Automatic calculation of symmetry-adapted tensors under spin-group symmetry: STENSOR, a new tool of the Bilbao Crystallographic Server

Elcoro L., Etxebarria J., Perez-Mato J. M., TAŞCI E.

Journal of Applied Crystallography, vol.59, pp.640-647, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 59
  • Publication Date: 2026
  • Doi Number: 10.1107/s1600576726000944
  • Journal Name: Journal of Applied Crystallography
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Chemical Abstracts Core, Chimica, Compendex, Index Islamicus, INSPEC
  • Page Numbers: pp.640-647
  • Keywords: Bilbao Crystallographic Server, magnetic point groups, spin point groups, spin–orbit coupling, symmetry-adapted tensors
  • Hacettepe University Affiliated: Yes

Abstract

We present STENSOR, a new computational tool integrated into the Bilbao Crystallographic Server, designed for the automatic calculation of symmetry-adapted tensors under spin-group symmetry. The program requires either a file containing the structural data of the magnetic compound or the generators of the oriented spin point group, together with the generalized Jahn symbol associated with the tensor of interest. The user can propose any arbitrary tensor type or select a particular one from a predefined list. The program output returns the symmetry-adapted tensor under the spin point group and under the magnetic point group, which is also calculated. The comparison of these two tensor forms allows the coefficients due to spin–orbit coupling effects to be distinguished from those that have a non-relativistic origin and thus are usually more important. Two examples are given to illustrate the operation of the program.