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The enantiomorphous (chiral) crystal class of the Sohncke-type insulatorPb(TiO)Cu4(PO4)4 permits the rotation of the plane of polarization of light(optical activity). Copper ions participate in antiferromagnetic order below atemperature 7 K, with magnetoelectric and piezomagnetic effects permitted.Lattice and magnetic symmetries of Pb(TiO)Cu4(PO4)4 are fully incorporated incalculated resonant x-ray Bragg diffraction patterns that are successfullycompared with existing limited measurements on paramagnetic and magneticallyordered Pb(TiO)Cu4(PO4)4 [Misawa et al. Phys. Rev. B 103, 174409 (2021)].Specifically, there is additional intensity in the ordered phase to a Braggspot (a chiral signature) from circular polarization in the primary beam ofx-rays. It is created by Cu axial magnetic dipoles, with the prospect of futureexperiments revealing interference between magnetic dipoles and charge-like(time-even, Templeton-Templeton) quadrupoles. Polar and magnetic (parity- andtime-odd) Dirac quadrupoles and octupoles are potentially strong sources ofdiffraction when the reflection vector is parallel to the unique direction inthe tetragonal lattice.

Magnetic properties of Sohncke-type Pb(TiO)Cu4(PO4)4