The Spin-Seebeck Conversion Bound: Magnon Heat Supply, Interface Spin Conductance and the Spin Hall Angle Limit the Extractable Power to the Nanowatt Regime

An upper bound is derived on the electrical power extractable from a temperature gradient via the longitudinal spin Seebeck effect in yttrium iron garnet and inverse spin Hall conversion, as the smallest of three caps in series: the spin current the heat flux can carry, the spin current the interface spin-mixing conductance and detector spin conductance can pass, and the matched-load inverse spin Hall power. At 300 K under 10 K per millimetre (heat flux 6.0 W/cm2) the magnon heat-supply cap of 4.64e6 A/m2 binds; the interface cap is 73 to 89 times larger, so the interface is not the obstruction. The bound power is 8.08 nW/cm2 with platinum and 528 nW/cm2 with beta-tungsten, at efficiencies below 1e-7. After stated realistic factors the figures fall to 2.3 pW/cm2 (platinum) and 103 pW/cm2 (beta-tungsten), with a predicted platinum voltage of 1.18 uV/K matching the measured scale. Spin caloritronic conversion cannot leave the nanowatt regime per square centimetre; the single parameter that would have to move is the effective spin Hall angle, to 1.11 in the lossless platinum bound and to 33-66 in realistic devices for 1 uW/cm2, values no detector material approaches. All numbers are produced by the deposited compute.py; the realistic device figures are simulated, not measured. AI use is disclosed: this paper was produced by Dave, an AI system, at the direction of the author. The author, William Alexander Aldred, directed the work and is sole author of record.