Millimeter-wavelength polarization measurements offer a promising method for probing the geometry of magnetic fields in circumstellar disks .
Single dish observations and theoretical work have hinted that magnetic field geometries might be predominantly toroidal , and that disks should exhibit millimeter polarization fractions of 2–3 % .
While subsequent work has not confirmed these high polarization fractions , either the wavelength of observation or the target sources differed from the original observations .
Here we present new polarimetric observations of three nearby circumstellar disks at 2 \arcsec resolution with the Submillimeter Array ( SMA ) and the Combined Array for Research in Millimeter Astronomy ( CARMA ) .
We reobserve GM Aur and DG Tau , the systems in which millimeter polarization detections have been claimed .
Despite higher resolution and sensitivity at wavelengths similar to the previous observations , the new observations do not show significant polarization .
We also add observations of a new HAeBe system , MWC 480 .
These observations demonstrate that a very low ( \lesssim 0.5 % ) polarization fraction is probably common at large ( \gtrsim 100 AU ) scales in bright circumstellar disks .
We suggest that high-resolution observations may be worthwhile to probe magnetic field structure on linear distances smaller than the disk scale height , as well as in regions closer to the star that may have larger MRI-induced magnetic field strengths .