  The spin Seebeck effect is studied across a charge insulating magnetic
junction, in which thermal-spin conjugate transport is assisted by the exchange
interactions between the localized spin in the center and electrons in metallic
leads. We show that, in contrast with bulk spin Seebeck effect, the figure of
merit of such nanoscale thermal-spin conversion can be infinite, leading to the
ideal Carnot efficiency in the linear response regime. We also find that in the
nonlinear spin Seebeck transport regime, the device possesses the asymmetric
and negative differential spin Seebeck effects. In the last, the situations
with leaking electron tunneling are also discussed. This nanoscale thermal spin
rectifier, by tuning the junction parameters, can act as a spin Seebeck diode,
spin Seebeck transistor and spin Seebeck switch, which could have substantial
implications for flexible thermal and information control in molecular spin
caloritronics.
