Spin-only magnetic moment (${\mu }_{\mathrm{eff}}$)

The spin-only magnetic moment neglects orbital contributions and approximates $g$ by two: ${\mu }_{\mathrm{eff}}=g\sqrt{S(S+1)}{\mu }_B=\sqrt{n(n+2)}{\mu }_B$ for $n$ parallel unpaired electrons. Four unpaired electrons give $\sqrt{24}{\mu }_B\simeq 4.90{\mu }_B$.

For uncoupled centres with approximately equal $g=2$, squared magnetic moments add: ${\mu }_{\mathrm{eff}}/{\mu }_B=2\sqrt{{\sum }_i{S}_i(S_i+1)}$. This does not assume that the individual spins add to a definite total spin; appreciable exchange interaction invalidates the independent-centre approximation.