, 65 , 134-146 Solid State Physicists Labels of Irreducible Representation O’Brien, M. C. & Chancey, C. Am. J. Phys., 1993, 61 , 688-697 Q Q Chemists 3 e g ⊗ e g = a 1g + e g Oh M X Crystal Field Splitting

Q i e iqx 1 Q 2 Q 2 M JT R JT Q x Q z Q x R Q z Q 4 Q 5 Q 6 R He, Z. & Millis, A. J. Phys. Rev. B, 2015, 91 , 195138 Varignon, J.; Bristowe, N. C. et al. ; Sci. Rep., 2015, 5 , 15364 Varignon, J.; Bristowe, N. C. & Ghosez, P. E Phys. Rev. Lett., 2016, 116 , 057602 Ederer, C.; Lin, C. & Millis, A. J. Phys. Rev. B, 2007, 76 , 155105 Perovskite Structure Same Individual Distortion Through Difgerent Cooperative Arrangements A Revised Notation! i = Vlecks Numbering q = q-vector in Cubic BZ Q q Van Vleck: The octahedral Complex MX 6 1 2 3 4 0 0 0 Strain X 0 0 M 0 R He, Z. & Millis, A. J. Phys. Rev. B, 2015, 91 , 195138 Kanamori, J. J. Appl. Phys., 1960, 31 , 14-23 Van Vleck, J. H. The Journal of Chemical Physics 7.1 (1939): 72-84. i Q R John Hasbrouck Van Vleck t 2g Q 1 a 1g Q 2 Q 3 e g t 2g t 2g 1 e g a 1g t 2g M2+, M3+, R3-, R3+, R4-... Q M Many difgerent Notations for this in the literature! Carpenter, M. A. & Howard, C. J. Acta Crystallogr. B., 2009, 65 , 134-146 Solid State Physicists Labels of Irreducible Representation O’Brien, M. C. & Chancey, C. Am. J. Phys., 1993, 61 , 688-697 Q Q Chemists 3 e g ⊗ e g = a 1g + e g Oh M X Crystal Field Splitting

Q i e iqx 1 Q 2 Q 2 M JT R JT Q x Q z Q x R Q z Q 4 Q 5 Q 6 R He, Z. & Millis, A. J. Phys. Rev. B, 2015, 91 , 195138 Varignon, J.; Bristowe, N. C. et al. ; Sci. Rep., 2015, 5 , 15364 Varignon, J.; Bristowe, N. C. & Ghosez, P. E Phys. Rev. Lett., 2016, 116 , 057602 Ederer, C.; Lin, C. & Millis, A. J. Phys. Rev. B, 2007, 76 , 155105 Perovskite Structure Same Individual Distortion Through Difgerent Cooperative Arrangements A Revised Notation! i = Vlecks Numbering q = q-vector in Cubic BZ Q q Van Vleck: The octahedral Complex MX 6 1 2 3 4 0 0 0 Strain X 0 0 M 0 R He, Z. & Millis, A. J. Phys. Rev. B, 2015, 91 , 195138 Kanamori, J. J. Appl. Phys., 1960, 31 , 14-23 Van Vleck, J. H. The Journal of Chemical Physics 7.1 (1939): 72-84. i Q R John Hasbrouck Van Vleck t 2g Q 1 a 1g Q 2 Q 3 e g t 2g t 2g 1 e g a 1g t 2g M2+, M3+, R3-, R3+, R4-... Q M Many difgerent Notations for this in the literature! Carpenter, M. A. & Howard, C. J. Acta Crystallogr. B., 2009, 65 , 134-146 Solid State Physicists Labels of Irreducible Representation O’Brien, M. C. & Chancey, C. Am. J. Phys., 1993, 61 , 688-697 Q Q Chemists 3 e g ⊗ e g = a 1g + e g Oh M X Crystal Field Splitting

