On the variation of magnetic susceptibility of a molecular crystal with temperature: The 2,4,6-triphenylverdazyl system

Abstract

Magnetic susceptibilities of spin-1 2 systems of orthorhombic and higher crystal symmetries have been numerically investigated while taking possible anisotropy in the coupling constants along different crystal axes into account. The work relies on the magnon-based theory of ferromagnetic ͑FM͒ and antiferromagnetic ͑AFM͒ crystal systems of types FFF, AFF, AAF, and AAA ͓J. Chem. Phys. 111, 9009 ͑1999͔͒. The AAF crystal, in particular, shows interesting changes in the temperature dependence of magnetic susceptibility when the ferromagnetic exchange coupling constant is varied. We especially show that the susceptibility anomalies of molecular crystals fit naturally within the framework of the extended magnon-theoretical formalism, and do not necessarily imply a FM→AFM or a reverse phase transition. A real system, molecular crystal of 2,4,6-triphenylverdazyl ͑2,4,6-TPV͒, has been investigated here. It was previously interpreted as an AAF system from observed susceptibility data ͓Tomiyoshi et al., Phys. Rev. B 49, 16031 ͑1994͔͒. The trend of the temperature dependence of magnetic susceptibility studied in the present work also indicates that the crystal belongs to the AAF category with a less prominent FM exchange coupling constant. To reinforce our conclusions, we have adopted a two-pronged strategy. First, the geometry of the 2,4,6-TPV monomer has been optimized here by ab initio unrestricted Hartree-Fock ͑UHF͒ calculations using the STO-3G basis set. The optimized geometry is almost planar. A subsequent calculation has been carried out with the phenyl rings twisted out of the plane of the nitrogen atoms. The STO-3G optimized geometry, and the same geometry except for the twisted phenyl rings, have been used to perform ab initio coupled-cluster ͑UCCSD-T͒ calculations with the same basis, and UHF as well as density-functional ͑UB3LYP͒ calculations using the 6-31G basis set. The calculated data can easily rationalize the twists while the species remains in crystal. The magnetic category of the crystal has been unambiguously confirmed as AFA from ab initio UHF and UB3LYP calculations of the total energy in different spin states of dimers and trimers along the crystal axes. The computed energy values, however, fail to yield accurate estimates of the exchange coupling constants J a , J b , and J c , because the latter are on the order of 1k B K corresponding to energy differences on the order of 10 Ϫ6 hartree between different spin states. In the second approach, the observed features of the susceptibility minimum and maximum have been used to determine the best values of the exchange coupling constants from the theoretical formulas for an anisotropic AFA crystal. The AFM (J a and J c ) and FM (J b ) exchange coupling constants and the Néel temperature (T N ) found from this analysis correspond to J a ϩJ c ϭϪ1.05 k B K, J b ϭ1.35 k B K, and T N ϭ1.75 K. The calculated J values significantly differ from those estimated from a linear Heisenberg chain model, but generate a susceptibility versus temperature graph that mimics...