  The enantiomorphous (chiral) crystal class of the Sohncke-type insulator
Pb(TiO)Cu4(PO4)4 permits the rotation of the plane of polarization of light
(optical activity). Copper ions participate in antiferromagnetic order below a
temperature 7 K, with magnetoelectric and piezomagnetic effects permitted.
Lattice and magnetic symmetries of Pb(TiO)Cu4(PO4)4 are fully incorporated in
calculated resonant x-ray Bragg diffraction patterns that are successfully
compared with existing limited measurements on paramagnetic and magnetically
ordered 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 Bragg
spot (a chiral signature) from circular polarization in the primary beam of
x-rays. It is created by Cu axial magnetic dipoles, with the prospect of future
experiments revealing interference between magnetic dipoles and charge-like
(time-even, Templeton-Templeton) quadrupoles. Polar and magnetic (parity- and
time-odd) Dirac quadrupoles and octupoles are potentially strong sources of
diffraction when the reflection vector is parallel to the unique direction in
the tetragonal lattice.
