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Magnetic Mode Calculations in Ideal Perovskite Sites

Hand calculations of magnetic modes in an ideal cubic Perovskite site involving LaMnO3 and TbMnO3. Covers physical and linear algebra problems, as well as group theory elements and representations.

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Magnetic Mode Calculations in Ideal Perovskite Sites

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  1. Hand calculations of magnetic modes A. Daoud-Aladine (ISIS)

  2. Physical problem Ideal cubic Perovskite Site A LaMnO3 TN=150K k=(0 0 0) La/Tb TbMnO3 TN=41K k=(0.28 0 0) O Mn Pnma m [010]O [001]C [101]O [010]C n m n a a

  3. Physical problem LaMnO3 TN=150K k=(0 0 0) (a) TbMnO3 TN=41K k=(0.28 0 0) (b) Pnma m [101]O [010]C m

  4. Linear algebra problem (a) (b) e1z Sk1 e2y Sk2 Sk3 a b e3x Pnma c Sk4

  5. Linear algebra problem e1z Sk1 Hermitian vector space (complex) of dimension 12 e2y Sk2 Sk3 a b e3x Pnma c Sk4

  6. The group G=Pnma Zero blocks elements

  7. The group of k: Gk (b) Gk= P21ma (a) Gk = Pnma 2x k G = Pnma a (x) b (y) c (z) mxy mxz

  8. Irreps of Gk (a) (b)

  9. Representation of gGk Sk1 Sk2 Sk3 Sk4 c b a (a and b) Trivial Ex1: Identity operation 1

  10. Representation of gGk (a and b) Trivial Ex1: Identity operation 1

  11. Representation of gGk Sk1 Sk2 Sk3 Sk4 c b a (a only) Trivial Ex2: Inversion -1

  12. Representation of gGk (a only) Trivial Ex2: Inversion -1

  13. Representation of gGk Sk1 Sk2 Sk3 Sk4 (a and b) Ex1: 21 axis along x Point Mn1: 1/2, 1/2, 0 = Mn3 0,0,1/2 c b Sk Spin . Sk a

  14. Representation of gGk e1z Sk1 e1y e1x 1 1’ Sk1’ (a and b) Ex1: 21 axis along x e1z e2y ap(21,3) c b e3x e3x a

  15. Representation of gGk (a and b) Ex1: 21 axis along x

  16. Representation of gGk (a only) Ex2: Glide plane n axis  x e1z e2y e3x

  17. Representation of gGk (a only) Ex2: Glide plane n axis  x e1z e2y e3x

  18. Representation of gGk (a only) Ex2: Glide plane n axis  x

  19. Decomposition

  20. Decomposition = 12

  21. Decomposition = 0 etc…

  22. Decomposition

  23. Projection

  24. Projection

  25. Projection

  26. Projection

  27. Magnetic structure (b) TbMnO3 TN=41K k=(0.28 0 0)

  28. Magnetic structure

  29. Magnetic structure (b)

  30. Magnetic structure Example (a)

  31. Magnetic structure

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