  We report measurements of the in-plane magnetoelastic coupling in ultra-thin
Ta|CoFeB|MgO layers as a function of uniaxial strain, conducted using a
four-point bending apparatus. For annealed samples, we observe a strong
dependence on the thickness of the CoFeB layer in the range 1.3-2.0 nm, which
can be modeled as arising from a combination of effective surface and volume
contributions to the magnetoelastic coupling. We point out that if similar
thickness dependence exists for magnetoelastic coupling in response to biaxial
strain, then the standard N\'eel model for the magnetic anisotropy energy
acquires a term inversely proportional to the magnetic layer thickness. This
contribution can significantly change the overall magnetic anisotropy, and
provides a natural explanation for the strongly nonlinear dependence of
magnetic anisotropy energy on magnetic layer thickness that is commonly
observed for ultrathin annealed CoFeB|MgO films with perpendicular magnetic
anisotropy.
