  We investigate electronic thermal rectification in ferromagnetic
insulator-based superconducting tunnel junctions. Ferromagnetic insulators
coupled to superconductors are known to induce sizable spin splitting in the
superconducting density of states, and also lead to efficient spin filtering if
operated as tunnel barriers. The combination of spin splitting and spin
filtering is shown to yield a substantial self-amplification of the electronic
heat diode effect due to breaking of the electron-hole symmetry in the system
which is added to the thermal asymmetry of the junction. Large spin splitting
and large spin polarization can potentially lead to thermal rectification
efficiency exceeding 5 .10^4 for realistic parameters in a suitable temperature
range, thereby outperforming up to a factor of 250 the heat diode effect
achievable with conventional superconducting tunnel junctions. These results
could be relevant for improved mastering of the heat currents in innovative
phase-coherent caloritronic nanodevices, and for enhanced thermal management of
quantum circuits at the nanoscale.
