STUDIES OF SMALL-POLARON MOTION .4. ADIABATIC THEORY OF HALL EFFECT

The two-dimensional molecular crystal model of Friedman and Holstein describing the motion of a small polaron in the presence of a magnetic field is studied in the adiabatic approximation. Upon averaging over the electronic coordinates, according to the standard prescription, one finds that the vibrational Hamiltonian contains (in addition to the usual terms, namely the carrier-free vibrational Hamiltonian supplemented by the energy of the excess electron expressed as a function of vibrational coordinates) a term which is linearly dependent on the lattice momentum and proportional to the magnetic field. In the adiabatic theory the effect of the magnetic field on the motion of the small polaron is found by studying the influence of the magnetic term of the vibrational Hamiltonian on the particular vibrational motions which correspond to the passage of the excess carrier from one site to a particular neighbor. In the present work, concerned only with the high temperature regime (in practice, temperatures above 1 2θDebye) within which the small polaron moves through the lattice by a succession of incoherent jumps between neighboring sites, the vibrational motion is treated classically, as is appropriate at sufficiently high temperatures. It is found that although the temperature dependence of the drift mobility that is herein calculated differs little from that derived in the Friedman-Holstein perturbation calculation, the Hall mobility temperature dependence (for reasonable choices of the physical parameters) differs markedly from the perturbation result. In particular, for appropriate choices of the physical parameters, the adiabatic Hall mobility can be a decreasing function of temperature. Thus the absence of an activated Hall mobility is not in itself evidence against small polaron motion. © 1969.