A Definition of the Magnetic Transition Temperature Using Valence Bond Theory

Macroscopic magnetic properties are analyzed using Valence Bond theory. Commonly the critical temperature T_C for magnetic systems is associated with a maximum in the energy-based heat capacity C_p(T). Here a more broadly applicable definition of the magnetic transition temperature T_C is described using the spin moment expectation value (i.e., applying the spin exchange density operator) instead of energy. Namely, the magnetic capacity C_s(T) reflects variation in the spin multiplicity as a function of temperature, which is shown to be related to ∂[χT(T)]/∂T. Magnetic capacity C_s(T) depends on long-range spin interactions that are not relevant in the energy-based heat capacity C_p(T). Differences between C_s(T) and C_p(T) are shown to be due to spin order/disorder within the crystal that can be monitored via a Valence Bond analysis of the corresponding magnetic wave function. Indeed the concept of the Boltzmann spin-alignment order is used to provide information about the spin correlation between magnetic units. As a final illustration, the critical temperature is derived from the magnetic capacity for several molecular magnets presenting different magnetic topologies that have been experimentally studied. A systematic shift between the transition temperatures associated with C_s(T) and C_p(T) is observed. It is demonstrated that this shift can be attributed to the loss of long-range spin correlation. This suggests that the magnetic capacity C_s(T) can be used as a predictive tool for the magnetic topology and thus for the synthetic chemists.