X-ray optical activity: Applications of sum rules

Abstract

Edge-selective sum rules are proposed for a variety of X-ray dichroisms related to natural or nonreciprocal optical activity. Four spherical operators are identified that mix orbitals of different parities in what is assumed to be the ground state. The orbital anapole moment Ω(1) is primarily responsible for the magnetochiral dichroism; the time-even rank-2 tensor N(2)=[L, Ω](2) for natural circular dichroism; the time-odd rank-2 tensor W(2)=[L, n](2) for nonreciprocal magnetic linear dichroisms. At higher orders, the time-odd rank-3 tensor Γ(3)=[L, L, Ω](3) can also contribute to all nonreciprocal dichroisms. The physical content of these operators is analyzed. For every magnetoelectric group, one can predict which dichroic effect can be measured with either a single crystal or a powdered sample. Experimental spectra are produced to illustrate the value of the sum rules and the practical conditions of their application. Regarding nonreciprocal activity, one should be cautious about discussing magnetic symmetry because the deep core hole can couple the true ground state with low-lying excited states.