  Motivated by thermal conductivity experiments in spin chain compounds, we
propose a phenomenological model to account for a ballistic magnetic transport
coupled to a diffusive phononic one, along the line of the seminal
two-temperature diffusive transport Sanders-Walton model. Although the
expression for the effective thermal conductivity is identical to that of
Sanders-Walton, the interpretation is entirely different, as the "magnetic
conductivity" is replaced by an "effective transfer conductivity" between the
magnetic and phononic component. This model also reveals the fascinating
possibility of visualizing the ballistic character of magnetic transport, for
appropriately chosen material parameters, as a two peak counter-propagating
feature in the phononic temperature. It is also appropriate for the analysis of
any thermal transport experiment involving a diffusive component coupled to a
ballistic one.
