We present a large spectroscopic campaign with Keck/MOSFIRE targeting Lyman-alpha emission ( Ly \alpha ) from intrinsically faint Lyman-break Galaxies ( LBGs ) behind 12 efficient galaxy cluster lenses .
Gravitational lensing allows us to probe the more abundant faint galaxy population to sensitive Ly \alpha equivalent width limits .
During the campaign we targeted 70 LBG candidates with MOSFIRE Y-band , selected photometrically to cover Ly \alpha over the range 7 < z < 8.2 .
We detect S / N > 5 emission lines in 2 of these galaxies and find that they are likely Ly \alpha at z = 7.148 \pm 0.001 and z = 7.161 \pm 0.001 .
We present new lens models for 4 of the galaxy clusters , using our previously published lens models for the remaining clusters to determine the magnification factors for the source galaxies .
Using a Bayesian framework that employs large scale reionization simulations of the intergalactic medium ( IGM ) as well as realistic properties of the interstellar medium and circumgalactic medium , we infer the volume-averaged neutral hydrogen fraction , \overline { x } _ { \mathrm { HI } } , in the IGM during reionization to be \overline { x } _ { \mathrm { HI } } = 0.88 ^ { +0.05 } _ { -0.10 } at z = 7.6 \pm 0.6 .
Our result is consistent with a late and rapid reionization scenario inferred by Planck .