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Skyrmionic spin Seebeck effect via dissipative thermomagnonic torques

We derive thermomagnonic torque and its "$β$-type" dissipative correction from the stochastic Landau-Lifshitz-Gilbert equation. The "$β$-type" dissipative correction describes viscous coupling between magnetic dynamics and magnonic current and it stems from spin mistracking of the magnetic order. We show that thermomagnonic torque is important for describing temperature gradient induced motion of skyrmions in helical magnets while dissipative correction plays an essential role in generating transverse Magnus force. We propose to detect such skyrmionic motion by employing the transverse spin Seebeck effect geometry.