Sum rules of L-edge x-ray magnetic circularly polarized emission for 3d transition metals

We propose sum rules of x-ray magnetic circularly polarized emission (XMCPE) at L edges for 3d transition metals. By making use of combinations of incident and emitted photon helicities, z-component expectation values of spin, orbital, magnetic dipole, and quadrupole terms can be obtained separately. The fundamental difference in the sum rules between x-ray magnetic circular dichroism and XMCPE arises from the variety of electron transitions involving core states split by the spin-orbit interaction. The additional electron transition in XMCPE causes complicated angular dependence of the sum rule relation for the spin moment. Our findings promote future L-edge XMCPE measurements, which have not been observed at present.

Automated summary

The study introduces sum rules of X-ray magnetic circularly polarized emission (XMCPE) at L edges for 3d transition metals, which can be used to separately obtain z-component expectation values of spin, orbital, magnetic dipole, and quadrupole terms through combinations of incident and emitted photon helicities. The fundamental difference in sum rules between X-ray magnetic circular dichroism and XMCPE stems from the variety of electron transitions involving core states split by the spin-orbit interaction, causing complicated angular dependence of the spin moment sum rule relation in XMCPE. These findings pave the way for future L-edge XMCPE measurements that are currently not observed.