# What magnetic interaction makes spin not conserved?

If $$[S_i,H]\neq0$$ or $$[S^2,H]\neq0$$, we might say spin is not a good quantum number in the system. But is there any more practical or detailed criterion? Or certain families of magnetic interaction forms always make it not conserved?

• You seem to say that whether $S_i$ or $S^2$ commute with H it's somehow the same thing and it's not. These two cases describe different conservation laws. Commutation with H is the most concise and general way to capture conserved quantities ("good quantum numbers") that I know of; anything else is likely going to be applicable only to specialized Hamiltonians and even then I doubt you can do better. – oleg Jul 29 at 23:58
• This is not a complete answer, but have you heard a spin-orbit interaction ($\propto L \cdot S$) in which S is no longer a good quantum number but the total ($J$) is. So the point is that whenever you another form of angular momenta where they can "interact" with spin, the spin is no longer a good quantum number. – rnels12 Jul 30 at 6:15