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

V[TCNE]_x is an organic-based ferrimagnetic semiconductor that has rapidly attracted attention for applications in magnon-based quantum information systems due to its low-loss (high-Q) magnetic excitations (α~4×10^-5, Q>7,000) rivaling those of the gold standard material, YIG. Low-damping V[TCNE]_x microstructures are predicted to couple solid state spins over micron distances, establishing the foundation for on-chip interconnected solid state qubits coherently coupled via magnonic excitations. Despite these attractive prospects, a thorough understanding of magnonic transport in V[TCNE]_x is lacking. Here, we present systematic longitudinal spin Seebeck effect (LSSE) studies on V[TCNE]_x, along with a theroetical model based on the bulk magnon spin current produced by a temperature gradient in the devices, allowing us to extract information regarding magnonic transport in V[TCNE]_x. Such information (e.g. magnon DOS, magnon-phonon coupling, magnon thermalization) is critical for understanding the highly coherent magnons in this system. For example, through these measurements we establish an initial lower bound for the magnon diffusion length of 1 micron in V[TCNE]_x at room temperature, competitive with similar studies in single-crystal YIG.