We have studied the properties of a hole tunneling in an alternate lattice of fermions weakly coupled by antiferromagnetic exchange. This model is applied to vacancies in solid3He, which has features in common with a Mott semiconductor. The vacancy induces a ferromagnetic polarization over a volume limited by exchange and entropy. Using a variational method, we describe this structure as a nonlinear excitation. This magnetic polaron is stable and self-trapped up to a temperature of the order of the tunneling frequency. At higher temperature, the ferromagnetic polarization is destroyed, and the vacancy undergoes a sort of Brownian motion. Assuming a vacancy concentration in the range 10−4–10−3, we may account for some low-temperature anomalies observed in the susceptibility, the entropy, and the specific heat of bcc3He. Most of these ideas can be applied to excess charge carriers in Mott insulators.