Soos, Zoltan Geza (1965) I. Theory of the linear Heisenberg antiferromagnet. II. Phonon effects in triplet exciton theory. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd01272004105953
Abstract
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PART I
In the Heisenberg model, the hamiltonian describing a linear array of tightlybound 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 onedimensional antiferromagnet are studied by transforming to pseudospin operators similar to those used by Anderson in superconductivity theory. In a selfconsistent molecularfield 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 singlestriplet 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 antiferromagneticallycoupled, tightlybound 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 strongcoupling 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 spinindependent, phononcoupled repulsion between excitons is rederived.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Degree Grantor:  California Institute of Technology 
Major Option:  Chemistry 
Thesis Committee: 

Defense Date:  1 January 1965 
Record Number:  etd01272004105953 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd01272004105953 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  368 
Collection:  CaltechTHESES 
Deposited By:  Imported from ETDdb 
Deposited On:  29 Jan 2004 
Last Modified:  25 Dec 2012 14:59 
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