Bilbao Crystallographic Server arrow STENSOR

STENSOR: Tensor calculations for Spin Groups

Tensor calculations for Spin Groups
STENSOR provides the symmetry-adapted form of tensor properties for any spin point group and for its maximal magnetic point subgroup for comparison. The input data can be introduced through two alternative ways:

  • Option A: A scif file, i.e. a CIF-type file that contains the structure description of a magnetic compound under its spin space group. The program will retrieve from the file only the resulting spin point group as input. If, instead, the file introduced is an mcif file, i.e. a CIF- type file with the magnetic structure described under a magnetic space group, then the program will consider as relevant spin point group, the one obtained by simply adding the spin-only symmetry associated with the collinearity or coplanarity of the spin arrangement.

  • Option B: A set of a generators of a spin group, the relation between the bases in the spin and lattice spaces the type of magnetic structure (collinear, coplanar or non-coplanar) and the direction parallel or perpendicular to the spins in collinear or coplanar alignments, respectively. The symmetry operations in the orbital space must be introduced in a reference system whose three basis vectors are lattice vectors of a crystal with the point group given. Two different formats are allowed (one generator per line): x,y,z,+1,u,v,w or x,y,z,u,v,w.
    Alternatively, a set of generators of a magnetic space group can also be introduced using the format x,y,z,+1. In this case, the program will consider as relevant spin point group, the one obtained by simply adding to the given magnetic point group the spin-only symmetry associated with the collinearity or coplanarity of the spin arrangement.


    • If both sets of parameters are given as input, the program will take the Option A.

    A tensor-type must also be introduced using the generalized Jahn symbol (see the details of the notation in the reference given below.)
    References. For more information about this program see the following articles:
    Elcoro, L., Etxebarria, J.; Perez-Mato, J.M., Tasci, E.S. "Automatic calculation of symmetry-adapted tensors under spin-group symmetry: STENSOR, a new tool of the Bilbao Crystallographic Server." J. Appl. Cryst. (2026) 59, 640-647. doi:10.1107/S1600576726000944
    Etxebarria, J.; Perez-Mato, J.M., Tasci, E.S., Elcoro, L. "Crystal tensor properties of magnetic materials with and without spin-orbit coupling. Application of spin point groups as approximate symmetries." Acta Cryst. (2025) A81, 317-338. doi:10.1107/S2053273325004127
    If you are using this program in the preparation of an article, please cite the above references.
    Enter the generalized Jahn symbol:

    Option A: Upload a scif or an mcif file with the structure data


    Option B: Give the structure data in the boxes below (help and examples of input data)

    Lattice and spin bases are the same. Otherwise give the relation:

    Enter a set of generators of the spin point group in the box below as in the example in the left column
    or the generators of a magnetic point group as in the example on the right column

    x,y,z,+1,u,v,w
    y,x,z,-1,v,u,w
    or
    x,y,z,u,v,w
    y,x,z,v,u,w
    x,y,z,+1
    y,x,z,-1


    Enter the type of spin alignment:CollinearCoplanarNon-coplanar

    Enter the direction parallel (collinear) or perpendicular (coplanar) to the spins:n1 = n2 = n3 = 


    k-Subgroupsmag
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