We investigate the thermal transport properties in superconductor-antiferromagnet-superconductor and superconductor-ferromagnet-superconductor junctions based on buckled two-dimensional materials (BTDMs). Owing to the unique buckled sublattice structures of BTDMs, in both junctions the phase dependence of the thermal conductance can be effectively controlled by perpendicular electric fields. The underlying mechanism for the electrical tunability of thermal conductance is elucidated resorting to the band structures of the magnetic regions. We also reveal the distinct manifestations of antiferromagnetic and ferromagnetic exchange fields in the thermal conductance. These results demonstrate that the perpendicular electric field can serve as a knob to externally manipulate the phase-coherent thermal transport in BTDMs-based Josephson junctions.
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