  We present the first results of the search for nonlinear memory from subsolar
mass binary black hole (BBH) mergers during the second observing run (O2) of
the LIGO and Virgo detectors. The oscillatory chirp signal from the inspiral
and merger of low mass BBHs ($M_\mathrm{Tot} \leq 0.4 M_\odot$) are at very
high frequencies and fall outside the sensitivity band of the current
ground-based detectors. However, the non-oscillatory memory signal during the
merger saturates towards the lower frequencies and can be detected for those
proposed BBHs. We show in this work that the morphology of the memory signal
depends minimally upon the source parameters of the binary, thus only the
overall amplitude of the signal changes and hence the result can be
interpolated for extremely low mass BBH mergers. We did not find any signal
which can be interpreted as a memory signal and we place upper limits on the
rate of BBH mergers with $M_\mathrm{Tot} \leq 0.4 M_\odot$ for the first time.
