Thermomagnetic anomalies in quantum magnon transport caused by tunable junction geometries in cold atomic systems

We investigate magnon-mediated spin and heat transport in a magnetic linear junction (MLJ), where two Heisenberg ferromagnets realized in optical lattices are connected through a linearly aligned interface. Employing the Schwinger–Keldysh approach, we show that in weak effective Zeeman fields, magnon Bose–Einstein statistics give rise to magnonic criticality, leading to a pronounced enhancement of spin and thermal conductances. The resulting singular transport behavior is strongly dependent on the junction geometry, and qualitatively differs from that of the point-contact setup studied previously. The enhanced conductances further induce a breakdown of the magnonic Wiedemann–Franz law. In the classical low-temperature regime well below the magnon gap, we find a magnonic Lorenz number that is temperature-independent but geometry-dependent, in sharp contrast to the universal value for Fermi liquids. Moreover, the MLJ interface geometry separates spin and heat relaxation processes between the two ferromagnets, producing decay times robust against temperature and effective Zeeman fields. Our results highlight geometry-sensitive magnon transport unique to bosonic systems and suggest new directions for thermomagnetic phenomena in tunable cold-atom platforms.