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We theoretically and numerically study spin turbulence (ST) with small spinmagnitude in spin-1 spinor Bose-Einstein condensates by using the spin-1 spinorGross-Pitaevskii (GP)equations. This kind of ST is realized in two cases: (i)with antiferromagnetic interaction and (ii) with ferromagnetic interactionunder a static magnetic field. The ST with small spin magnitude can exhibit twocharacteristic power laws in the spectrum of the spin-dependent interactionenergy: -1 and -7/3 power laws in the low- and high-wave-number regions,respectively. These power laws are derived from a Kolmogorov-type dimensionalscaling analysis for the equations of motion of the spin vector and nematictensor. To confirm these power laws, we perform a numerical calculation of thespin-1 spinor GP equations in a two-dimensional uniform system. In case (i),the -7/3 power law appears in the high-wave-number region, but the spectrum inthe low-wave-number region deviates from the -1 power law. In contrast, both -1and -7/3 power laws are found to clearly appear in case (ii).

Spin turbulence with small spin magnitude in spin-1 spinor Bose-Einstein condensates