  The generation of localized magnetic field gradients by on-chip nanomagnets
is important for a variety of technological applications, in particular for
spin qubits. To advance beyond the empirical design of these nanomagnets, we
propose a systematic and general approach based on the micromagnetic
formulation of an optimal field gradient source. We study the different field
configurations that can be realized and find out quantitatively the most
suitable ferromagnetic layer geometries. Using micromagnetic simulations, we
then investigate the minimum requirements for reaching magnetic saturation in
these nanomagnets. In terms of either longitudinal or transverse field
gradient, the results provide an optimal solution for uniform, saturated
nanomagnets, where the magnetic material can be selected according to the
strength of the external fields that can be used.
