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

SLIDE 1

LaMnO3 Revisited

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

SLIDE 2

Outline

(Re)classifying Cooperative Jahn-Teller Distortions in Perovskites LaMnO3 Bulk Epitaxial Thin Films An Approach to a Ferromagnetic/Ferroelectric Multiferroic RMnO3 Compound

2

SLIDE 3

(Re)classifying Cooperative Jahn-Teller Distortions in Perovskites

SLIDE 4

Van Vleck: The octahedral Complex MX6

John Hasbrouck Van Vleck

M

Crystal Field Splitting

X Oh

eg eg a1g eg Q1 a1g Q2 Q3 eg t2g t2g a1g eg t2g Q4 Q5 Q6 t2g

Many difgerent Notations for this in the literature!

Chemists Q Q

O’Brien, M. C. & Chancey, C. Am. J. Phys., 1993, 61, 688-697

Labels of Irreducible Representation M2+, M3+, R3-, R3+, R4-...

Carpenter, M. A. & Howard, C. J. Acta Crystallogr. B., 2009, 65, 134-146

Solid State Physicists QM

1

QR

1 Q2 Q2 MJT RJT Qx Qz Qx R Qz 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 Qi eiqx

Qq

i

1 2 3 4 0 0 0 Strain X 0 0 M 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.

3

SLIDE 5

Van Vleck: The octahedral Complex MX6

John Hasbrouck Van Vleck

M

Crystal Field Splitting

X Oh

eg ⊗ eg = a1g + eg Q1 a1g Q2 Q3 eg t2g t2g a1g eg t2g Q4 Q5 Q6 t2g

Many difgerent Notations for this in the literature!

Chemists Q Q

O’Brien, M. C. & Chancey, C. Am. J. Phys., 1993, 61, 688-697

Labels of Irreducible Representation M2+, M3+, R3-, R3+, R4-...

Carpenter, M. A. & Howard, C. J. Acta Crystallogr. B., 2009, 65, 134-146

Solid State Physicists QM

1

QR

1 Q2 Q2 MJT RJT Qx Qz Qx R Qz 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 Qi eiqx

Qq

i

1 2 3 4 0 0 0 Strain X 0 0 M 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.

3

SLIDE 6

Van Vleck: The octahedral Complex MX6

John Hasbrouck Van Vleck

M

Crystal Field Splitting

X Oh

eg ⊗ eg = a1g + eg Q1 a1g Q2 Q3 eg t2g t2g a1g eg t2g Q4 Q5 Q6 t2g

Many difgerent Notations for this in the literature!

Chemists Q Q

O’Brien, M. C. & Chancey, C. Am. J. Phys., 1993, 61, 688-697

Labels of Irreducible Representation M2+, M3+, R3-, R3+, R4-...

Carpenter, M. A. & Howard, C. J. Acta Crystallogr. B., 2009, 65, 134-146

Solid State Physicists QM

1

QR

1 Q2 Q2 MJT RJT Qx Qz Qx R Qz 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 Qi eiqx

Qq

i

1 2 3 4 0 0 0 Strain X 0 0 M 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.

3

SLIDE 7

Van Vleck: The octahedral Complex MX6

John Hasbrouck Van Vleck

M

Crystal Field Splitting

X Oh

eg ⊗ eg = a1g + eg Q1 a1g Q2 Q3 eg t2g t2g a1g eg t2g Q4 Q5 Q6 t2g

Many difgerent Notations for this in the literature!

Chemists Q Q

O’Brien, M. C. & Chancey, C. Am. J. Phys., 1993, 61, 688-697

Labels of Irreducible Representation M2+, M3+, R3-, R3+, R4-...

Carpenter, M. A. & Howard, C. J. Acta Crystallogr. B., 2009, 65, 134-146

Solid State Physicists QM

1

QR

1 Q2 Q2 MJT RJT Qx Qz Qx R Qz 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 Qi eiqx

Qq

i

1 2 3 4 0 0 0 Strain X 0 0 M 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.

3

SLIDE 8

Van Vleck: The octahedral Complex MX6

John Hasbrouck Van Vleck

M

Crystal Field Splitting

X Oh

eg ⊗ eg = a1g + eg Q1 a1g Q2 Q3 eg t2g ⊗ t2g = a1g + eg + t2g Q4 Q5 Q6 t2g

Many difgerent Notations for this in the literature!

Chemists Q Q

O’Brien, M. C. & Chancey, C. Am. J. Phys., 1993, 61, 688-697

Labels of Irreducible Representation M2+, M3+, R3-, R3+, R4-...

Carpenter, M. A. & Howard, C. J. Acta Crystallogr. B., 2009, 65, 134-146

Solid State Physicists QM

1

QR

1 Q2 Q2 MJT RJT Qx Qz Qx R Qz 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 Qi eiqx

Qq

i

1 2 3 4 0 0 0 Strain X 0 0 M 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.

3

SLIDE 9

Van Vleck: The octahedral Complex MX6

John Hasbrouck Van Vleck

M

Crystal Field Splitting

X Oh

eg ⊗ eg = a1g + eg Q1 a1g Q2 Q3 eg t2g ⊗ t2g = a1g + eg + t2g Q4, Q5, Q6 t2g

Many difgerent Notations for this in the literature!

Chemists Q Q

O’Brien, M. C. & Chancey, C. Am. J. Phys., 1993, 61, 688-697

Labels of Irreducible Representation M2+, M3+, R3-, R3+, R4-...

Carpenter, M. A. & Howard, C. J. Acta Crystallogr. B., 2009, 65, 134-146

Solid State Physicists QM

1

QR

1 Q2 Q2 MJT RJT Qx Qz Qx R Qz 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 Qi eiqx

Qq

i

1 2 3 4 0 0 0 Strain X 0 0 M 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.

3

SLIDE 10

Van Vleck: The octahedral Complex MX6

John Hasbrouck Van Vleck

M

Crystal Field Splitting

X Oh

eg ⊗ eg = a1g + eg Q1 a1g Q2 Q3 eg t2g ⊗ t2g = a1g + eg + t2g Q4, Q5, Q6 t2g

Many difgerent Notations for this in the literature!

