Generation of basis vectors for magnetic structures and displacement modes

TL;DR

This paper introduces a novel method using basis sets and unitary irreducible representations to efficiently generate symmetry-adapted basis vectors for magnetic structures and displacement modes, addressing previous computational challenges.

Contribution

It presents an elegant solution leveraging basis sets and confirms the unitarity of irreducible representations in Kovalev's tabulation, enhancing the calculation of symmetry-adapted functions.

Findings

Effective basis set approach for magnetic and structural modes

Validation of unitarity of Kovalev's irreducible representations

Improved computational efficiency in symmetry analysis

Abstract

Increasing attention is being focussed on the use of symmetry-adapted functions to describe magnetic structures, structural distortions, and incommensurate crystallography. Though the calculation of such functions is well developed, significant difficulties can arise, such as the generation of too many or too few basis functions to minimally span the linear vector space. We present an elegant solution to these difficulties using the concept of basis sets, and discuss previous work in this area using this concept. Further, we highlight the significance of unitary irreducible representations in this method, and provide the first validation that the irreducible representations of the crystallographic space groups tabulated by Kovalev are unitary