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We study the effect of magnetic field on the rheology of magneticmicro-swimmers suspensions. We use a model of a dilute suspension under simpleshear and subjected to a constant magnetic field. Particle shear stress isobtained for both pusher and puller types of micro-swimmers. In the limit oflow shear rate, the rheology exhibits a constant shear stress, called actuatedstress, which only depends on the swimming activity of the particles. Thisstress is induced by the magnetic field and can be positive (brake state) ornegative (motor state). In the limit of low magnetic fields, a scaling relationof the motor-brake effect is derived as a function of the dimensionlessparameters of the model. In this case, the shear stress is an affine functionof the shear rate. The possibilities offered by such an active system tocontrol the rheological response of a uid are finally discussed.

Actuated rheology of magnetic micro-swimmers suspensions : emergence of motor and brake states