Chemists Qθ, Qϵ

O’Brien, M. C. & Chancey, C. Am. J. Phys., 1993, 61, 688-697

Labels of Irreducible Representation M2+, M3+, R3-, R3+, R4-...

Carpenter, M. A. & Howard, C. J. Acta Crystallogr. B., 2009, 65, 134-146

Solid State Physicists QM

1 , QR 1 , Q+ 2 , Q− 2 , MJT, RJT, Qx, Qz, Qx R, Qz 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 Qi eiqx

Qq

i

1 2 3 4 0 0 0 Strain X 0 0 M 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.

3

SLIDE 11

Van Vleck: The octahedral Complex MX6

John Hasbrouck Van Vleck

M

Crystal Field Splitting

X Oh

eg ⊗ eg = a1g + eg Q1 a1g Q2 Q3 eg t2g ⊗ t2g = a1g + eg + t2g Q4, Q5, Q6 t2g

Many difgerent Notations for this in the literature!

Chemists Qθ, Qϵ

O’Brien, M. C. & Chancey, C. Am. J. Phys., 1993, 61, 688-697

Labels of Irreducible Representation M2+, M3+, R3-, R3+, R4-...

Carpenter, M. A. & Howard, C. J. Acta Crystallogr. B., 2009, 65, 134-146

Solid State Physicists QM

1 , QR 1 , Q+ 2 , Q− 2 , MJT, RJT, Qx, Qz, Qx R, Qz 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 Qi eiqx

Qq

i

1 2 3 4 0 0 0 Strain X 0 0 M 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.

3

SLIDE 12

Van Vleck: The octahedral Complex MX6

John Hasbrouck Van Vleck

M

Crystal Field Splitting

X Oh

eg ⊗ eg = a1g + eg Q1 a1g Q2 Q3 eg t2g ⊗ t2g = a1g + eg + t2g Q4, Q5, Q6 t2g

Many difgerent Notations for this in the literature!

Chemists Qθ, Qϵ

O’Brien, M. C. & Chancey, C. Am. J. Phys., 1993, 61, 688-697

Labels of Irreducible Representation M2+, M3+, R3-, R3+, R4-...

Carpenter, M. A. & Howard, C. J. Acta Crystallogr. B., 2009, 65, 134-146

Solid State Physicists QM

1 , QR 1 , Q+ 2 , Q− 2 , MJT, RJT, Qx, Qz, Qx R, Qz 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 Qi · ei⃗

q⃗ x

Qq

i

1 2 3 4 Γ = (0, 0, 0) = Strain X = (π, 0, 0) M = (π, π, 0) R = (π, π, π)

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.

3

SLIDE 13

Q1-Modes and Strains

4

SLIDE 14

Q1-Modes and Strains RNiO3

Mercy, A.et al., Nat. Commun., 2017, 8, 1677

4

SLIDE 15

Q1-Modes and Strains

4

SLIDE 16

Q1-Modes and Strains

Park, S. Y. et al. Phys. Rev. Lett., 2017, 118, 087602

4

SLIDE 17

Q2/Q3-Modes and Strains

5

SLIDE 18

Q2/Q3-Modes and Strains LaMnO3

• 0.4
• 0.2

0.2 0.4

• Amp. [Å]

0.05 0.1 0.15 0.2 ∆E/fu [eV] Q2

R -FM

Q3

R -FM

Q2

M

• F

M

5

SLIDE 19

Q4, Q5, Q6-Modes and Strains

6

SLIDE 20

Q4, Q5, Q6-Modes and Strains

0.84 0.86 0.88 0.9 0.92 0.94 Goldschmidt Factor t

• 0.02

0.02 0.04 Amp.

N d P r L a

Tb Ce Ho Er Tm Yb Lu Y

0.82 0.84 0.86 0.88 0.9 0.92

Y G d S m N d L a

RVO3 RTiO3

Q3

Γ

Q4z

Γ Martínez-Lope, M. J. et al. Inorg. Chem., 2008, 47, 2634-264 Komarek, A. C. et al. Phys. Rev. B, 2007, 75, 224402

6

SLIDE 21

LaMnO3

Bulk

SLIDE 22

JTD In LaMnO3

GS

Pnma a−a−c+ + JTD

O-Phase 750K T 1200K Metallic

ϕ ϕ

Mn3 d4 O’-Phase T TJT 750K Ins. - AFM-A T < 140K

QM

2

Q3

Q4z

How is the ground-state reached? What is the shape of APES? How does the structure couple with the metal to insulator and magnetic transition ? Let’s ask DFT!

K-Mesh 14x14x14 - Ecut 600eV Exc = PBEsol + (U J) U=5.5 eV J=1.5 eV Ground State Structure Band Gap (1.1 eV - Exp 1.1 - 1.9 eV) Anistropy of Dielectric Tensor Magnetic Exchange Constants

7

SLIDE 23

JTD In LaMnO3

GS

Pnma a−a−c+ + JTD

O-Phase 750K < T < 1200K Metallic

ϕz

+

AX

x y z x y z b a c b a c

ϕ-

xy

x

Cubic

Mn3 d4 O’-Phase T TJT 750K Ins. - AFM-A T < 140K

QM

2

Q3

Q4z

How is the ground-state reached? What is the shape of APES? How does the structure couple with the metal to insulator and magnetic transition ? Let’s ask DFT!

K-Mesh 14x14x14 - Ecut 600eV Exc = PBEsol + (U J) U=5.5 eV J=1.5 eV Ground State Structure Band Gap (1.1 eV - Exp 1.1 - 1.9 eV) Anistropy of Dielectric Tensor Magnetic Exchange Constants

7

SLIDE 24

JTD In LaMnO3

GS

Pnma a−a−c+ + JTD

O-Phase 750K < T < 1200K Metallic

ϕz

+

AX

x y z x y z b a c b a c

ϕ-

xy

x

Cubic

Mn3+ = d4 O’-Phase T TJT 750K Ins. - AFM-A T < 140K

QM

2

Q3

Q4z

How is the ground-state reached? What is the shape of APES? How does the structure couple with the metal to insulator and magnetic transition ? Let’s ask DFT!

