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The family of hexaferrites possess the largest known magnetoelectric coefficients of any material, and understanding the origins of the strong coupling between magnetism and electrical polarization relies upon knowledge of its intricate magnetic structure. By characterising the magnetic phase diagram of the novel hexaferrite Ba_0.5Sr_1.5Mg₂Fe₁₂O₂₂ by SQUID magnetometry and magnetocurrent measurements, we revealed a number of metamagnetic states, one of which exhibits striking magnetoelectric effects. This phase has a commensurate, k=(0,0,1.5), fan-type magnetic structure, which we have studied in detail by spatially resolved soft x-ray circular dichroism. We find that the observed circular dichroism is of pure magnetic origin, as opposed to arising from charge- magnetic interference suggested in previous studies, and hence it is directly sensitive to magnetic polarity. This has enabled us to spatially resolve the evolution of the microscopic magnetoelectric polarity of the system as a function of magnetic field and temperature.