  The search for superconducting systems exhibiting nonreciprocal transport
and, specifically, the diode effect, has proliferated in recent years. This
trend encompasses a wide variety of systems, including planar hybrid
structures, asymmetric SQUIDs, and certain noncentrosymmetric superconductors.
A common feature of such systems is a gyrotropic symmetry, realized on
different scales and characterized by a polar vector. Alongside time-reversal
symmetry breaking, the presence of a polar axis allows for magnetoelectric
effects, which, when combined with proximity-induced superconductivity, results
in spontaneous non-dissipative currents that underpin the superconducting diode
effect. This symmetry established, we present a comprehensive theoretical study
of transport in a lateral Josephson junctions composed of a normal metal
supporting the spin Hall effect, and attached to a ferromagnetic insulator. Due
to the presence of the latter, magnetoelectric effects arise without requiring
external magnetic fields. We determine the dependence of the anomalous current
on the spin relaxation length and the transport parameters commonly used in
spintronics to characterize the interface between the metal and the
ferromagnetic insulator. Therefore, our theory naturally unifies nonreciprocal
transport in superconducting systems with classical spintronic effects, such as
the spin Hall effect, spin galvanic effect, and spin Hall magnetoresistance. We
propose an experiment involving measurements of magnetoresistance in the normal
state and nonreciprocal transport in the superconducting state. Such
experiment, on the one hand, allows for determining the parameters of the model
and thus verifying with a greater precision the theories of magnetoelectric
effects in normal systems. On the other hand, it contributes to a deeper
understanding of the underlying microscopic origins that determine these
parameters.
