  We have studied the ground state of a fullerene--based magnet, the
$\alpha'$--phase tetra--$kis$--(dimethylamino)--ethylene--C$_{60}$
($\alpha'$--TDAE--C$_{60}$), by electron spin resonance (ESR) and magnetic
torque measurements. Below T$_N=7$ K, non--paramagnetic field dependent
resonances with a finite excitation gap (1.7 GHz) are observed along the
$a$--axis. Strong enhancement in their intensity as temperature is decreased is
inconsistent with excitation from a singlet state, which had been proposed for
the $\alpha'$--phase ground state. Below T$_N$, non--quadratic field dependence
of magnetic torque signal is also observed in contrast to quadratic field
dependence in the paramagnetic phase. The angle--dependent torque signals below
T$_N$ indicate the existence of an anisotropy of the bulk magnetization. From
both experiments, we propose an antiferromagnetic ground state driven by the
cooperative orientational ordering of C$_{60}$ in the
$\alpha'$--TDAE--C$_{60}$.
