Neutron Scattering from Magnetic Materials part 2 doc

... 3d n SLJGround-state term Ti 3+ ,V 4+ 3d 1 1 2 2 3 2 2 D 3 2 V 3+ 3d 2 13 2 3 F 2 Cr 3+ ,V 2+ 3d 3 3 2 3 3 2 4 F 3 2 Mn 3+ ,Cr 2+ 3d 4 22 0 5 D 0 Fe 3+ ,Mn 2+ 3d 5 5 2 0 5 2 6 S 5 2 Fe 2+ 3d 6 22 4 5 D 4 Co 2+ 3d 7 3 2 3 9 2 4 F 9 2 Ni 2+ 3d 8 13 4 3 F 4 Cu 2+ 3d 9 1 2 2 5 2 2 D 5 2 Magnetic ... 0, 1 2 ) ∗ ( 1 2 , 0, 0)( 1 2 , 1 2...

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... this the scattering cross-section can be written as  d 2 σ dΩ dE   ± =  γe 2 mc 2  2  1 2 gF(Q)  2  k  k  exp  −2W(Q)  1 +Q 2 z  1 2 S × 2 3 v 0  q,τ  n q + 1 2 ± 1 2  δ( ¯ hω q ∓ ¯ hω)δ(Q ... lowering operators as d 2 σ dΩ dE  =  γe 2 mc 2  2  1 2 gF(Q)  2  k  k  exp  −2W(Q)  ×   1 −Q 2 z  1 2 ¯ h  ∞ −∞ dt exp(−iωt)  S z...

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... 17 6.5.Spinwaves 18 6.6.Scatteringfromspinwaves 20 6.7.Paramagneticscattering 21 6.8.Crystal-fieldexcitations 22 7.Concludingremarks 23 References 23 NEUTRON SCATTERING FROM MAGNETIC MATERIALS Edited ... r 0 ) 2 (2 ) 3 2N m v 0 g 2 S 4  1 +  Q 2 z  f 2 (Q)e −2W(Q) ×  τ q n q +1δ(Q −q −τ )δ  E − ¯ hω(q)  , (79)  d 2 σ dΩ dE  m,−1 = k 1 k 0 (γ r 0 ) 2 (2...

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... G 1 , g 2 ∈ G 2 ) we have g 1 g 2 = g 2 g 1 .LetR 1 :G 1 → G(E 1 ) be a representation of G 1 and R 2 :G 2 → G(E 2 ) a representation of G 2 . The tensor product R 1 ⊗R 2 of R 1 and R 2 is the ... E 1 ⊗E 2 ) associating to each g =g 1 g 2 in G, where g 1 ∈ G 1 and g 2 ∈ G 2 , the operator R(g) such that ∀  V 1 ∈ E 1 , ∀  V 2 ∈ E 2 , R(g)[  V 1 ⊗  V 2 ]=[R...

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... 6 2 4 2. 333 f 5 (Sm 3+ )55 /25 /2 6.000 f 6 (Eu 3+ ) 3 3 0 No moment f 7 (Gd 3+ )07 /27 /2 0.000 f 8 (Tb 3+ ) 3 3 6 0.333 f 9 (Dy 3+ )55 /21 5 /2 0.500 f 10 (Ho 3+ ) 6 2 8 0.600 f 11 (Er 3+ )63 /21 5 /2 ... spin-flip 1 82 J. Schweizer Table 1 Coefficients C 2 for the different fillings of an f shell f shell LS J c 2 =2/ g J −1 f 1 (Ce 3+ )31 /25 /2 1.333 f 2 (Pr 3+ ) 5 1 4 1.50...

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... was correct. 23 2 P.J . B ro w n incident polarisation is parallel to z is  P 2 zz +P 2 yz  1 /2 = ((R zz −R yy ) 2 +R 2 yz ) 1 /2 R zz +R yy =  1 − J 2 yz (R zz +R yy ) 2  1 /2 (22 ) when J yz is ... M ⊥x M ⊥y M ⊥z |M ⊥ | 2 (a) 0 √ 2A cosφ √ 2A 2A 2 (1 +cos 2 φ) (b) 0 2A cosφ 04A 2 cos 2 φ (c) 0 0 2A 4A 2 . Fig. 9. Possible magnetic structures for a tetragon...

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... equations 2 ¯ hω q,0 =(a 1 +a 2 +b 1 −b 2 ) +2 (q), (49) 2 ¯ hω q,1 =−(a 1 +a 2 +b 1 −b 2 ) +2 (q), (50) where 2 (q) =  (a 1 −a 2 +b 1 +b 2 ) 2 −S 1 S 2  4J (q)  2  1 /2 , (51) a 1 =g 1 µ B H, ( 52) a 2 =g 2 µ B H, ... written as ¯ hω q,a −J (0)(S 2 −S 1 )(−1) a +   J (0)(S 1 −S 2 )  2 − 16 3 S 1 S 2 q 2 J (0)J (2)  J (0)(S 1 −S 2 )  1 +(−1...

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... 21 5 80 5.51 2. 05 EuO 69 12 6 2. 01 1. 02 EuS 10. 62. 62. 31. 82 1.61 been investigated by inelastic neutron scattering. The neutron scattering investigation of the spin dynamics of the doped ferromagnetic ... above T C a damped harmonic oscillator form given by F α (Q,ω)= ¯ h 2 γ 2 ω 2 0 ( ¯ h 2 ω 2 − ¯ h 2 ω 2 0 ) 2 +γ 2 ¯ h 2 ω 2 (16) was used. Here γ is...

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... material  − ¯ h 2 2m ∇ 2 +V(r)  Ψ =EΨ, (2) where ∇ 2 = ∂ 2 ∂x 2 + ∂ 2 ∂y 2 + ∂ 2 ∂z 2 , (3) and where the first term of the Hamiltonian operator in the brackets on the left-hand side (LHS) of (2) represents ... Phys. Rev. 181 920 (1969). [20 ] G.M. Drabkin et al., JETP Lett. 2 353 (1965). [21 ] S. Brehmer et al., Phys. Rev. B 60 329 (1999). [22 ] M. Muller et al., Ph...

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... required, ˇ U SAM→LAB =     cos ε 2 isin ε 2 00 isin ε 2 cos ε 2 00 0 0 cos ε 2 +isin ε 2 00+isin ε 2 cos ε 2     . ( 120 ) The inverse of ( 120 ) is ˇ U −1 SAM→LAB =     cos ε 2 −isin ε 2 00 −isin ε 2 cos ε 2 00 0 ... by     t + t − iQ 2 t + iQ 2 t −     = 1  l=N    A 11 A 12 A 13 A 14 A 21 A 22 A 23 A 24 A 31 A 32 A 33 A 34 A 4...

Ngày tải lên: 12/08/2014, 02:23