The energy levels of a pair of antiferromagnetically coupled S = 5/2 spins. Possible transitions in inelastic neutron scat- tering events are shown, but now ignore them. Think instead of the level degeneracy. It’s 2S + 1, right?

So, let’s apply external magnetic field B, and look only at the ground state and the first excited level. The latter state’s multiplicity is 2S+1= 3, so it now splits into a “three-pronged fork”: For the total spin Sc=1, its z component can take the values of (Sc)z= -1, 0, +1. The energies of the sub- states are: 2|J| - gμB(Sc)zB About the symbols used: I took the fig- ures from an earlier presentation. Here Sc is the total spin, the same as S in the preceding figu- re and in the text explanations on the slides. Note: if B increases, then after passing “1” this level becomes the ground state! E=2|J| - gμBB

state becomes the ground state, For the second excited level, the total spin S = 2. The spin’s z component can thus take the values of Sz = -2, -1, 0, +1, +2. Since the energy of the split sublevels is E = 6|J| - gμBSzB, the lowest of the five is for Sz = 2 and is equal to 6|J| - 2gμBB . One can readily check that these two lines intersect when 2|J| - gμBB 6|J| - 2gμBB Therefore, for this state becomes the ground state,