Bilbao Crystallographic Server STENSOR

Description of the input parameters

• Relation between the bases

  The 9 components m_ij of the matrix M that relates both set of basis vectors should be given (by default the program assumes the identity matrix),
  a_s = m₁₁ a + m₁₂ b + m₁₃ c
  b_s = m₂₁ a + m₂₂ b + m₂₃ c
  c_s = m₃₁ a + m₃₂ b + m₃₃ c
  
  The components of the matrix can be introduced as integer numbers (1,2,...), as rational numbers (1/2,1/4,...) or as decimal numbers using, at least, 6 significan digits for non-fractional numbers (0.166666,-0.333333,0.5,-1.732051,...) to represent (1/6,-1/3,1/2,-sqrt(3),...).

• Generators of the spin point group.

  The generators of the spin point group must be introduced in the x,y,z,u,v,w form (see some examples below). Alternatively, the generators can be introduced as a 7-component operation, x,y,z,+1,u,v,w where the ±1 component is the determinant of the matrix that represents the operation in the spin space.

• Type of magnetic structure.

  It must be selected one of the options: collinear, coplanar, non-coplanar.

• Direction parallel/perpendicular to the spins.

  The three indices (n₁,n₂,n₃) define the direction,
  
  n = n₁ a_s + n₂ b_s + n₃ c_s
  
  parallel to the spins in a collinear magnetic structure or perpendicular to the spin planes in a coplanar structure. In the first case it will be assumed that P_SOintr=^∞_nm1 and in the second one P_SOintr=^m_n1.
  If the "Non-coplanar" option has been chosen and some components of n habe been introduced, these values will not be considered in the calculation.

Examples of input parameters

• Collinear structure DyB₄ (entry 0.22 in MAGNDATA)
  
  Relation between the two basis: identity matrix, m_ij=δ_ij
  
  Symmetry operations:
  
  x,y,z,u,v,w
  -x,y,z,u,v,w
  x,-y,z,-u,-v,-w
  x,y,-z,u,v,w
  
  Type of magnetic structurre: collinear
  
  Components of the direction of the spins: (n₁,n₂,n₃)=(0,0,1)
  


• Collinear structure MnF₂ (entry 0.15 in MAGNDATA)
  
  Relation between the two basis: identity matrix, m_ij=δ_ij
  
  Symmetry operations:
  
  -y,x,z,-u,-v,-w
  x,y,-z,u,v,w
  y,x,z,u,v,w
  
  Type of magnetic structurre: collinear
  
  Components of the direction of the spins: (n₁,n₂,n₃)=(0,0,1)
  


• Coplanar structure CoSO₄ (entry 1.519 in MAGNDATA)
  
  Relation between the two basis: identity matrix, m_ij=δ_ij
  
  Symmetry operations:
  
  x,y,z,-u,-v,-w
  -x,y,z,u,v,w
  x,-y,z,u,-v,w
  x,y,-z,u,-v,w
  
  Type of magnetic structurre: coplanar
  
  Components of the direction of the spins: (n₁,n₂,n₃)=(1,0,0)
  


• Coplanar structure Mn₃Ge (entry 0.377 in MAGNDATA)
  
  Relation between the two basis: identity matrix, m_ij=δ_ij
  
  Symmetry operations:
  
  x,y,-z,u,v,w
  -x+y,y,z,-u+v,v,w
  -x,-y,-z,u,v,w
  x-y,x,z,-v,u-v,w
  
  Type of magnetic structurre: coplanar
  
  Components of the direction of the spins: (n₁,n₂,n₃)=(0,0,1)