Theoretical studies on models for organic ferromagnetism

Abstract

The thesis examines the three models in existence which predict ferromagnetism in purely organic systems. These models are (i) Mataga-Ovchinnikov model which predicts high-spin ground state in alternant polymers with degenerate, nondisjoint, nonbonded molecular orbitals, (ii) McConnell’s mechanism I, which predicts a high-spin ground state when two radicals are so stacked to have registry between sites with positive spin density on one molecule and negative spin density on another molecule, and (iii) McConnell’s mechanism II, which predicts a high-spin ground state in a donor-acceptor stack if the lowest virtually excited state is a high-spin state. In this thesis, with the help of interacting many-body model Hamiltonians, we study the stability of the high-spin states in the parameter space of the models as well as with respect to various perturbations. The models employed are one-band and multi-band Hubbard and Pariser-Parr-Pople (PPP) models and spin-1/2 Heisenberg model. In Chapter 1, we briefly review the electronic properties of organic solids with particular emphasis on magnetism. Several models for organic ferromagnetism are introduced and the current experimental and theoretical status is presented. We then introduce model Hamiltonians necessary for a quantitative study of ?-conjugated organic systems, in the context of magnetism. The VB technique for solving these model Hamiltonians is briefly discussed. The new features of the technique incorporated by us into the VB scheme, namely two-integer representation of VB diagrams, direct uncrossing of VB diagrams while setting up the Hamiltonian matrix, deriving rules for handling exchange terms in the Hamiltonian and transformation of eigenstates in VB basis to eigenstates in Slater determinantal basis to facilitate matrix element computations are dealt with at some length. In Chapter 2, the stability of the high-spin ground state in a typical Mataga polymer with respect to breaking the alternancy symmetry and distortion of the backbone conjugation has been examined. In the PPP and Hubbard models the ground state continues to be a high-spin state, even when alternancy symmetry is broken by introducing large site energy differences. The bond order calculations in all these models show that the low-spin state is susceptible to dimerization of the backbone. In the distorted chains, the low-spin state is stabilized to a greater extent leading to low-spin ground states at least in ‘soft’ lattices. In Chapter 3, McConnell’s second mechanism based on intramolecular exchange is examined. From full configuration interaction calculations on stacked cyclic polyene radicals/radical-ions, within the Hubbard and the Pariser-Parr-Pople (PPP) models, we show that the ground state is not always a triplet state as predicted by the McConnell mechanism for organic ferromagnetism. The (2n + 1)-membered cyclic polyene radical stacks always possess a singlet ground state since kinetic exchange dominates over direct exchange. In 2n-membered cyclic polyene radical-ions, for small n (n < 3) the ground state is a singlet. For larger n values, the ground state is predicted to be a triplet since the difference in kinetic energy between the singlet and the triplet states is not large and the direct exchange is expected to dominate. However, intra-atomic Hund’s rule exchange is much stronger and hence we examine the stacked acetylenic ion-radical systems. The acetylenic ion-radical system is found to possess a high-spin ground state which is stable with respect to different geometries of packing and substitutions. The stability of the high-spin state is attributed to the degeneracy of the atomic orbitals involved in conjugation. These systems are suggested to be prime candidates for observing organic ferromagnetism. In Chapter 4, we examine in detail the competition between kinetic exchange and direct exchange in McConnell’s second mechanism for organic ferromagnetism. We employ multiband Hubbard and PPP models and study mixed donor-acceptor stacks with doubly degenerate acceptor orbitals and nondegenerate donor orbitals at 2/3 filling. Model exact results for 2, 3 and 4 D-A units show that McConnell’s prediction of high-spin ground state in these systems is in general incorrect. The larger phase-space available for low-spin state leads to its kinetic stabilization in preference to high-spin states. However, for large electron correlation strengths, the direct exchange dominates over the kinetic exchange resulting in a high-spin ground state. In Chapter 5, we study McConnell’s spin density model for organic ferromagnetism. Typically, molecules which belong to this class are pseudo ortho-, meta- and para-dicarbene substituted [2,2] paracyclophanes. We employ a Heisenberg spin model in these studies as the number of active orbitals are too large to include charge degrees of freedom in an exact calculation. The ground state is always a quintet in pseudo-ortho and para isomers and the lowest energy spin excitation is to a triplet state while the pseudo-meta isomer possesses a singlet ground state. The possibility of obtaining high-spin molecules and eventually an organic ferromagnet in one dimension as was proposed by McConnell seems justified.