  In young sun-like stars and field M dwarf stars, chromospheric and coronal
magnetic activity indicators such as H$\alpha$, X-ray and radio emission are
known to saturate with low Rossby number ($Ro \lesssim 0.1$), defined as the
ratio of rotation period to convective turnover time. The mechanism for the
saturation is unclear. In this paper, we use photospheric Ti I and Ca I
absorption lines in $Y$ band to investigate magnetic field strength in M dwarfs
for Rossby numbers between 0.01 and 1.0. The equivalent widths of the lines are
magnetically enhanced by photospheric spots, a global field or a combination of
the two. The equivalent widths behave qualitatively similar to the
chromospheric and coronal indicators: we see increasing equivalent widths
(increasing absorption) with decreasing $Ro$ and saturation of the equivalent
widths for $Ro \lesssim 0.1$. The majority of M dwarfs in this study are fully
convective. The results add to mounting evidence that the magnetic saturation
mechanism occurs at or beneath the stellar photosphere.
