  We study the effects of electron-electron interactions on the energy levels
of GaAs quantum wires (QWs) using finite-bias spectroscopy. We probe the energy
spectrum at zero magnetic field, and at crossings of opposite-spin-levels in
high in-plane magnetic field B. Our results constitute direct evidence that
spin-up (higher energy) levels pin to the chemical potential as they populate.
We also show that spin-up and spin-down levels abruptly rearrange at the
crossing in a manner resembling the magnetic phase transitions predicted to
occur at crossings of Landau levels. This rearranging and pinning of subbands
provides a phenomenological explanation for the 0.7 structure, a
one-dimensional (1D) nanomagnetic state, and its high-B variants.
