Low-dimensional Molecular Magnetic Materials Studied By Density Matrix Renormalization Group

In recent years, it is a pioneering research issue for molecular solid magnetic materials. In this thesis, based on molecular magnetic materials synthesized experimentally, by use of density matrix renormalization group (DMRG) and quantum transfer matrix renormalization group (TMRG) method, we theoretically study a series of low-dimensional quantum magnetic systems, such as, quasi-one-dimensional organic magnet with interchain coupling model, quasi-one-dimensional organic π-conjugated spin system with high spin ground state, one-dimensional ferromagnetic and antiferromagnetic alternating spin model, two-leg spin ladder model, and molecule-based ferromagnetic chain. We discuss the magnetic interaction mechanism and phase properties of these magnetic systems at zero temperature and finite temperature and explain particular physical phenomena by experiments. Thus, our work has important guidance meaning for designing and synthesizing molecule-based magnets with high transition temperature. For the interchain coupling model of the quasi-one-dimensional organic ferromagnets, we use the two-step DMRG method to calculate the total energy, the spin configuration and the dimerization. It is found that the interchain coupling decreases the total energy of the system and increases the spin gap so that the stability of ferromagnetic state becomes stronger. To obtain high-spin ground state for designing and synthesizing organic magnetic materials, it is necessary to control spin–spin interactions of organic radicals. So we use finite-chain DMRG to study the intramolecular spin alignment of the stable radicals through π-conjugation for the purely organic spin systems, and electronical controllable on magnetism. It is found that the ferromagnetic coupling between the π-electrons and the localized spin play an important role in spin alignment for organic spin systems. In the half-filled odd case and the hole-doped even case, the ground state is a spin quartet, and there exist strong ferromagnetic correlation and a large energy gap with the increase of the system size. Low-dimensional molecular magnetic materials can leads to a better theoretical understanding of the ferro-and antiferromagnetic coupling mechanism. In this thesis the TMRG method is used to study the thermodynamic and the magnetic properties of a novel one-dimensional fumarate-bridged Cu(II) compound [C u (μ?C4H2O4)(NH3)2]n (H2O)n by the one-dimensional ferromagnetic and antiferromagnetic alternating model and spin ladder model, respectively. It is found that the latter model is more appropriate to describe the influence on the magnetic property by inter-molecule and intra-molecule for the Cu(II) complex. So far the research of molecule-based ferrimagnets has not been well documented. In this thesis we investigate the thermodynamics and magnetic behavior of the ferromagnetic biradical-monoradical alternating chain at finite temperature. For the symmetric Hamiltonian case, when the exchange interaction between the biradical and the monoradical molecules is much weaker than that within the biradical, the three sublattice spins tend to parallel alignment and an obvious ferromagnetic behavior appears upon lowering the temperature. When lowering the spatial symmetry of intermolecular magnetic interaction, the ferrimagnetic state is suppressed, which is because a formation of singlet pairs between the S = 1/2 monoradical and the S = 1 biradical molecule cause competition with the ferromagnetic ordering of the system.