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Origin of the spin Seebeck effect probed by temperature dependent measurements in Gd$_{3}$Fe$_{5}$O$_{12}$

We probe the spin Seebeck effect in Gd$_{3}$Fe$_{5}$O$_{12}$/Pt hybrid structures as a function of temperature and observe two sign changes of the spin Seebeck signal with decreasing temperature. A first sign change occurs at a temperature close to the Gd$_{3}$Fe$_{5}$O$_{12}$ magnetic compensation point at around 280 K. There the spin Seebeck signal changes sign abruptly with unaltered amplitude, indicating that the spin current is mainly caused by the magnetic Fe sub-lattices, which reorient their directions at this temperature. A second, more gradual sign change takes place around the ordering temperature of the Gd sub-lattice in the range of 65-85 K, showing that the Gd magnetic sub-lattice dominates the thermally driven spin current at lower temperatures. These sign changes together with the non-monotonous dependence of the spin Seebeck signal on the temperature demonstrate that the magnonic spin current is not simply replicating the effective magnetization of Gd$_{3}$Fe$_{5}$O$_{12}$. Rather, the thermally generated net spin current results from a complex interplay of the three magnetic sub-lattices involved.