text: f E 
  2 = (1/2)(S2 
  f E 
  1 = 
  
  S4 + S1  S3  S1  S4  S2  S3), 
  
  · 
  1/12(S1  · 
  S4 + S2  · 
  S3 + S2 
  − 
  · 
  S4 + S1 
  − 
  S3 
  p 
  · 
  2S1  · 
  2S3  · 
  S4). 
  · 
  S2 
  
  − 
  · 
  According to TABLE I we have f E 
  2 = (√3/2)τ y. Then the coupling becomes 
  f E 
  
  ·  − 
  
  The τ z 
  j · 
  treat it as 
  need an anharmonic coupling Hperturbation = QE 
  QE 
  der (9 J ′4 λ)/(16 k4) τ x 
  (9 J ′4 λ)/(16 k4). 
  
  (√3/2)τ x and 
  1 = 
  − 
  k τ y 
  τ x 
  
  is [equation (1.8) in Ref.35], 
  
  Finally we have made up a spin-lattice model HSL, 
  Sm interaction for physical spins, 
  which involves only Sℓ · 
  2j)2 
  (QE 
  
  (13) 
  Hcluster, SL + 
  
  X 
  x−links <jk> 
  QE 
  2k 
  λy QE 
  2j · 
  
  QE 