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.
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