tailieunhanh - Neutron Scattering from Magnetic Materials part 5

Tham khảo tài liệu 'neutron scattering from magnetic materials part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Representation analysis of magnetic structures 115 where Rap Ta atp -Tap e T it is easily shown that dkv a dkv fi exp -i a k - k ĩfỊ dkv afi . 42 Three different instances are then encountered If the space group is symmorphic that is all the Ta are identically null then the dkv are merely the irreducible representations of the little co-group G0 k . If the space group is nonsymmorphic that is at least one Ta 0 and if k is inside the Brillouin zone then a k k in the Brillouin zone k is equivalent to itself and the dkv are again the irreducible representations of the little co-group G0 k . If the space group is nonsymmorphic that is at least one Ta 0 and if k is at the surface of the Brillouin zone then the representations are with weight. A method developed by Olbrychski 37 allows us to directly determine the small irreducible representation 8kv which can be used when the space group is nonsymmorphic and k is at the surface of the Brillouin zone but is not restricted to this instance. The method was concretely used in works such as 5 38 39 . The little group f is abstractly determined by defining relations among the generators as follows ãị e ãj e ãj e ãi i j 1 2 3 i j 43a aj Tj e ãi j Tj -1 s ữjãi 43b 1T1 2 2 . amịĩm e 4 u 1 . s 43c which reflect the abstract definition of T equation 43a the invariance of T equation 43b and an abstract definition of an adapted point group equation 43c . All the small irreducible representations dkv are then generated from the set of matrices 8kv e ãi 8kv ữj ịĩj i 1 2 3 j 1 . m 44 satisfying the following relations 8kv e ãi exp -ik- ãi 1 dv 45a u 8kv 1 1 2 2 . am m exp -ik- Ry 1 dv u 1 . s. 45b Irreducible representations dkv of the little co-groups G0 k . The irreducible representations dkv of G0 k that is the projective or else loaded representations can be easily searched by the standard methods discussed in Section . As an example the orthogonality theorem rewrites in terms of the dkv as nr-fti E dkyaydmnya J-k-8ji8mn8 n 46 .