  We present a Gaussian state analysis of the entanglement generation between
two macroscopic atomic ensembles due the continuous probing of collective spin
variables by optical Faraday rotation. The evolution of the mean values and the
variances of the atomic variables is determined and the entanglement is
characterized by the Gaussian entanglement of formation (GEoF) and the
logarithmic negativity. The effects of induced opposite Larmor rotation of the
samples and of light absorption and atomic decay are analyzed in detail.
