We present ALMA 1.3 mm (230 GHz) observations of the HD 32297 and HD 61005 debris disks, two of the most iconic debris disks due to their dramatic swept-back wings seen in scattered light images. These observations achieve sensitivities of 14 and 13 $mu$Jy beam$^{-1}$ for HD 32297 and HD 61005, respectively, and provide the highest resolution images of these two systems at millimeter wavelengths to date. By adopting a MCMC modeling approach, we determine that both disks are best described by a two-component model consisting of a broad ($Delta R/R> 0.4$) planetesimal belt with a rising surface density gradient, and a steeply falling outer halo aligned with the scattered light disk. The inner and outer edges of the planetesimal belt are located at $78.5pm8.1$ AU and $122pm3$ AU for HD 32297, and $41.9pm0.9$ AU and $67.0pm0.5$ AU for HD 61005. The halos extend to $440pm32$ AU and $188pm8$ AU, respectively. We also detect $^{12}$CO J$=2-1$ gas emission from HD 32297 co-located with the dust continuum. These new ALMA images provide observational evidence that larger, millimeter-sized grains may also populate the extended halos of these two disks previously thought to only be composed of small, micron-sized grains. We discuss the implications of these results for potential shaping and sculpting mechanisms of asymmetric debris disks.
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