We investigate the rotation velocity of the first stars by modelling the angular momentum transfer in the primordial accretion disc .
Assessing the impact of magnetic braking , we consider the transition in angular momentum transport mode at the Alfv \acute { e } n radius , from the dynamically dominated free-fall accretion to the magnetically dominated solid-body one .
The accreting protostar at the centre of the primordial star-forming cloud rotates with close to breakup speed in the case without magnetic fields .
Considering a physically-motivated model for small-scale turbulent dynamo amplification , we find that stellar rotation speed quickly declines if a large fraction of the initial turbulent energy is converted to magnetic energy ( \gtrsim 0.14 ) .
Alternatively , if the dynamo process were inefficient , for amplification due to flux-freezing , stars would become slow rotators if the pre-galactic magnetic field strength is above a critical value , \simeq 10 ^ { -8.2 } G , evaluated at a scale of n _ { H } = 1 { cm ^ { -3 } } , which is significantly higher than plausible cosmological seed values ( \sim 10 ^ { -15 } G ) .
Because of the rapid decline of the stellar rotational speed over a narrow range in model parameters , the first stars encounter a bimodal fate : rapid rotation at almost the breakup level , or the near absence of any rotation .