Effect of a magnetic field on the spin- and charge-density-wave order in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">La</mml:mi></mml:mrow><mml:mrow><mml:mn>1.45</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Nd</mml:mi></mml:mrow><mml:mrow><mml:mn>0.4</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Sr</mml:mi></mml:mrow><mml:mrow><mml:mn>0.15</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">CuO</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

The spin-density wave (SDW) and charge-density wave (CDW) order in superconducting ${\mathrm{La}}_{1.45}{\mathrm{Nd}}_{0.4}{\mathrm{Sr}}_{0.15}{\mathrm{CuO}}_{4}$ were studied under an applied magnetic field, using neutron and x-ray diffraction techniques. In zero field, incommensurate (IC) SDW order appears below $\ensuremath{\sim}40\mathrm{K},$ which is characterized by neutron diffraction peaks at $(1/2\ifmmode\pm\else\textpm\fi{}0.134,1/2\ifmmode\pm\else\textpm\fi{}0.134,0).$ The intensity of these IC peaks increases rapidly below ${T}_{\mathrm{Nd}}\ensuremath{\sim}8\mathrm{K}$ due to an ordering of the ${\mathrm{Nd}}^{3+}$ spins. The application of a 1 T magnetic field parallel to the c axis markedly diminishes the intensity below ${T}_{\mathrm{Nd}},$ while only a slight decrease in intensity is observed at higher temperatures for fields up to 7 T. Our interpretation is that the c-axis field suppresses the parasitic ${\mathrm{Nd}}^{3+}$ spin order at the incommensurate wave vector without disturbing the stripe order of ${\mathrm{Cu}}^{2+}$ spins. Consistent with this picture, the CDW order, which appears below 60 K, shows no change for magnetic fields up to 4 T. These results stand in contrast to the significant field-induced enhancement of the SDW order observed in superconducting ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ with $x\ensuremath{\sim}0.12$ and stage-4 ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4+y}.$ The differences can be understood in terms of the relative volume fraction exhibiting stripe order in zero field, and the collective results are consistent with the idea that suppression of superconductivity by vortices nucleates local patches of stripe order.