Q i e iqx 1 Q 2 Q 2 M JT R JT Q x Q z Q x R Q z Q 4 Q 5 Q 6 1 Varignon, J.; Bristowe, N. C. & Ghosez, P. E Phys. Rev. Lett., 2016, 116 , 057602 Ederer, C.; Lin, C. & Millis, A. J. Phys. Rev. B, 2007, 76 , 155105 Perovskite Structure Same Individual Distortion Through Difgerent Cooperative Arrangements A Revised Notation! i = Vlecks Numbering q = q-vector in Cubic BZ Q q i 2 He, Z. & Millis, A. J. Phys. Rev. B, 2015, 91 , 195138 3 4 0 0 0 Strain X 0 0 M 0 R He, Z. & Millis, A. J. Phys. Rev. B, 2015, 91 , 195138 Kanamori, J. J. Appl. Phys., 1960, 31 , 14-23 Van Vleck, J. H. The Journal of Chemical Physics 7.1 (1939): 72-84. Varignon, J.; Bristowe, N. C. et al. ; Sci. Rep., 2015, 5 , 15364 Van Vleck: The octahedral Complex MX 6 R Q Q 1 a 1g Q 2 Q 3 e g John Hasbrouck Van Vleck Many difgerent Notations for this in the literature! Chemists t 2g Q Solid State Physicists Q R O’Brien, M. C. & Chancey, C. Am. J. Phys., 1993, 61 , 688-697 Q M 1 Carpenter, M. A. & Howard, C. J. Acta Crystallogr. B., 2009, 65 , 134-146 M2+, M3+, R3-, R3+, R4-... Labels of Irreducible Representation 3 e g ⊗ e g = a 1g + e g Oh M t 2g ⊗ t 2g = a 1g + e g + t 2g X Crystal Field Splitting

Q i e iqx 1 Q 2 Q 2 M JT R JT Q x Q z Q x R Q z Kanamori, J. J. Appl. Phys., 1960, 31 , 14-23 Q q Varignon, J.; Bristowe, N. C. et al. ; Sci. Rep., 2015, 5 , 15364 Varignon, J.; Bristowe, N. C. & Ghosez, P. E Phys. Rev. Lett., 2016, 116 , 057602 Ederer, C.; Lin, C. & Millis, A. J. Phys. Rev. B, 2007, 76 , 155105 Perovskite Structure Same Individual Distortion Through Difgerent Cooperative Arrangements A Revised Notation! i = Vlecks Numbering q = q-vector in Cubic BZ Van Vleck, J. H. The Journal of Chemical Physics 7.1 (1939): 72-84. i He, Z. & Millis, A. J. Phys. Rev. B, 2015, 91 , 195138 1 He, Z. & Millis, A. J. Phys. Rev. B, 2015, 91 , 195138 3 4 0 0 0 Strain X 0 0 M 0 R 2 Van Vleck: The octahedral Complex MX 6 R Q Q 1 a 1g Q 2 Q 3 e g John Hasbrouck Van Vleck Many difgerent Notations for this in the literature! Chemists t 2g Q Solid State Physicists Q R O’Brien, M. C. & Chancey, C. Am. J. Phys., 1993, 61 , 688-697 Q M 1 Carpenter, M. A. & Howard, C. J. Acta Crystallogr. B., 2009, 65 , 134-146 M2+, M3+, R3-, R3+, R4-... Labels of Irreducible Representation 3 e g ⊗ e g = a 1g + e g Oh M t 2g ⊗ t 2g = a 1g + e g + t 2g X Q 4 , Q 5 , Q 6 Crystal Field Splitting

Q i e iqx Van Vleck: The octahedral Complex MX 6 1 Varignon, J.; Bristowe, N. C. & Ghosez, P. E Phys. Rev. Lett., 2016, 116 , 057602 Ederer, C.; Lin, C. & Millis, A. J. Phys. Rev. B, 2007, 76 , 155105 Perovskite Structure Same Individual Distortion Through Difgerent Cooperative Arrangements A Revised Notation! i = Vlecks Numbering q = q-vector in Cubic BZ Q q i 2 He, Z. & Millis, A. J. Phys. Rev. B, 2015, 91 , 195138 3 4 0 0 0 Strain X 0 0 M 0 R He, Z. & Millis, A. J. Phys. Rev. B, 2015, 91 , 195138 Kanamori, J. J. Appl. Phys., 1960, 31 , 14-23 Van Vleck, J. H. The Journal of Chemical Physics 7.1 (1939): 72-84. Varignon, J.; Bristowe, N. C. et al. ; Sci. Rep., 2015, 5 , 15364 3 John Hasbrouck Van Vleck O’Brien, M. C. & Chancey, C. Am. J. Phys., 1993, 61 , 688-697 Q 1 a 1g Q 2 Q 3 e g Many difgerent Notations for this in the literature! Chemists t 2g Labels of Irreducible Representation Carpenter, M. A. & Howard, C. J. Acta Crystallogr. B., 2009, 65 , 134-146 Solid State Physicists Q M M2+, M3+, R3-, R3+, R4-... e g ⊗ e g = a 1g + e g Q θ , Q ϵ Oh M t 2g ⊗ t 2g = a 1g + e g + t 2g X 1 , Q + 1 , Q R 2 , Q − 2 , M JT , R JT , Q x , Q z , Q x R , Q z R ... Q 4 , Q 5 , Q 6 Crystal Field Splitting