37. Non-collinear systems
One can classify magnetic materials into two following types:
Collinear systems
Non-collinear systems

38. Ferromagnetism Antiferromagnetism Ferrimagnetism Diamagnetism
Collinear magnetic systems can be listed as follows:
Ferromagnetism
Antiferromagnetism
Ferrimagnetism
Diamagnetism

39. Antiferromagnetism
Ferromagnetism
Ferrimagnetism

40. Canted Antiferromagnetic materials Canted Ferrimagnetic materials
Non-collinear magnetic systems can be listed as follows:
Canted Antiferromagnetic materials
Canted Ferrimagnetic materials
Helical spin array

42. CeIn3
CeSn3 Ce
In or Sn
Cubic
Non-Cubic
Point Groups
Collinear Systems

43. USb2
Collinear Systems

44. Non-Collinear Systems

45. Non-Collinear Systems

46. Non-Collinear Systems
Spin wave

47. What is a difference between them?

48. Why?
Non-Magnetic systems
Magnetic systems

50. LDA:

51. LDA
B || m
In a collinear case moments are aligned along an arbitrary direction. The spin quantization axis can be chosen along m direction. Thus x and y components of the exchange field will vanish resulting in:

52. Since:
Potential matrix is diagonal in spin space:
Up and down panels of the Hamiltonian are decupled. Each part is set up and diagonalized separatly.
Note that spin orbit coupling (SOC) couples these panels. Usually the off-diagonal term of density matrix, resulting from this coupling is ignored.

53. In a non-collinear case moments vary in space and all three components of the scalar product must be considered.
Since:
Potential matrix is not diagonal:

54. WIENNCM