I. Theory of the Linear Heisenberg Antiferromagnet. II. Phonon Effects in Triplet Exciton Theory

Citation

Soos, Zoltán Géza (1965) I. Theory of the Linear Heisenberg Antiferromagnet. II. Phonon Effects in Triplet Exciton Theory. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/8NTG-SP91. https://resolver.caltech.edu/CaltechETD:etd-01272004-105953

Abstract

NOTE: Tect or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. PART I In the Heisenberg model, the hamiltonian describing a linear array of tightly-bound electrons that are exchangecoupled to their neighbors is [...], where [...] is the alternation parameter, [...] is the electron spin on the jth site, and J > 0 (antiferromagnetic coupling). The solutions of the one-dimensional antiferromagnet are studied by transforming to pseudo-spin operators similar to those used by Anderson in superconductivity theory. In a self-consistent molecular-field approximation, the ground state energy, the excitation spectrum, and the coherence between antiparallel spins are found for arbitrary [...] and temperature. At 0[degrees]K, the solutions agree with or improve upon previous calculations of the properties of the regular ([...]) or the alternating ([...]) antiferromagnet. For T > 0, good agreement is found with the experimental paramagnetic susceptibilities of organic crystals whose spin properties may be represented by a regular or an alternating antiferromagnet. The temperature dependence of the excitation energies agrees with the observed behavior of the singles-triplet energy gap in triplet exciton systems. The high temperature and weak alternation extension of triplet exciton theory is presented. PART II Certain organic crystals consist of linear chains of antiferromagnetically-coupled, tightly-bound electrons; their EPR (electron paramagnetic resonance) properties are discussed in terms of triplet excitons. We consider a deformable lattice and investigate the influence of phonons on triplet excitons. For low exciton density (i.e., at low temperature) the excitons, on account of the phonons, are localized and diffusional; they resemble chargeless polarons in the strong-coupling limit. A general expression for the rate, and its temperature dependence, of an exciton process in a phonon bath at thermal equilibrium is found. In particular, we obtain the diffusion constant for exciton motion, the activation energy for diffusion, and the rates of exciton creation and annihilation; we estimate these parameters for Wurster's blue perchlorate. Even at 0[degrees]K, diffusional excitons are mobile enough to account for the absence of hyperfine structure in the EPR spectra. Modifications, due to the phonons, of the parameters of the effective exciton hamiltonian are obtained and a spin-independent, phonon-coupled repulsion between excitons is rederived.

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