Antiferromagnetically Coupled Systems

For all known cases of iron-sulfur proteins, J > 0, meaning that the system is antiferromagnetically coupled through the Fe-S-Fe moiety. Equation (4) produces a series of levels, each characterized by a total spin S, with an associated energy, which are populated according to the Boltzmann distribution. Note that for each S level there is in principle an electron relaxation time. For most purposes it is convenient to refer to an effective relaxation time for the whole cluster. 

This tells us that the reduced magnetic entropy change will be lower in an antiferromagnetic system than in an uncoupled one, as can be seen below, as the spins are not fully saturated below the conditions of lowest temperature and strongest field. The antiferromagnetic coupling in Gd(III)7 is also a hindrance, with behaviour similar to Gd(III)5, when compared to the relevant Brillouin functions. 

If we first consider the three scenarios at the same field, we can immediately see how the paramagnetic material shows the largest magnetocaloric effect, followed by a ferromagnetically coupled system, and then the antiferromagnetic case. 

A more general point is that the maximum spin is often not attained due to antiferromagnetic coupling. In Gd(III) systems, Msat can usually be attained in moderate fields, whereas when transition metals are involved the spin state can be less than the maximum possible. Here, Gd(III)4Cu(II)8 has a spin of S = 18, the maximum possible (albeit field induced). 

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