We present a theory of magnetic response in a finite-size two-dimensional superconductors with Rashba spin-orbit coupling. The interplay between the latter and an in-plane Zeeman field leads on the one hand to an out-of-plane spin polarization which accumulates at the edges of the sample over the superconducting coherence length, and on the other hand, to circulating supercurrents decaying away from the edge over a macroscopic scale. In a long finite stripe of width W both, the spin polarization and the currents, contribute to the total magnetic moment induced at the stripe ends. These two contributions scale with W and W2 respectively, such that for sufficiently large samples it can be detected by current magnetometry techniques.
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