Criteria for accurate determination of the magnon relaxation length from the nonlocal spin Seebeck effect

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.