Spin-Density-Wave Transitions in a Magnetic Field

We report new Hall measurements on ${\mathrm{}\left(\mathrm{TMTSF}\right)\mathrm{}}_2$P${\mathrm{F}}_6$ under pressure. Our data, and a simple model, directly link the novel magnetic-field-induced state first seen in the Bechgaard salts to a well-characterized ambient-pressure spin-density-wave state. Comparison of the data for different salts suggests that (1) incommensurability associated with a two-dimensional lattice in a magnetic field splits the Landau levels into Landau subbands, and (2) coupling to soft modes changes the field-induced spin-density-wave transitions from second order to first order.