K-Mesh 14x14x14 - Ecut 600eV Exc = PBEsol + (U J) U=5.5 eV J=1.5 eV Ground State Structure Band Gap (1.1 eV - Exp 1.1 - 1.9 eV) Anistropy of Dielectric Tensor Magnetic Exchange Constants

7

SLIDE 25

JTD In LaMnO3

GS

Pnma a−a−c+ + JTD

O-Phase 750K < T < 1200K Metallic

ϕz

+

AX

x y z x y z b a c b a c

ϕ-

xy

x

Cubic

Mn3+ = d4

→

O’-Phase T < TJT = 750K Ins. - AFM-A T < 140K

QM

2

QΓ

3

QΓ

4z

How is the ground-state reached? What is the shape of APES? How does the structure couple with the metal to insulator and magnetic transition ? Let’s ask DFT!

K-Mesh 14x14x14 - Ecut 600eV Exc = PBEsol + (U J) U=5.5 eV J=1.5 eV Ground State Structure Band Gap (1.1 eV - Exp 1.1 - 1.9 eV) Anistropy of Dielectric Tensor Magnetic Exchange Constants

7

SLIDE 26

JTD In LaMnO3

GS

Pnma a−a−c+ + JTD

O-Phase 750K < T < 1200K Metallic

ϕz

+

AX

x y z x y z b a c b a c

ϕ-

xy

x

Cubic

Mn3+ = d4

→

O’-Phase T < TJT = 750K Ins. - AFM-A T < 140K

QM

2

QΓ

3

QΓ

4z

How is the ground-state reached? What is the shape of APES? How does the structure couple with the metal to insulator and magnetic transition ? Let’s ask DFT!

K-Mesh 14x14x14 - Ecut 600eV Exc = PBEsol + (U J) U=5.5 eV J=1.5 eV Ground State Structure Band Gap (1.1 eV - Exp 1.1 - 1.9 eV) Anistropy of Dielectric Tensor Magnetic Exchange Constants

7

SLIDE 27

JTD In LaMnO3

GS

Pnma a−a−c+ + JTD

O-Phase 750K < T < 1200K Metallic

ϕz

+

AX

x y z x y z b a c b a c

ϕ-

xy

x

Cubic

Mn3+ = d4

→

O’-Phase T < TJT = 750K Ins. - AFM-A T < 140K

QM

2

QΓ

3

QΓ

4z

How is the ground-state reached? What is the shape of APES? How does the structure couple with the metal to insulator and magnetic transition ? Let’s ask DFT!

K-Mesh 14x14x14 - Ecut = 600eV Exc = PBEsol + (U|J) U=5.5 eV J=1.5 eV Ground State Structure Band Gap (1.1 eV - Exp 1.1 - 1.9 eV) Anistropy of Dielectric Tensor Magnetic Exchange Constants

7

SLIDE 28

ϕz

+

AX

x y z x y z b a c b a c

ϕ-

xy

x

Cubic

F

elQM 2 1QM2 2 el i H0 QM

2

j el MO

F

elQM 2 1QM2 2 2 2QM2 2 el i H0 QM

2

j el MO

R F

elQM 2 1QM2 2 2 2QM2 2 1APxy

QM

2 Γ

F

elQM 2 1QM2 2 2 2QM2 2 1APxy

QM

2 3Q3 QM2 2 4Q

2

3 QM2 2

Tetragonal Strain Q3 controls MO

el is a function of

R and MO Selection Rules for Jahn-Teller Active Coordinates in Perovskite Solids depending on Magnetic Space Group ? Include Spin-Phonon and Spin-Strain Coupling?

8

SLIDE 29

ϕz

+

AX

x y z x y z b a c b a c

ϕ-

xy

x

Cubic

Energy [eV]

AFM-A FM

• Amp. Q

M 2

Cubic-LC

• 1

1

• 2
• 1.5
• 1
• 0.5

0.5

• 1

1

• 1

1 a

• a
• c

+ + AX

a

• a
• c

+

F ∝ αelQM

2 + β1QM2 2 el i H0 QM

2

j el MO

F

elQM 2 1QM2 2 2 2QM2 2 el i H0 QM

2

j el MO

R F

elQM 2 1QM2 2 2 2QM2 2 1APxy

QM

2 Γ

F

elQM 2 1QM2 2 2 2QM2 2 1APxy

QM

2 3Q3 QM2 2 4Q

2

3 QM2 2

Tetragonal Strain Q3 controls MO

el is a function of

R and MO Selection Rules for Jahn-Teller Active Coordinates in Perovskite Solids depending on Magnetic Space Group ? Include Spin-Phonon and Spin-Strain Coupling?

8

SLIDE 30

ϕz

+

AX

x y z x y z b a c b a c

ϕ-

xy

x

Cubic

Energy [eV]

AFM-A FM

• Amp. Q

M 2

Cubic-LC

• 1

1

• 2
• 1.5
• 1
• 0.5

0.5

• 1

1

• 1

1 a

• a
• c

+ + AX

a

• a
• c

+

F ∝ αelQM

2 + β1QM2 2

αel = ⟨ Ψ0

i

• ∂H0

∂QM

2

• Ψ0

j

⟩ ⇒ αel(MO) F

elQM 2 1QM2 2 2 2QM2 2 el i H0 QM

2

j el MO

R F

elQM 2 1QM2 2 2 2QM2 2 1APxy

QM

2 Γ

F

elQM 2 1QM2 2 2 2QM2 2 1APxy

QM

2 3Q3 QM2 2 4Q

2

3 QM2 2

Tetragonal Strain Q3 controls MO

el is a function of

R and MO Selection Rules for Jahn-Teller Active Coordinates in Perovskite Solids depending on Magnetic Space Group ? Include Spin-Phonon and Spin-Strain Coupling?

