Dichroism as a probe for parity-breaking phases of spin-orbit coupled metals

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.