Magnetic symmetries of terbium tetraboride (TbB4) revealed by resonant x-ray Bragg diffraction

Abstract

A recent experimental study of TbB4 at a low temperature using resonant x-ray Bragg diffraction implies a magnetic symmetry not found in any other rare-earth tetraboride. The evidence for this assertion is a change in the intensity of a TbB4 Bragg spot on reversing the handedness (chirality) of the primary x-ray beam [Misawa et al., Phys. Rev. B 108, 134433 (2023)]. It reveals a magnetic chiral signature in TbB4 that is forbidden in phases of rare-earth tetraborides known to date. For, the previous magnetic symmetries are parity-time (PT)-symmetric with anti-inversion present in the magnetic crystal class. Misawa et al. appeal to a (PT)-symmetric diffraction pattern to interpret their interesting experimental results. In addition to the use of symmetry that does not permit a chiral signature, calculated patterns impose cylindrical symmetry on Tb sites with no justification. We review magnetic symmetries for TbB4 consistent with a published neutron powder diffraction pattern and susceptibility measurements. The investigated symmetry templates are non-centrosymmetric, non-collinear antiferromagnetic constructions with propagation vector k = (0, 0, 0). An inferred chiral signature for a parity-even absorption event has an interesting composition. There is the anticipated product of Tb axial dipoles and charge-like quadrupoles (from Templeton-Templeton scattering). Beyond this contribution, though, symmetry allows a product of dipoles in the chiral signature. A predicted change in the intensity of a Bragg spot with rotation of the crystal about the reflection vector (an azimuthal angle scan) can be tested in future experiments. Likewise, contributions to Bragg diffraction patterns from Tb anapoles and higher-order Dirac multipoles.