8

SLIDE 31

ϕz

+

AX

x y z x y z b a c b a c

ϕ-

xy

x

Cubic

Energy [eV]

AFM-A FM

• Amp. Q

M 2

Cubic-LC

• 1

1

• 2
• 1.5
• 1
• 0.5

0.5

• 1

1

• 1

1 a

• a
• c

+ + AX

a

• a
• c

+

F ∝ αelQM

2 + β1QM2 2

αel = ⟨ Ψ0

i

• ∂H0

∂QM

2

• Ψ0

j

⟩ ⇒ αel(MO)

• 1

1

• 2
• 1.5
• 1
• 0.5

0.5 Energy [eV]

• 1

1

• 1

1

• Amp. Q

M 2 0.75 1

• 1.2
• 1.15

a a

• a
• c

+

F ∝ αelQM

2 + β1QM2 2

+ β2φ2QM2

2

αel = ⟨ Ψ0

i

• ∂H0

∂QM

2

• Ψ0

j

⟩ ⇒ αel(MO, {R}) F

elQM 2 1QM2 2 2 2QM2 2 1APxy

QM

2 Γ

F

elQM 2 1QM2 2 2 2QM2 2 1APxy

QM

2 3Q3 QM2 2 4Q

2

3 QM2 2

Tetragonal Strain Q3 controls MO

el is a function of

R and MO Selection Rules for Jahn-Teller Active Coordinates in Perovskite Solids depending on Magnetic Space Group ? Include Spin-Phonon and Spin-Strain Coupling?

8

SLIDE 32

ϕz

+

AX

x y z x y z b a c b a c

ϕ-

xy

x

Cubic

Energy [eV]

AFM-A FM

• Amp. Q

M 2

Cubic-LC

• 1

1

• 2
• 1.5
• 1
• 0.5

0.5

• 1

1

• 1

1 a

• a
• c

+ + AX

a

• a
• c

+

F ∝ αelQM

2 + β1QM2 2

αel = ⟨ Ψ0

i

• ∂H0

∂QM

2

• Ψ0

j

⟩ ⇒ αel(MO)

• 1

1

• 2
• 1.5
• 1
• 0.5

0.5 Energy [eV]

• 1

1

• 1

1

• Amp. Q

M 2 0.75 1

• 1.2
• 1.15

a a

• a
• c

+

F ∝ αelQM

2 + β1QM2 2

+ β2φ2QM2

2

αel = ⟨ Ψ0

i

• ∂H0

∂QM

2

• Ψ0

j

⟩ ⇒ αel(MO, {R})

• 1

1

• 2
• 1.5
• 1
• 0.5

0.5 Energy [eV]

• 1

1

• 1

1

• Amp. Q

M 2 0.75 1

• 1.65
• 1.6

0.75 1

• 1.2
• 1.15

a a

• a
• c

+

• F ∝ αelQM

2 + β1QM2 2

+ β2φ2QM2

2

+ γ1APxyφ−QM

2 Γ

F

elQM 2 1QM2 2 2 2QM2 2 1APxy

QM

2 3Q3 QM2 2 4Q

2

3 QM2 2

Tetragonal Strain Q3 controls MO

el is a function of

R and MO Selection Rules for Jahn-Teller Active Coordinates in Perovskite Solids depending on Magnetic Space Group ? Include Spin-Phonon and Spin-Strain Coupling?

8

SLIDE 33

ϕz

+

AX

x y z x y z b a c b a c

ϕ-

xy

x

Cubic

Energy [eV]

AFM-A FM

• Amp. Q

M 2

Cubic-LC

• 1

1

• 2
• 1.5
• 1
• 0.5

0.5

• 1

1

• 1

1 a

• a
• c

+ + AX

a

• a
• c

+

F ∝ αelQM

2 + β1QM2 2

αel = ⟨ Ψ0

i

• ∂H0

∂QM

2

• Ψ0

j

⟩ ⇒ αel(MO)

• 1

1

• 2
• 1.5
• 1
• 0.5

0.5 Energy [eV]

• 1

1

• 1

1

• Amp. Q

M 2 0.75 1

• 1.2
• 1.15

a a

• a
• c

+

F ∝ αelQM

2 + β1QM2 2

+ β2φ2QM2

2

αel = ⟨ Ψ0

i

• ∂H0

∂QM

2

• Ψ0

j

⟩ ⇒ αel(MO, {R})

• 1

1

• 2
• 1.5
• 1
• 0.5

0.5 Energy [eV]

• 1

1

• 1

1

• Amp. Q

M 2 0.75 1

• 1.65
• 1.6

0.75 1

• 1.2
• 1.15

a a

• a
• c

+

• F ∝ αelQM

2 + β1QM2 2

+ β2φ2QM2

2

+ γ1APxyφ−QM

2

• 1

1

• 2
• 1.5
• 1
• 0.5

0.5 Energy [eV]

• 1

1

• 1

1

• Amp. Q

M 2 0.75 1

• 1.65
• 1.6

0.75 1

• 1.2
• 1.15

a a

• a
• c

+

AFM-A FM

• 1

1

• 1

1

• 1

1

Cubic - LC + Q3

Γ

a

• a
• c

+ + AX

a

• a
• c

+

F ∝ αelQM

2 + β1QM2 2

+ β2φ2QM2

2

+ γ1APxyφ−QM

2 + β3QΓ 3 QM2 2

+ β4QΓ2

3 QM2 2

Tetragonal Strain Q3 controls MO

el is a function of

R and MO Selection Rules for Jahn-Teller Active Coordinates in Perovskite Solids depending on Magnetic Space Group ? Include Spin-Phonon and Spin-Strain Coupling?

