The longitudinal spin Seebeck effect refers to the generation of a spin current when heat flows across a normal metal/magnetic insulator interface. Until recently, most explanations of the spin Seebeck effect use the interfacial temperature difference as the conversion mechanism between heat and spin fluxes. However, recent theoretical and experimental works claim that a magnon spin current is generated in the bulk of a magnetic insulator even in the absence of an interface. This is the so-called intrinsic spin Seebeck effect. Here, by utilizing a non-local spin Seebeck geometry, we provide additional evidence that the total magnon spin current in the ferrimagnetic insulator yttrium iron garnet (YIG) actually contains two distinct terms: one proportional to the gradient in the magnon chemical potential (pure magnon spin diffusion), and a second proportional to the gradient in magnon temperature ($ abla T_m$). We observe two characteristic decay lengths for magnon spin currents in YIG with distinct temperature dependences: a temperature independent decay length of ~ 10 ${mu}$m consistent with earlier measurements of pure ($ abla T_m = 0$) magnon spin diffusion, and a longer decay length ranging from about 20 ${mu}$m around 250 K and exceeding 80 ${mu}$m at 10 K. The coupled spin-heat transport processes are modeled using a finite element method revealing that the longer range magnon spin current is attributable to the intrinsic spin Seebeck effect ($ abla T_m eq 0$), whose length scale increases at lower temperatures in agreement with our experimental data.
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