What is Effective magnetic moment?

The effective magnetic moment of a paramagnetic ion is $\mu_{\mathrm{eff}} = \sqrt{3k\chi_{\mathrm m}T/(\mu_0N_A)}$, in cgs $\mu_{\mathrm{eff}}/\mu_B = 2.828\sqrt{\chi_{\mathrm m}T}$. Its spin-only moment is the value $2\sqrt{S(S+1)}\,\mu_B$ that the spins alone would give with $g = 2$; the excess of the measured moment over it is the orbital contribution.