8

SLIDE 34

ϕz

+

AX

x y z x y z b a c b a c

ϕ-

xy

x

Cubic

Energy [eV]

AFM-A FM

• Amp. Q

M 2

Cubic-LC

• 1

1

• 2
• 1.5
• 1
• 0.5

0.5

• 1

1

• 1

1 a

• a
• c

+ + AX

a

• a
• c

+

F ∝ αelQM

2 + β1QM2 2

αel = ⟨ Ψ0

i

• ∂H0

∂QM

2

• Ψ0

j

⟩ ⇒ αel(MO)

• 1

1

• 2
• 1.5
• 1
• 0.5

0.5 Energy [eV]

• 1

1

• 1

1

• Amp. Q

M 2 0.75 1

• 1.2
• 1.15

a a

• a
• c

+

F ∝ αelQM

2 + β1QM2 2

+ β2φ2QM2

2

αel = ⟨ Ψ0

i

• ∂H0

∂QM

2

• Ψ0

j

⟩ ⇒ αel(MO, {R})

• 1

1

• 2
• 1.5
• 1
• 0.5

0.5 Energy [eV]

• 1

1

• 1

1

• Amp. Q

M 2 0.75 1

• 1.65
• 1.6

0.75 1

• 1.2
• 1.15

a a

• a
• c

+

• F ∝ αelQM

2 + β1QM2 2

+ β2φ2QM2

2

+ γ1APxyφ−QM

2

• 1

1

• 2
• 1.5
• 1
• 0.5

0.5 Energy [eV]

• 1

1

• 1

1

• Amp. Q

M 2 0.75 1

• 1.65
• 1.6

0.75 1

• 1.2
• 1.15

a a

• a
• c

+

AFM-A FM

• 1

1

• 1

1

• 1

1

Cubic - LC + Q3

Γ

a

• a
• c

+ + AX

a

• a
• c

+

F ∝ αelQM

2 + β1QM2 2

+ β2φ2QM2

2

+ γ1APxyφ−QM

2 + β3QΓ 3 QM2 2

+ β4QΓ2

3 QM2 2

• 1

1

• 2
• 1.5
• 1
• 0.5

0.5 Energy [eV]

• 1

1

AFM-A FM

• 1

1

• 1

1

• 1

1

• Amp. Q

M 2

• 1

1

0.75 1

• 1.65
• 1.6

0.75 1

• 1.2
• 1.15

1 1.25

• 1
• 0.95

1 1.25

• 1.65
• 1.6

Tetragonal Strain Q3 controls MO

el is a function of

R and MO Selection Rules for Jahn-Teller Active Coordinates in Perovskite Solids depending on Magnetic Space Group ? Include Spin-Phonon and Spin-Strain Coupling?

8

SLIDE 35

ϕz

+

AX

x y z x y z b a c b a c

ϕ-

xy

x

Cubic

Energy [eV]

AFM-A FM

• Amp. Q

M 2

Cubic-LC

• 1

1

• 2
• 1.5
• 1
• 0.5

0.5

• 1

1

• 1

1 a

• a
• c

+ + AX

a

• a
• c

+

F ∝ αelQM

2 + β1QM2 2

αel = ⟨ Ψ0

i

• ∂H0

∂QM

2

• Ψ0

j

⟩ ⇒ αel(MO)

• 1

1

• 2
• 1.5
• 1
• 0.5

0.5 Energy [eV]

• 1

1

• 1

1

• Amp. Q

M 2 0.75 1

• 1.2
• 1.15

a a

• a
• c

+

F ∝ αelQM

2 + β1QM2 2

+ β2φ2QM2

2

αel = ⟨ Ψ0

i

• ∂H0

∂QM

2

• Ψ0

j

⟩ ⇒ αel(MO, {R})

• 1

1

• 2
• 1.5
• 1
• 0.5

0.5 Energy [eV]

• 1

1

• 1

1

• Amp. Q

M 2 0.75 1

• 1.65
• 1.6

0.75 1

• 1.2
• 1.15

a a

• a
• c

+

• F ∝ αelQM

2 + β1QM2 2

+ β2φ2QM2

2

+ γ1APxyφ−QM

2

• 1

1

• 2
• 1.5
• 1
• 0.5

0.5 Energy [eV]

• 1

1

• 1

1

• Amp. Q

M 2 0.75 1

• 1.65
• 1.6

0.75 1

• 1.2
• 1.15

a a

• a
• c

+

AFM-A FM

• 1

1

• 1

1

• 1

1

Cubic - LC + Q3

Γ

a

• a
• c

+ + AX

a

• a
• c

+

F ∝ αelQM

2 + β1QM2 2

+ β2φ2QM2

2

+ γ1APxyφ−QM

2 + β3QΓ 3 QM2 2

+ β4QΓ2

3 QM2 2

• 1

1

• 2
• 1.5
• 1
• 0.5

0.5 Energy [eV]

• 1

1

AFM-A FM

• 1

1

• 1

1

• 1

1

• Amp. Q

M 2

• 1

1

0.75 1

• 1.65
• 1.6

0.75 1

• 1.2
• 1.15

1 1.25

• 1
• 0.95

1 1.25

• 1.65
• 1.6

Tetragonal Strain QΓ

3 controls MO

αel is a function of {R} and MO Selection Rules for Jahn-Teller Active Coordinates in Perovskite Solids depending on Magnetic Space Group ? Include Spin-Phonon and Spin-Strain Coupling?

8

SLIDE 36

LaMnO3

Epitaxial Thin Films

SLIDE 37

Ferromagnetic LaMnO3 on SrTiO3

9

SLIDE 38

Ferromagnetic LaMnO3 on SrTiO3

9

SLIDE 39

Ferromagnetic LaMnO3 on SrTiO3

9

SLIDE 40

Ferromagnetic LaMnO3 on SrTiO3

c c

Roqueta J.,et al. Cryst. Growth Des. 15.11 (2015)

Å

LMO-STO LMO-Bulk P-1 Pnma FM AFM-A Q3

• 0.005
• 0.04

Q4z

• 0.018
• 0.036

QM

2 (Å)

0.117 0.19 QR

3 (Å)

0.077

• z (Å)

0.44 0.49

xy (Å)

0.62 0.65 AX (Å) 0.26 0.33 Band Gap (eV) 0.49 1.15

10

SLIDE 41

Ferromagnetic LaMnO3 on SrTiO3

c c

Roqueta J.,et al. Cryst. Growth Des. 15.11 (2015)

