Exploring the shear strain contribution to the uniaxial magnetic anisotropy of (Ga,Mn)As

We present an experimental and $k⋅p$ theoretical study on the origin of the strong in-plane uniaxial magnetic anisotropy in (Ga,Mn)As layers, unexpected from the cubic crystalline structure. The symmetry lowering can be accounted for by structural or effective shear strains. We find theoretically out-of-plane and in-plane magnetic anisotropy constants being linear with the shear strain. Searching for a real shear strain arising from lattice relaxation, we perform two types of measurements: anomalous x-ray diffraction and strain-induced optical birefringence, at room temperature. Working on a strongly anisotropic (Ga,Mn)As layer, the estimated $ϵxy=10−4$ was not found although it lied an order of magnitude above the detection threshold. This ensemble of results indicates as unlikely a relaxation-driven uniaxial anisotropy. As previously suggested theoretically, the magnetic symmetry-lowering could instead originate from the anisotropic incorporation of Mn atoms during growth. This would yield a perfectly in-plane matched lattice, with an anisotropy that could nevertheless be modeled as an effective shear strain and modified by an external shear stress, in agreement with the existing experimental literature.