# Jahn Teller distortion and magnetic moments.

It is relatively well known that the discrepancy between the observed and experimental magnetic moments in the first row transition metals is attributed to spin-orbit coupling when it comes to metal ions with $A_2$ and $E$ ground states. For example, Cu(II) has an $E_{2g}$ ground state term has the observed moment is slightly higher (1.96 BM for a phenanthroline complex) than the theoretically predicted "spin only" value (~1.73 BM, attributed to 1 unpaired electron). I also know that this is calculated by a formula which makes use of the spin-orbit coupling coefficient:

$μ_{eff}$ = $μ_{s.o.}$(1-$α λ$ /$Δ_o$)

where, $α$ takes up the values 2 (for E ground state) and 4 (for $A_2$ ground state), $\lambda$ is the spin orbit coupling coefficient, $Δ_o$ is the crystal field splitting energy.

My question relates to the possible effect of a Jahn Teller distortion on the magnetic moment of, say, Cu(II). Intuitively, a distortion should reduce the orbital contribution to angular momentum by the loss of orbital degeneracy. On the other hand, for Cu(II), for example, the $e_g$ set is magnetically non active. So does splitting basically have no effect on the orbital part of the angular momentum? The $t_{2g}$ set should be magnetically inactive as well because of being fully filled for Cu(II).