The nonlocal transport of thermally generated magnons not only unveils the underlying mechanism of the spin Seebeck effect, but also allows for the extraction of the magnon relaxation length ($lambda_m$) in a magnetic material, the average distance over which thermal magnons can propagate. In this study, we experimentally explore in yttrium iron garnet (YIG)/platinum systems much further ranges compared with previous investigations. We observe that the nonlocal SSE signals at long distances ($d$) clearly deviate from a typical exponential decay. Instead, they can be dominated by the nonlocal generation of magnon accumulation as a result of the temperature gradient present away from the heater, and decay geometrically as $1/d^2$. We emphasize the importance of looking only into the exponential regime (i.e., the intermediate distance regime) to extract $lambda_m$. With this principle, we study $lambda_m$ as a function of temperature in two YIG films which are 2.7 and 50 $mu$m in thickness, respectively. We find $lambda_m$ to be around 15 $mu$m at room temperature and it increases to 40 $mu$m at $T=$ 3.5 K. Finite element modeling results agree with experimental studies qualitatively, showing also a geometrical decay beyond the exponential regime. Based on both experimental and modeling results we put forward a general guideline for extracting $lambda_m$ from the nonlocal spin Seebeck effect.
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