  In this work we study the asymmetric heat flow, i.e., thermal rectification,
of a one-dimensional, mass-graded system consisting of acoupled harmonic
oscillator lattice (ballistic spacer) and two diffusive leads attached to the
boundaries of the former with both nearest-neighbor and next-nearest-neighbor
(NNN) interactions. The latter enhance the rectification properties of the
system and specially its independence on system size. The system presents a
maximum rectification efficiency for a very precise value of the parameter that
controls the coupling strength of the NNN interactions that depend on the
temperature range wherein the device operates. The origin of this maximum value
is the asymmetric local heat flow response corresponding to the NNN
contribution at both sides of the lighter mass-loaded diffusive lead as
quantified by the spectral properties. Upon variation of the system's
parameters the performance of the device is always enhanced in the presence of
NNN interactions.