STO a=b=c 3.905 Å

c0 a0 b0

a b c

LMO-STO LMO-Bulk P-1 Pnma FM AFM-A Q3

• 0.005
• 0.04

Q4z

• 0.018
• 0.036

QM

2 (Å)

0.117 0.19 QR

3 (Å)

0.077

• z (Å)

0.44 0.49

xy (Å)

0.62 0.65 AX (Å) 0.26 0.33 Band Gap (eV) 0.49 1.15

10

SLIDE 42

Ferromagnetic LaMnO3 on SrTiO3

c c

Roqueta J.,et al. Cryst. Growth Des. 15.11 (2015)

STO a=b=c 3.905 Å

c0 a0 b0

a b c

LMO-STO LMO-Bulk P-1 Pnma FM AFM-A QΓ

3

• 0.005
• 0.04

QΓ

4z

• 0.018
• 0.036

QM

2 (Å)

0.117 0.19 QR

3 (Å)

0.077

• φ+

z (Å)

0.44 0.49 φ−

xy (Å)

0.62 0.65 AX (Å) 0.26 0.33 Band Gap (eV) 0.49 1.15

10

SLIDE 43

Ferromagnetic LaMnO3 on SrTiO3

c c

Roqueta J.,et al. Cryst. Growth Des. 15.11 (2015)

STO a=b=c 3.905 Å

c0 a0 b0

a b c

LMO-STO LMO-Bulk P-1 Pnma FM AFM-A QΓ

3

• 0.005
• 0.04

QΓ

4z

• 0.018
• 0.036

QM

2 (Å)

0.117 0.19 QR

3 (Å)

0.077

• φ+

z (Å)

0.44 0.49 φ−

xy (Å)

0.62 0.65 AX (Å) 0.26 0.33 Band Gap (eV) 0.49 1.15

10

SLIDE 44

Ferromagnetic LaMnO3 on SrTiO3

c c

Roqueta J.,et al. Cryst. Growth Des. 15.11 (2015)

STO a=b=c 3.905 Å

c0 a0 b0

a b c

LMO-STO LMO-Bulk P-1 Pnma FM AFM-A QΓ

3

• 0.005
• 0.04

QΓ

4z

• 0.018
• 0.036

QM

2 (Å)

0.117 0.19 QR

3 (Å)

0.077

• φ+

z (Å)

0.44 0.49 φ−

xy (Å)

0.62 0.65 AX (Å) 0.26 0.33 Band Gap (eV) 0.49 1.15

10

SLIDE 45

QR

3 JTD

∆Ε [meV]

• 2
• 1

1 2 No Q2

M

• 80
• 60
• 40
• 20

20 40 Amp. Q3

R

0% a

• a
• c

+

50% a

• a
• c

+

100% a

• a
• c

+

∆Ε ∆Ε ∆Ε ∆Ε ∆Ε

11

SLIDE 46

QR

3 JTD

∆Ε [meV]

• 2
• 1

1 2 No Q2

M

• 80
• 60
• 40
• 20

20 40 Amp. Q3

R

0% a

• a
• c

+

50% a

• a
• c

+

100% a

• a
• c

+

∆Ε [meV]

• 2
• 1

1 2 No Q2

M

• 80
• 60
• 40
• 20

20 40 Amp. Q3

R

∆Ε ∆Ε ∆Ε ∆Ε

11

SLIDE 47

QR

3 JTD

∆Ε [meV]

• 2
• 1

1 2 No Q2

M

• 80
• 60
• 40
• 20

20 40 Amp. Q3

R

0% a

• a
• c

+

50% a

• a
• c

+

100% a

• a
• c

+

∆Ε [meV]

• 2
• 1

1 2 No Q2

M

• 80
• 60
• 40
• 20

20 40 Amp. Q3

R

∆Ε [meV]

• 2
• 1

1 2 No Q2

M

• 80
• 60
• 40
• 20

20 40 Amp. Q3

R

∆Ε ∆Ε ∆Ε

11

SLIDE 48

QR

3 JTD

∆Ε [meV]

• 2
• 1

1 2 No Q2

M

• 80
• 60
• 40
• 20

20 40 Amp. Q3

R

0% a

• a
• c

+

50% a

• a
• c

+

100% a

• a
• c

+

∆Ε [meV]

• 2
• 1

1 2 No Q2

M

• 80
• 60
• 40
• 20

20 40 Amp. Q3

R

∆Ε [meV]

• 2
• 1

1 2 No Q2

M

• 80
• 60
• 40
• 20

20 40 Amp. Q3

R

∆Ε [meV]

• 2
• 1

1 2 No Q2

M

With Q2

M

• 80
• 60
• 40
• 20

20 40

• 2
• 1

1 2 Amp. Q3

R

∆Ε ∆Ε

11

SLIDE 49

QR

3 JTD

∆Ε [meV]

• 2
• 1

1 2 No Q2

M

• 80
• 60
• 40
• 20

20 40 Amp. Q3

R

0% a

• a
• c

+

50% a

• a
• c

+

100% a

• a
• c

+

∆Ε [meV]

• 2
• 1

1 2 No Q2

M

• 80
• 60
• 40
• 20

20 40 Amp. Q3

R

∆Ε [meV]

• 2
• 1

1 2 No Q2

M

• 80
• 60
• 40
• 20

20 40 Amp. Q3

R

∆Ε [meV]

• 2
• 1

1 2 No Q2

M

With Q2

M

• 80
• 60
• 40
• 20

20 40

• 2
• 1

1 2 Amp. Q3

R

∆Ε [meV]

• 2
• 1

1 2 No Q2

M

With Q2

M

• 80
• 60
• 40
• 20

20 40

• 2
• 1

1 2 Amp. Q3

R

∆Ε

11

SLIDE 50

QR

3 JTD

∆Ε [meV]

• 2
• 1

1 2 No Q2

M

• 80
• 60
• 40
• 20

20 40 Amp. Q3

R

0% a

• a
• c

+

50% a

• a
• c

+

100% a

• a
• c

+

∆Ε [meV]

