A Definition of the Magnetic Transition Temperature Using Valence Bond Theory

Abstract

Macroscopic magnetic properties are analyzed using Valence Bond theory. Commonly the critical temperature T for magnetic systems is associated with a maximum in the energy-based heat capacity C(T). Here a more broadly applicable definition of the magnetic transition temperature T is described using the spin moment expectation value (i.e., applying the spin exchange density operator) instead of energy. Namely, the magnetic capacity C(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(T) depends on long-range spin interactions that are not relevant in the energy-based heat capacity C(T). Differences between C(T) and C(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(T) and C(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(T) can be used as a predictive tool for the magnetic topology and thus for the synthetic chemists.

Approaching the isotropic spin-ladder regime: structure and magnetism of all-pyrazine-bridged copper(ii)-based antiferromagnetic ladders

“…Therefore, from our C p ( T ) data it would be hard to distinguish whether the main contribution to the heat capacity comes from long- or short-range spin correlations. Recently, we have put forward the magnetic capacity C s ( T ), 42 as a new descriptor of the magnetic topology, since it is a measure of the thermal variation of the spin multiplicity of the system and reflects the importance of magnetically non-connected spin alignment and how the dominant effect of long-range spin correlation governs the magnetic behavior of molecule-based crystals (as well as metal-coordinated molecular magnetic materials). In the same study it was also concluded that C p ( T ) measures the energy variation due to the 3D propagation of the interaction of two magnetically connected spins, that is, to short-range ordering.…”

Disentangling the magnetic dimensionality of an alleged magnetically isolated cuprate spin-ladder CuHpCl system: a long-lasting issue

“…Therefore, the crystallographic data plays a non-innocent role in determining the values of the critical field. Having clarified this issue, now we are left with the analysis of the magnetic wavefunction [45] of CuHpCl to provide a deeper insight into the origin of the behavior of the intermediate partially polarized phase.…”

“…Let us finally draw attention to our recently proposed descriptor of the magnetic topology, the magnetic capacity C s (T), [45] since it is a measure of the thermal variation of the spin multiplicity of the system and reflects the importance of magnetically non-connected spin alignment and how the dominant effect of long-range spin correlation governs the magnetic behavior of molecule-based crystals (and in general of magnetic compounds). In the same study it was also concluded that C p (T) measures the energy variation due to the 3D propagation of the interaction of two magnetically connected spins, that is, to short-range ordering.…”

“…Finally, the importance of long-range spin correlation will be assessed by analysis of the magnetic wavefunction. [45] Computational Details…”

“…Complementary to heat capacity C p (T), the magnetic capacity C s (T) will be evaluated to assess the importance of long-range spin correlation in CuHpCl, [45] since the analysis of the magnetic wavefunction enables both the study of the 3D propagation of two magnetically connected spins, i.e. short-range ordering, and magnetically non-connected spin alignment, i.e.…”