  Probing electrical and magnetic properties in aqueous environments remains a
frontier challenge in nanoscale sensing. Our inability to do so with
quantitative accuracy imposes severe limitations, for example, on our
understanding of the ionic environments in a diverse array of systems, ranging
from novel materials to the living cell. The Nitrogen-Vacancy (NV) center in
fluorescent nanodiamonds (FNDs) has emerged as a good candidate to sense
temperature, pH, and the concentration of paramagnetic species at the
nanoscale, but comes with several hurdles such as particle-to-particle
variation which render calibrated measurements difficult, and the challenge to
tightly confine and precisely position sensors in aqueous environment. To
address this, we demonstrate relaxometry with NV centers within
optically-trapped FNDs. In a proof of principle experiment, we show that
optically-trapped FNDs enable highly reproducible nanomolar sensitivity to the
paramagnetic ion, (\mathrm{Gd}^{3+}). We capture the three distinct phases of
our experimental data by devising a model analogous to nanoscale Langmuir
adsorption combined with spin coherence dynamics. Our work provides a basis for
routes to sense free paramagnetic ions and molecules in biologically relevant
conditions.
