Parity and spin forbidden optical excitations

In optical excitation, we are normally looking at the transition matrix element:

M_ij^E=<φ_i|exE|φ_f>, where φ_i and φ_j are the wave functions of the initial and final states, E is the electric field.

Following observations are important concerning the M_ij^E.

• M_ij^E vanishes for a lattice structure with inversion symmetry. In this case the excitation is called parity forbidden excitation.
• The operator exE does not involve spin degree of freedom. So in order to have non-zero, the spin of φ_i and φ_j has to be the same. If the initial and final states have different spin, the excitation is called spin forbidden excitation.
  

How come we do see the "forbidden" excitation? Here are what happens in real material to circumvent the forbiddenness.

	Parity forbideness	Spin forbideness
Single site	Existence of phonon reduces the symmetry magnetic dipole excitation MijM=<φi|μB|φf>	spin-orbit coupling
Collective		Exciton + magnon
		Exciton + Exciton