• 2
• 1

1 2 No Q2

M

• 80
• 60
• 40
• 20

20 40 Amp. Q3

R

∆Ε [meV]

• 2
• 1

1 2 No Q2

M

• 80
• 60
• 40
• 20

20 40 Amp. Q3

R

∆Ε [meV]

• 2
• 1

1 2 No Q2

M

With Q2

M

• 80
• 60
• 40
• 20

20 40

• 2
• 1

1 2 Amp. Q3

R

∆Ε [meV]

• 2
• 1

1 2 No Q2

M

With Q2

M

• 80
• 60
• 40
• 20

20 40

• 2
• 1

1 2 Amp. Q3

R

∆Ε [meV]

• 2
• 1

1 2 No Q2

M

With Q2

M

• 80
• 60
• 40
• 20

20 40

• 2
• 1

1 2 Amp. Q3

R

11

SLIDE 51

QR

3 JTD

∆Ε [meV]

• 2
• 1

1 2 No Q2

M

With Q2

M

• 80
• 60
• 40
• 20

20 40

• 2
• 1

1 2 Amp. Q3

R

• 2

2

• 2

2

• 2

2 E - EF [eV]

• 2

2 Γ X S Y Γ Z U R T Z Y T U X S R

• 2

2 Cubic a-a-c+ a-a-c+ + Q3

R

a-a-c+ + Q2

M

a-a-c+ +Q2

M+Q3 R

12

SLIDE 52

Strain Engineering in LaMnO3

LaMnO3 Substrate

ϕ ϕ

− Γ Γ

ϕ ϕ

−

13

SLIDE 53

Strain Engineering in LaMnO3

LaMnO3 Substrate

• 20

20 40 60 E/fu [meV]

3.875 3.895 3.915 3.935 3.955 3.975 3.995

Lattice Constant a0[Å] FM c AFM-A c

• 1.5
• 1
• 0.5

0.5 1 1.5 Epitaxial Strain [%] Pnma c AFM-A

P-1 c FM

ϕ ϕ

− Γ Γ

ϕ ϕ

−

13

SLIDE 54

Strain Engineering in LaMnO3

LaMnO3 Substrate

• 20

20 40 60 E/fu [meV]

3.875 3.895 3.915 3.935 3.955 3.975 3.995

Lattice Constant a0[Å] FM c AFM-A c

• 1.5
• 1
• 0.5

0.5 1 1.5 Epitaxial Strain [%] Pnma c AFM-A

P-1 c FM

• 20

20 40 60 E/fu [meV]

3.875 3.895 3.915 3.935 3.955 3.975 3.995

Lattice Constant a0[Å] FM c AFM-A c 0.25 0.5 0.75

• Amp. [Å]

ϕ

+ z

ϕ

− xy

A X

• 1.5
• 1
• 0.5

0.5 1 1.5 Epitaxial Strain [%] Pnma c AFM-A

P-1 c FM

Γ Γ

ϕ ϕ

−

13

SLIDE 55

Strain Engineering in LaMnO3

LaMnO3 Substrate

• 20

20 40 60 E/fu [meV]

3.875 3.895 3.915 3.935 3.955 3.975 3.995

Lattice Constant a0[Å] FM c AFM-A c

• 1.5
• 1
• 0.5

0.5 1 1.5 Epitaxial Strain [%] Pnma c AFM-A

P-1 c FM

• 20

20 40 60 E/fu [meV]

3.875 3.895 3.915 3.935 3.955 3.975 3.995

Lattice Constant a0[Å] FM c AFM-A c 0.25 0.5 0.75

• Amp. [Å]

ϕ

+ z

ϕ

− xy

A X

• 1.5
• 1
• 0.5

0.5 1 1.5 Epitaxial Strain [%] Pnma c AFM-A

P-1 c FM

• 20

20 40 60 E/fu [meV]

3.875 3.895 3.915 3.935 3.955 3.975 3.995

Lattice Constant a0[Å] FM c AFM-A c

• 0.04
• 0.02

0.02 Amp. Q3

Γ

Q2

Γ

0.25 0.5 0.75

• Amp. [Å]

ϕ

+ z

ϕ

− xy

A X

• 1.5
• 1
• 0.5

0.5 1 1.5 Epitaxial Strain [%] 0.1 0.2

• Amp. [Å]

Q

R 3

Q

M 2

Pnma c AFM-A P-1 c FM 13

SLIDE 56

Strain Engineering in LaMnO3

LaMnO3 Substrate

• 20

20 40 60 E/fu [meV]

3.875 3.895 3.915 3.935 3.955 3.975 3.995

Lattice Constant a0[Å] FM c AFM-A c

• 1.5
• 1
• 0.5

0.5 1 1.5 Epitaxial Strain [%] Pnma c AFM-A

P-1 c FM

• 20

20 40 60 E/fu [meV]

3.875 3.895 3.915 3.935 3.955 3.975 3.995

Lattice Constant a0[Å] FM c AFM-A c 0.25 0.5 0.75

• Amp. [Å]

ϕ

+ z

ϕ

− xy

A X

• 1.5
• 1
• 0.5

0.5 1 1.5 Epitaxial Strain [%] Pnma c AFM-A

P-1 c FM

• 20

20 40 60 E/fu [meV]

3.875 3.895 3.915 3.935 3.955 3.975 3.995

Lattice Constant a0[Å] FM c AFM-A c

• 0.04
• 0.02

0.02 Amp. Q3

Γ

Q2

Γ

0.25 0.5 0.75

• Amp. [Å]

ϕ

+ z

ϕ

− xy

A X

• 1.5
• 1
• 0.5

0.5 1 1.5 Epitaxial Strain [%] 0.1 0.2

• Amp. [Å]

Q

R 3

Q

M 2

Pnma c AFM-A P-1 c FM

0.25 0.5 0.75 1 1.25 1.5 EGap [eV] FM c AFM-A c

• 1.5
• 1
• 0.5

0.5 1 1.5 Epitaxial Strain [%] 4 6 8 10 ε∞ εaa εbb εcc Pnma c AFM-A

P-1 c FM 13

SLIDE 57

An Approach to a Ferromagnetic/Ferroelectric Multiferroic RMnO3 Compound

SLIDE 58

La0.5Bi0.5MnO3 Solid Solution on SrTiO3 Break The Inversion Symmetry Through Cationic Order!

