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The superposition of topological phonons and flexoelectronic chargeseparation in an inhomogeneously strain Si give rise to topological electronicmagnetism of phonons. The topological electronic magnetism of phonons is alsoexpected to give rise to stationary spin current or spin superfluidity. In thisexperimental study, we present possible evidence of spin superfluidity in aninhomogeneously strained p-Si thin films samples. The spin superfluidity isuncovered using non-local resistance measurement. A resonance behavior isobserved in a non-local resistance measurement at 10 kHz and between 270 K and281.55 K, which is attributed to the second sound. The observation of secondsound and spatially varying non-local resistance phase are the evidences forspin superfluidity. The spatially varying non-local resistance with oppositephase are also observed in Pt/MgO/p-Si sample. The overall non-local responsescan be treated as a standing waveform from temporal magnetic moments of thetopological phonons.

Topological phonons in an inhomogeneously strained silicon-6: Possible  evidence of the high temperature spin superfluidity and the second sound of  topological phonons