Magnetic operators for Ti3+ and Cu2+ ground states

Abstract

Abstract We have checked the XMCD sum rules through an analytical calculation of Cu 2+ L 2,3 edges in octahedral symmetry. It is found that XMCD sum rules are fully satisfied in the framework of the crystal field multiplet approach resulting from the very general arguments developed in their derivations by B.T. Thole and collaborators. Analytical expressions for the orbital magnetic moment 〈 L z 〉, the spin magnetic moment 〈 S z 〉 and the magnetic dipole term 〈 T z 〉 are obtained as functions of crystal field strength and spin–orbit couplings. The nullity of 〈 T z 〉 is specially examined through group theory considerations, and it is found that at low temperature the 〈 T z 〉 contribution can be much larger than the 〈 S z 〉 contribution in the spin sum rule. The case of Ti 3+ in octahedral symmetry is also considered and it is found that, even for no spin–orbit coupling, 〈 T z 〉 can be non-zero.