  Effective range is a quantity to characterize the energy dependence in
two-body scattering strength, and is widely used in cold atomic systems
especially across narrow resonances. Here we show that the effective range can
significantly modify the magnetic property of one-dimensional (1D) spin-$1/2$
fermions in the strongly repulsive regime. In particular, the effective range
breaks the large spin degeneracy in the hard-core limit, and induces a
Heisenberg exchange term in the spin chain that is much more sensitive to the
local density than that induced by the bare coupling. With an external harmonic
trap, this leads to a very rich magnetic pattern where the anti-ferromagnetic
(AFM) and ferromagnetic (FM) correlations can coexist and distribute in highly
tunable regions across the trap. Finally, we propose to detect the
range-induced magnetic order in the tunneling experiment. Our results can be
directly tested in 1D Fermi gases across narrow resonance, and suggest a
convenient route towards the local manipulation of quantum magnetism in cold
atoms.
