We study conductance and adiabatic pumped charge and spin currents in a graphene quantum pump with Corbino geometry in the presence of an applied perpendicular magnetic field. The pump is driven by the periodic and out of phase modulations of the magnetic field and an electrostatic potential applied to the ring area of the pump. We show that the Zeeman splitting, despite of its smallness, can suppress the conductance oscillations at the zero doping and in a threshold value for the flux piercing the ring area which depends on the inner lead radius and thus on the flux penetrating in it. Moreover, it generates a considerable spin conductance at infinitesimal nonzero doping and at the magnetic flux, that charge conductance starts to suppress. We find that the pumped charge and spin currents increase by the magnetic field with small oscillations until they start to suppress due to the effect of the nonzero doping and the Zeeman splitting. In graphene Corbino pumps with small inner leads the Zeeman splitting shows its effect in a large value of the magnetic field and thus we can get a considerable pumped charge and spin currents at the enough small magnetic fields.Comment: 14 pages, 13 figure

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