Magnetic symmetries of terbium tetraboride <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>Tb</mml:mi><mml:msub><mml:mi mathvariant="normal">B</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow><mml

A recent experimental study of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>Tb</a:mi><a:msub><a:mi mathvariant="normal">B</a:mi><a:mn>4</a:mn></a:msub></a:mrow></a:math> 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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>Tb</c:mi><c:msub><c:mi mathvariant="normal">B</c:mi><c:mn>4</c:mn></c:msub></c:mrow></c:math> Bragg spot on reversing the handedness (chirality) of the primary x-ray beam [R. Misawa, K. Arakawa, T. Yoshioka, H. Ueda, F. Iga, K. Tamasaku, Y. Tanaka, and T. Kimura, ]. It reveals a magnetic chiral signature in <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mi>Tb</e:mi><e:msub><e:mi mathvariant="normal">B</e:mi><e:mn>4</e:mn></e:msub></e:mrow></e:math> that is forbidden in phases of rare-earth tetraborides known to date, as the previous magnetic symmetries are parity-time (PT) symmetric with anti-inversion present in the magnetic crystal class. Misawa appeal to a PT-symmetric diffraction pattern to interpret their interesting diffraction patterns. 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 <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mi>Tb</g:mi><g:msub><g:mi mathvariant="normal">B</g:mi><g:mn>4</g:mn></g:msub></g:mrow></g:math> consistent with a published neutron powder diffraction pattern and susceptibility measurements. On the basis of this information, noncollinear antiferromagnetic order exists below a temperature <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mrow><i:mo>≈</i:mo><i:mspace width="0.16em"/><i:mn>44</i:mn></i:mrow></i:math> K with no ferromagnetic component. Our symmetry-informed patterns encapsulate Tb electronic degrees of freedom in terms of multipoles consistent with established sum rules for dichroic signals. The investigated symmetry templates are noncentrosymmetric, noncollinear antiferromagnetic constructions with propagation vector <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mrow><k:mi mathvariant="bold">k</k:mi><k:mo>=</k:mo><k:mo>(</k:mo><k:mrow><k:mn>0</k:mn><k:mo>,</k:mo><k:mspace width="0.16em"/><k:mn>0</k:mn><k:mo>,</k:mo><k:mspace width="0.16em"/><k:mn>0</k:mn></k:mrow><k:mo>)</k:mo></k:mrow></k:math>. An inferred chiral signature for a parity-even absorption event has an interesting composition. There is the anticipated product of Tb axial dipoles and chargelike 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. Published by the American Physical Society 2024