  Thermal rectification and negative differential thermal resistance are two
important features that have direct technological relevance. In this paper, we
study the classical one dimensional Heisenberg model, thermally driven by heat
baths attached at the two ends of the system, and in presence of an external
magnetic field that varies monotonically in space. Heat conduction in this
system is studied using a local energy conserving dynamics. It is found that,
by suitably tuning the spatially varying magnetic field, the homogeneous
symmetric system exhibits both thermal rectification and negative differential
thermal resistance. Thermal rectification, in some parameter ranges, shows
interesting dependences on the average temperature T and the system size N -
rectification improves as T and N is increased. Using the microscopic dynamics
of the spins we present a physical picture to explain the features observed in
rectification as exhibited by this system and provide supporting numerical
evidences. Emergence of NDTR in this system can be controlled by tuning the
external magnetic field alone which can have possible applications in the
fabrication of thermal devices.
