Maximum Variational Principle for Conduction Problems in a Magnetic Field, and the Theory of Magnon Drag
A maximum variational principle is shown to be applicable for conduction problems (including "drag" effects) in the presence of a magnetic field. The part of the diagonal tensor element that is even in the magnetic field is maximized. The relation between the "high-field" work of Chambers, Lifshitz, and co-workers and the variational method is pointed out, the latter being applied to accommodate open orbit effects, and to obtain interpolation formulas to span high- and low-field solutions (keeping in view the phonon drag effects). It was found that standard operator expansion techniques are useful for obtaining solutions for the high-field limit. Symmetry considerations are facilitated by use of some of the operators suggested by the variational problem, and it is shown that if no drag effects are present and a time of relaxation permitted, some new relations emerge for the cross coefficients connecting the charge flow and temperature gradient. Finally, because the scattering by spin waves is analogous to the scattering of phonons, (since double-magnon processes are shown to be negligible at low temperatures), the theory of "magnon-drag" follows precisely that of phonon drag, and the effects can be automatically incorporated in all the expressions.