Abstract
We theoretically examine the minimal factors for the emergence of magnon turbulence under current. We show that the turbulence emerges even in the nanocontact, where only the exchange term and the spin-transfer torque contribute in the determination of the magnetic structure and dynamics therein. Namely, the sufficient factors for the emergence of the turbulence are only the exchange and the spin-transfer torque. We also show that the critical spin current density of the magnon turbulence is related to a current-induced exchange length. The emergence of the magnon turbulence is characterized by a crossover of the length and the system size.
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