  Recently, a general formalism was presented for gyrotropic, ferroelectric,
and multipolar order in spin-orbit coupled metals induced by spin-spin
interactions. Here, I point out that the resulting order parameters are
equivalent to expectation values of operators that determine natural circular
dichroic signals in optical and x-ray absorption. Some general properties of
these operator equivalents and the resulting dichroisms are mentioned, and I
list several material examples in this connection, including Weyl semimetals.
The particular case of the tensor order in the pyrochlore superconductor
Cd2Re2O7 is treated in more detail, including calculations of the x-ray
absorption and circular dichroism at the O K edge.
