  We propose and experimentally demonstrate a new cooling mechanism leading to
purification of a spinor Bose-Einstein Condensate (BEC). Our scheme starts with
a BEC polarized in the lowest energy spin state. Spin excited states are
thermally populated by lowering the single particle energy gap set by the
magnetic field. Then these spin-excited thermal components are filtered out,
which leads to an increase of the BEC fraction. We experimentally demonstrate
such cooling for a spin 3 52Cr dipolar BEC. Our scheme should be applicable to
Na or Rb, with perspective to reach temperatures below 1 nK.
