  We show that an ensemble of $^2\Sigma$ molecules in the rotationally ground
state trapped on an optical lattice exhibits collective spin excitations that
can be controlled by applying superimposed electric and magnetic fields. In
particular, we show that the lowest energy excitation of the molecular ensemble
at certain combinations of electric and magnetic fields leads to the formation
of a magnetic Frenkel exciton. The exciton bandwidth can be tuned by varying
the electric or magnetic fields. We show that the exciton states can be
localized by creating vacancies in the optical lattice. The localization
patterns of the magnetic exciton states are sensitive to the number and
distribution of vacancies, which can be exploited for engineering many-body
entangled spin states. We consider the dynamics of magnetic exciton wavepackets
and show that the spin excitation transfer between molecules in an optical
lattice can be accelerated or slowed down by tuning an external magnetic or
electric field.
