  Flexible spintronics has opened new avenue to promising devices and
applications in the field of wearable electronics. Particularly, miniaturized
strain sensors exploiting the spintronic function have attracted considerable
attention, in which the magnetoelasticity linking magnetism and lattice
distortion is a vital property for high-sensitive detection of strain. This
paper reports the demonstration that the magnetoelastic properties of Fe$_4$N
can be significantly varied by partially replacing Fe with Co or Mn. The high
quality Fe$_4$N film exhibits large negative magnetostriction along the [100]
direction ($\lambda_{100}$) of -121 ppm while Fe$_{3.2}$Co$_{0.8}$N shows
$\lambda_{100}$ of +46 ppm. This wide-range tunability of $\lambda_{100}$ from
-121 to +46 across 0 allows us to thoroughly examine the correlation between
the magnetoelasticity and other magnetic properties. The strong correlation
between $\lambda_{100}$ and magnetic damping ($\alpha$) is found. The enhanced
extrinsic term of $\alpha$ is attributable to the large two magnon scattering
coming from the large magnetostriction. In addition, the density of states at
the Fermi level plays a primal role to determine both $\lambda_{100}$ and the
intrinsic term of $\alpha$. Thanks to the giant tunability and the bipolarity
of magnetoelasticity, magnetic nitrides are candidate materials for
high-sensitive spintronic strain sensors.
