Magnon Diffusion Length and Longitudinal Spin Seebeck Effect in Vanadium Tetracyanoethylene (V[TCNE]$_x$, $x \sim 2$)

Spintronic, spin caloritronic, and magnonic phenomena arise from complex interactions between charge, spin, and structural degrees of freedom that are challenging to model and even more difficult to predict. This situation is compounded by the relative scarcity of magnetically-ordered materials with relevant functionality, leaving the field strongly constrained to work with a handful of well-studied systems that do not encompass the full phase space of phenomenology predicted by fundamental theory. Here we present an important advance in this coupled theory-experiment challenge, wherein we extend existing theories of the spin Seebeck effect (SSE) to explicitly include the temperature-dependence of magnon non-conserving processes. This expanded theory quantitatively describes the low-temperature behavior of SSE signals previously measured in the mainstay material yttrium iron garnet (YIG) and predicts a new regime for magnonic and spintronic materials that have low saturation magnetization, $M_S$, and ultra-low damping. Finally, we validate this prediction by directly observing the spin Seebeck resistance (SSR) in the molecule-based ferrimagnetic semiconductor vanadium tetracyanoethylene (V[TCNE]$_x$, $x \sim 2$). These results validate the expanded theory, yielding SSR signals comparable in magnitude to YIG and extracted magnon diffusion length ($\lambda_m>1$ $\mu$ m) and magnon lifetime for V[TCNE]$_x$ ($\tau_{th}\approx 1-10$ $\mu$ s) exceeding YIG ($\tau_{th}\sim 10$ ns). Surprisingly, these properties persist to room temperature despite relatively low spin wave stiffness (exchange). This identification of a new regime for highly efficient SSE-active materials opens the door to a new class of magnetic materials for spintronic and magnonic applications.