  A theoretical investigation of a plausible construct for electronic structure
in iridate perovskites demonstrates the existence of magnetic multipoles
hitherto not identified. The strange multipoles, which are parity-even,
time-odd and even rank tensors, are absent from the so-called jeff = 1/2 model.
We prove that the strange multipoles contribute to magnetic neutron
diffraction, and we estimate their contribution to intensities of Bragg spots
for Sr2IrO4. The construct encompasses the jeff = 1/2 model, and it is
consistent with the known magnetic structure, ordered magnetic moment, and
published resonant x-ray Bragg diffraction data. Over and above time-odd
quadrupoles and hexadecapoles, whose contribution changes neutron Bragg
intensities by an order of magnitude, according to our estimates, are
relatively small triakontadipoles recently proposed as the primary magnetic
order-parameter of Sr2IrO4.
