Title: Giant tunability of magnetoelasticity in Fe$_4$N system: Platform for unveiling correlation between magnetostriction and magnetic damping

Abstract: 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.