  Here we report the first detection of polarization signals induced by the
Zeeman effect in spectral lines of the E^4\Pi-A^4\Pi system of FeH located
around 1.6 $\mu$m. Motivated by the tentative detection of this band in the
intensity spectrum of late-type dwarfs, we have investigated the full Stokes
sunspot spectrum finding circular and linear polarization signatures that we
associate with the FeH lines of the E^4\Pi-A^4\Pi band system. We investigate
the Zeeman effect in these molecular transitions pointing out that in Hund's
case (a) coupling the effective Land\'e factors are never negative. For this
reason, the fact that our spectropolarimetric observations indicate that the
Land\'e factors of pairs of FeH lines have opposite signs, prompt us to
conclude that the E^4\Pi-A^4\Pi system must be in intermediate angular momentum
coupling between Hund's cases (a) and (b). We emphasize that theoretical and/or
laboratory investigations of this molecular system are urgently needed for
exploiting its promising diagnostic capabilities.
