hand calculations of magnetic modes
DESCRIPTION
Hand calculations of magnetic modes. A. Daoud-Aladine (ISIS). Physical problem. Ideal cubic Perovskite. Site A. LaMnO 3 T N =150K k=(0 0 0). La/Tb. TbMnO 3 T N =41K k=(0.28 0 0). O. Mn. P nma. m. [010] O [001] C. [101] O [010] C. n. m. n. a. a. Physical problem. - PowerPoint PPT PresentationTRANSCRIPT
Hand calculations of magnetic modes
A. Daoud-Aladine (ISIS)
Physical problem
Site A
Ideal cubic Perovskite
Pnma
[010]O
[001]C
[101]O
[010]C
La/Tb
n
n
aa
m
m
Mn O
LaMnO3 TN=150K k=(0 0 0)
TbMnO3 TN=41K k=(0.28 0 0)
(b)
(a)
Pnma
[101]O
[010]C m
m
LaMnO3 TN=150K k=(0 0 0)
TbMnO3 TN=41K k=(0.28 0 0)
Physical problem
(b)
(a)
a
b
c
1z
2y
3x
Linear algebra problem
Sk1
Sk2
Sk3
Sk4
Pnma
a
b
c
1z
2y
3x
Linear algebra problem
Sk1
Sk2
Sk3
Sk4
Hermitian vector space
(complex)of dimension 12
Pnma
The group G=Pnma
Zero blocks elements
The group of k: Gk
G = Pnmaa (x)
b (y)
c (z)
k
mxy mxz
(a) Gk = Pnma
(b) Gk=
P21ma
2x
Irreps of Gk
(a)
(b)
Representation of gGk
c
b
a
Sk1
Sk2
Sk3
Sk4
(a and b) Trivial Ex1: Identity operation 1
Representation of gGk
(a and b) Trivial Ex1: Identity operation 1
Representation of gGk
(a only) Trivial Ex2: Inversion -1
c
b
a
Sk1
Sk2
Sk3
Sk4
Representation of gGk
(a only) Trivial Ex2: Inversion -1
Representation of gGk
c
b
a
Sk1
Sk2
Sk3
Sk4
Point
Sk . SkSpin
Mn1: 0,0,1/2 1/2, 1/2, 0 = Mn3
(a and b) Ex1: 21 axis along x
Representation of gGk
1z
2y
3x 3x
ap(21,3)
1
1z
1y1x
1’c
b
a Sk1’
Sk1
(a and b) Ex1: 21 axis along x
Representation of gGk(a and b) Ex1: 21 axis along x
Representation of gGk(a only) Ex2: Glide plane n axis x
1z
2y
3x
Representation of gGk(a only) Ex2: Glide plane n axis x
1z
2y
3x
Representation of gGk(a only) Ex2: Glide plane n axis x
Decomposition
Decomposition
= 12
Decomposition
= 0 etc…
Decomposition
Projection
Projection
Projection
Projection
Magnetic structure
(b) TbMnO3 TN=41K k=(0.28 0 0)
Magnetic structure
Magnetic structure(b)
Example (a)
Magnetic structure
Magnetic structure