Effect of a magnetic field on long-range magnetic order in stage-4 and stage-6 superconducting La 2 CuO 4+y

We have measured the enhancement of the static incommensurate spin-density wave (SDW) order by an applied magnetic field in stage-4 and stage-6 samples of superconducting ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4+y}.$ We show that the stage-6 ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4+y}$ ${(T}_{c}=32\mathrm{K})$ forms static long-range SDW order with the same wave vector as that in the previously studied stage-4 material. We have measured the field dependence of the SDW magnetic Bragg peaks in both stage-4 and stage-6 materials at fields up to 14.5 T. A recent model of competing SDW order and superconductivity describes these data well.