The Magnetic Properties And Thermodynamics Of Low-dimensional Molecule-based Ferrimagnetisms And The Frustrated Diamond-like Spin Chain

In recent years, it is a pioneering research issue for the molecular solid magnetic materials. In particular, the synthesis and design of organic molecule-based magnetism have been attracting much attention from both experimental and theoretical points of view. Among these organic molecule-based magnetism, the most famous one is the molecule- based ferrimagnetism synthesized by D. Shiomi et al., which is composed of S=1 biradical and S=1/2 monoradical molecules alternating with antiferromagnetic interactions along the chain, and the S=1 site is composed of two S=1/2 spins by a finite ferromagnetic interaction. The organic molecular complex exhibits excellent ferrimagnetic order at low temperature, however, the magnetic transition temperature Tc of which is as low as about 6 K, which makes the organic magnetic material far from practical functionality. Such that, the magnetic coupling mechanism and the quantum magnetic transition of these organic ferrimagnetisms need to be studied in detail, and the new schemes to design and synthesize the organic molecule-based ferrimagneism with high Curie temperature should be put forward from a theoretical point of view.Based on the molecular magnetic materials synthesized experimentally, we have described above organic molecule-based magnetic materials as a spin-1/2 ferrimagnetic diamond-like chain. Firstly, we consider the diamond-like spin chain as a one-dimensional isotropic XY Heisenberg Hamiltonian model, and the magnetic properties and the thermodynamics of which have been studied by means of two-time Green's function theory within Tyablikov's decoupling approximation. The numerical results show that the spin-wave excitation spectra of the system are composed of three distinct branches of elementary excitations, the two of which, originate from the ferromagnetic interaction'excitations, and the third originates from the antiferromagnetic ones. The magnetic field dependence of the magnetization at low temperature displays as a 1/3 plateau with three critical fields, and the temperature dependence of the magnetization at various magnetic field shows rich ferrimagnetic behaviors. Meanwhile, when the intramolecular ferromagnetic interaction is less than the intermolecular antiferromagnetic ones, the temperature dependence of the specific heat of the system shows a distinct double-peak structure. With a deep research of the specific heat of the system, it is concluded that, with the further increasing of the intramolecule ferromagnetic interaction, the biradical having two S=1/2 spins becomes closer and closer to that of effective S=1 monomolecular for the thermodynamic properties.Secondly, we consider the diamond-like spin chain as a one-dimension general Heisenberg Hamiltonian model, the magnetic and thermodynamic properties of which are studied by means of Green's function with combination to Tyablikov's decoupling approximation. It can be found that the intermolecular antiferromagnetic interactions play an important role on the formation of the ferrimagnetic order along the spin chain. And the lower space symmetry of the antiferromagnetic interactions has contribution to the spontaneous magnetization and the increasing of the Curie temperature. Meanwhile, the formation of dimer between the biradical and the monoradical has contribution to the the spontaneous magnetization and the decreasing of the Curie temperature, meanwhile, the trimer among the molecules plays a simliar role. So that, to synthesis the organic molecule-based ferrimagnetism with high Tc, the space symmetry of magnetic interactions, the dimer, and the trimer along the spin chain should be taken into account.As far as the above-mentioned spin-1/2 diamond-like spin model, we find that the model can be viewed as one of the simplest one-dimensional quantum frustrated system, assuming that the exchange interactions along the chain are all anitferromagnetic ones, and has already received a substantial amount of theoretical attention. Based on the foregoing theoretical model and method, the magnetization, the magnetic susceptibility, and the specific heat of the frustrated spin system have been discussed. It is found that the magnetic field dependence of the magnetization of the frustrated diamond-like spin chain also displays as a 1/3 plateau, and the temperature dependence of the magnetic susceptibility shows a double-peak structure at low temperature, the peak at lower temperature origins from the effect of spin frustration, and the one located at higher temperature origin from the antiferromagnetic interactions. It should be pointed out that our theoretical results are employed to explain the measurements and unusual behaviors on the frustrated compound Cu3(CO3)2(OH)2 successfully. Meanwhile, the curves of the specific heat of the general symmetrical frustrated diamond-like spin chain shows a distinct double-peak structure due to the effect of frustration in the absence of the magnetic field, nevertheless, it is interesting that, when a weak and finite magnetic field is applied to the spin system, an additional little peak appears at the intermediate temperature, and the curves of the specific heat show a three-peak structure due to the external field-induced magnetic order.In the end, we have applied other numerical methods, such as the quantum transfer matrix method and the finite-lattice exact diagonalization method, to study the magnetic and thermodynamic properties of the spin-1/2 diamond-like spin chain, and the numerical results can be compared with ones of the Green's function method.