  Ultralow dissipation plays an important role in sensing applications and
exploring macroscopic quantum phenomena using micro-and nano-mechanical
systems. We report a diamagnetic-levitated micro-mechanical oscillator
operating at a low temperature of 3K with measured dissipation as low as 0.59
$\mu$Hz and a quality factor as high as $2 \times 10^7$. To the best of our
knowledge the achieved dissipation is the lowest in micro- and nano-mechanical
systems to date, orders of magnitude improvement over the reported
state-of-the-art systems based on different principles. The cryogenic
diamagnetic-levitated oscillator described here is applicable to a wide range
of mass, making it a good candidate for measuring both force and acceleration
with ultra-high sensitivity. By virtue of the naturally existing strong
magnetic gradient, this system has great potential in quantum spin mechanics
study.
