Magnetostrictive properties in Fe$_{4-x}$Co$_{x}$N films: Insight from experiments and first-principles calculations
The ferromagnetic nitride Fe$_{4}$N has attracted attention for application in spintronic devices due to its high spin polarization and large magnetostriction. We present a combined experimental and theoretical study on the magnetostriction of Fe$_{4-x}$Co$_{x}$N films across a wide composition range. The Fe$_{4-x}$Co$_{x}$N films were grown on SrTiO$_{3}$(001) substrates using molecular beam epitaxy, and the magnetostriction constants along the [100] direction ($λ$$_{100}$) and [111] direction ($λ$$_{111}$) were precisely evaluated using an optical cantilever method. The experimental results reveal that $λ$$_{111}$ remains positive in the whole composition range and shows a maximum value of +82 ppm around x = 0.9. The variation in $λ$$_{111}$ with x is much smaller than that in $λ$$_{100}$, for which giant tunability and sign reversal are observed. First-principles calculations show reasonable agreement with the experimental $λ$$_{111}$ for x ${\ge}$ 1.6, but give negative values at lower x, and an exceptionally large negative $λ$$_{111}$ is obtained at x = 0.8, where the Fermi level coincides with a pronounced minority-spin peak in the density of states. The calculated $λ$$_{111}$ depends strongly on the smearing parameter, indicating that the rhombohedral magnetostriction is highly sensitive to the treatment of atomic disorder. The saturation magnetostriction constant ($λ$$_{s}$) derived from $λ$$_{100}$ and $λ$$_{111}$ is also compared with the $λ$$_{s}$ measured for the (001)-oriented polycrystalline Fe$_{4-x}$Co$_{x}$N films, and a possible scenario for deviation between them is discussed. Our findings clarify the basic features of magnetostriction in the Fe$_{4-x}$Co$_{x}$N system, providing essential magnetoelastic parameters for designing nitride-based spintronic devices.