On the ferromagnetic and antiferromagnetic properties of molecular crystals
Authors: Datta Sambhu N. , Misra Anirban 
Published: July 2002

Ferro- and antiferromagnetic molecular crystals are in several ways quite distinct from the conventional metallic alloys or oxidic crystals studied in solid state physics. The exchange coupling constants are usually very small for crystals of free radical molecules. Some molecular crystals show a typical magnetic behavior at a very low temperature range and another kind of behavior at a higher temperature. This feature cannot be quantitatively explained by using the conventional Ising model of ferromagnetic (FM) and antiferromagnetic (AFM) materials. In this work we show that a magnon-based approach is capable of explaining the observed AFM→FM and FM→AFM transitions in crystals of free radical molecules in a natural manner. A three-dimensional lattice is, in general, anisotropic in magnetic properties. For instance, in a molecular crystal, FM interactions may be observed along a particular direction while AFM interactions dominate along the others. Also, the coupling constants can vary widely along the three crystal axes. We have classified ferro- and antiferromagnetic molecular crystals into four distinct types, viz., FFF, AFF, AAF, and AAA, for orthorhombic or higher crystal symmetries. The anisotropic Heisenberg spin Hamiltonian operators for these four systems have been expressed in terms of magnon variables. The magnon dispersion relations have been determined, and by using these relationships the magnon population has been calculated for the low temperature range as well as for the medium and high temperature ranges. These calculations rely on the choice of the population distribution function. The low temperature calculation involves the Planck distribution. Since the magnon–magnon interaction increases very rapidly above the Neél temperature, we have made use of the classical limit, that is, a Boltzmann distribution for each spin site, and the zeroth-order one-magnon energy to calculate the magnon population at higher temperature ranges. All these calculations are based on the consideration of a macroscopically large crystal of a specific shape, and the validity of the results rests on the assumption that the bulk magnetic properties remain unchanged for a macroscopically large crystal of any other shape. Then we have derived expressions for the overall magnetization in macroscopically large crystals of the four types in the two temperature ranges, and the corresponding magnetic susceptibilities (χ). In doing so, we have made use of a typical Weiss molecular field in each case. The resulting expressions are general enough, that is, they are for an anisotropic crystal and remain valid in wide ranges of temperature. They also agree with available experimental data. The FFF and the AAA systems do not exhibit any unusual trend. As T→0, the FFF system attains saturation whereas the AFF, AAF, and AAA systems all show an approximate T2 dependence of χ∥. At a sufficiently high temperature, all four types exhibit bulk paramagnetism that follow the Curie–Weiss-type law. The FFF susceptibility develops a characteristic (T−TC)−1 dependence on temperature whereas the antiferromagnetic systems have susceptibilities proportional to (T+TN)−1 where TC and TN are the Curie–Weiss point and the Neél temperatures, respectively. Expressions derived in this work can easily explain an AFM→FM transition occurring in the AFF and AAF molecular crystals at a very low temperature. The low temperature antiferromagnetic susceptibility is singular at a temperature T0 that is sufficiently small and usually varies within 0–5 K. The low temperature expression holds up to a fraction of a degree below T0. The singularity indicates that the high temperature expression becomes valid at a temperature slightly above T0. The high temperature susceptibility is basically ferromagnetic in nature, thereby explaining the AFM→FM transition that should occur at a temperature around the singular point. At least one AAF substance, phenyl-substituted triphenyl verdazyl, shows a FM→AFM transition at about 100 K. This phenomenon, which has not been explained heretofore, can be accounted for if we include the possibility of a temperature-dependent ferromagnetic Weiss constant of the form γ(T)=γ0 exp[−T/T*]. The critical temperature T* is usually very large so that γ normally appears to be independent of temperature, but it can be of the order of one hundred degrees Kelvin when stereo–electronic effects cause a lateral displacement in the stacking of the free radical monomers along the FM direction. A concise account of the limitation of the theory has been given in the form of concluding remarks.