Finite-element modeling of thermal gradients during non-local thermal spin injection

A new spin Seebeck experiment has been demonstrated, in which a laser is focused on an electrically isolated Pt absorbing pad on yttrium iron garnet (YIG), thermally generating a spin current in YIG.[1] The spins diffuse laterally and are detected non-locally on a remote Pt detector via the inverse spin Hall effect ($V_{ISHE}^{non-local} )$. This geometry is expected to remove parasitic thermal transport voltages unrelated to the magnonic spin current that could contaminate $V_{ISHE}^{non-local} $. To validate this, 3D steady-state heat conduction equations are solved to determine the stray temperature gradient at the Pt detector as a function of distance from the laser heating source. We find that the temperature gradient beneath the Pt detector vanishes when the laser is laterally displaced (along x) by 50$\mu $m. The gradient along the interface normal follows $\nabla T_{z} (x)\sim e^{-1.76x}$ and the gradient parallel to the interface follows $\nabla T_{x} (x)\sim e^{-0.08x}$. Both gradients decay much faster than the measured $V_{ISHE}^{non-local} (x)\sim e^{-0.025x}$ demonstrating the validity of the non-local geometry in probing laterally diffused spin. [1]B. Giles, et al., 2015 APS March meeting abstract