cron: output of a script?

I've got a cronjob that looks like this

0 0 * * 7 [ $(date +\%d) -le 07 ] && /home/archiver/archiver.sh &> /home/archiver/output

And it works from the cron+bash perspective in that it'll run on the first Sunday of every month (or so I assume. It ran today, but we'll see about next Sunday, haha).

But the &> /home/archiver/output didn't seem to take. The script is pretty talkative and /home/archiver/output has a modified/changed timestamp of 00:00:01, but is completely empty.

What am I missing to capture the script's output?