Cation Order E fu meV MO Space Group BG (eV) Layered

• FM

P-1

• Layered
• 5

FM P1

• Chains
• 3

FM P-1

• Rock-Salt
• 10

FM P1 0.38

14

SLIDE 59

La0.5Bi0.5MnO3 Solid Solution on SrTiO3 Break The Inversion Symmetry Through Cationic Order!

La0.5Bi0.5MnO3 SrTiO3

Cation Order ∆E/fu(meV) MO Space Group BG (eV) Layered

• FM

P-1

• Layered
• 5

FM P1

• Chains
• 3

FM P-1

• Rock-Salt
• 10

FM P1 0.38

14

SLIDE 60

La0.5Bi0.5MnO3 Solid Solution on SrTiO3 Break The Inversion Symmetry Through Cationic Order!

La0.5Bi0.5MnO3 SrTiO3

Cation Order ∆E/fu(meV) MO Space Group BG (eV) Layered

• FM

P-1

• Layered
• 5

FM P1

• Chains
• 3

FM P-1

• Rock-Salt
• 10

FM P1 0.38

14

SLIDE 61

Conclusions

• Qq

i a Clear and Revised Notation for Cooperative Jahn-Teller

Distortions in Perovskites

• Decomposition of Distorded Perovskite Structures into orthonormal

Modes and Strains Allows for Profound Studies of Structural-Electronic Interactions in Perovskite Crystal (ISODISTORT: http://stokes.byu.edu/iso/isodistort.php &/or AMPLIMODES: http://www.cryst.ehu.es/cryst/amplimodes.html)

• Study of the APES With Ab-Inito Methods Show That The Magnetic

AFM-A to FM Transition is Controlled by Tetragonal Strain QΓ

3

• A First-Order Jahn-Teller Efgect Takes Place Only in Specifjc

Magnetic Orderings. Do we Need a Revised Jahn-Teller Theorem for Magnetic Space Groups in Solids ?

• The Characterization of Strain/Lattice/Electronic Interplays Permits

to Derive New Design-Ideas for Materials with Remarkable Combination of Properties

15

SLIDE 62

Thank you for your attention!

Questions?

16

SLIDE 63

Modes and Strains under Temperature

300 400 500 600 700 800 900 1000

T (K)

• 0.04
• 0.03
• 0.02
• 0.01

0.01

Amp.

300 400 500 600 700 800 900 1000

T(K)

0.1 0.2 0.3 0.4 0.5 0.6

• Amp. (Å)

AX

Q2

M

Q3

Γ

Q4z

Γ

ϕxy

• ϕz

+

Modes Strains O' O O' O

Thygesen, P. M. M. et al. Phys. Rev. B, 2017, 95, 174107

SLIDE 64

Full Potential Energy Surface

• 1

1

• 2
• 1,5
• 1
• 0,5

0,5 Energy [eV]

• 1

1

AFM-A FM

• 1

1

• 1

1

• 1

1

• 1

1

• 1

1

0,75 1

• 1,65
• 1,6
• 1

1

0,75 1

• 1,9
• 1,85

0,75 1

• 1,2
• 1,15
• 1

1

0,75 1

• 0,95
• 0,9

1 1,25

• 1,15
• 1,1

1 1,25

• 1,8
• 1,75

a

• a
• c

+ + AX

a

• a
• c

+

a

• a
• c

+

a

• a
• c

+ + AX

a

• a
• c

+

a

• a
• c

+ + AX

Cubic-LC Cubic -LC + QΓ

3 + QΓ 4z

a)

b) c)

• Amp. QM

2

Cubic - LC + QΓ

3

SLIDE 65

Full Potential Energy Surface

• 1

1

• 2
• 1,5
• 1
• 0,5

0,5 Energy [eV]

• 1

1

AFM-A FM

• 1

1

• 1

1

• 1

1

• 1

1

• 1

1

0,75 1

• 1,65
• 1,6
• 1

1

0,75 1

• 1,9
• 1,85

0,75 1

• 1,2
• 1,15
• 1

1

0,75 1

• 0,95
• 0,9

1 1,25

• 1,15
• 1,1

1 1,25

• 1,8
• 1,75

a

• a
• c

+ + AX

a

• a
• c

+

a

• a
• c

+

a

• a
• c

+ + AX

a

• a
• c

+

a

• a
• c

+ + AX

Cubic-LC Cubic -LC + QΓ

3 + QΓ 4z

a)

b) c)

• Amp. QM

2

Cubic - LC + QΓ

3

Cubic Cubic + Q4

Γ

Cubic + ϕ Cubic + ϕ + Q4

Γ

a) b) c) d) x y

SLIDE 66

Strain APES

• 0.03 -0.015

0.015

• 25
• 12.5

12.5 25 ∆E /fu [meV] ±0.03 -0.015 0.015 0.03 Amp.

Q3

Γ

• AFM-A

Q3

Γ - FM

Q4z

Γ

Q4z

Γ

• AFM-A
• FM

a) P-1 b) Pnma

+ΔQ3

R

+ΔQ2

M

SLIDE 67

LaMnO3 LaNiO3 Bilayers on SrTiO3

Gibert, M., Nano Letters, 2015, 15, 7355-736

SLIDE 68

Projected Band Structure

Γ X S Y Γ Z U R T Z Y T U X S R

• 3
• 2
• 1

1 2 3 E - EF [eV]

O- p Mn-eg Mn-t2g La-f

SLIDE 69

Infmuence of U|J Parameters

AFM-A FM

U=5, J=1.5 U=8, J=2 Energy [eV]

• 0.2
• 0.4
• 0.6
• 1
• 0.5

0.5 ±1

• 0.5

0.5 1

• Amp. QM

2