  A scheme to achieve spin squeezing using a geometric phase induced by a
single mechanical mode is proposed. The analytical and numerical results show
that the ultimate degree of spin squeezing depends on the parameter
$\frac{n_{th}+1/2}{Q\sqrt{N}}$, which is the ratio between the thermal
excitation, the quality factor and square root of ensemble size. The undesired
coupling between the spin ensemble and the bath can be efficiently suppressed
by Bang-Bang control pulses. With high quality factor, the ultimate limit of
the ideal one-axis twisting spin squeezing can be obtained for an NV ensemble
in diamond.
