We present SNSPDs from NbN nanowires shaped after square-spiral that allows an increase not only in critical currents but also an extension of spectral detection efficiencies by just applying an external magnetic field. Using negative electron-beam lithography with the positive resist for shaping nanowires, made it possible to reduce the inner bend radius. Consequently, the effect of critical-current enhancement in the magnetic field becomes stronger than it was demonstrated earlier. Here we achieved a 13% increase of the critical current in the magnetic field. We measured spectra of the single-photon detection efficiency in the wavelength range from 400 to 1100 nm in the magnetic field. At zero field, the square spiral has the spectrum similar to that of a meander. At the field providing the maximum of the critical current, the detection efficiency and the cut-off wavelength in the spectrum increase by 20 % and by 54%, correspondingly. The magnetic-field dependence of dark count rate is well described by proposed analytical model.