Coulomb blockade anisotropic magnetoresistance effect in a (Ga,Mn)As single-electron transistor

We observe low-field hysteretic magnetoresistance in a (Ga,Mn)As single-electron transistor which can exceed 3 orders of magnitude. The sign and size of the magnetoresistance signal are controlled by the gate voltage. Experimental data are interpreted in terms of electrochemical shifts associated with magnetization rotations. This Coulomb blockade anisotropic magnetoresistance is distinct from previously observed anisotropic magnetoresistance effects as it occurs when the anisotropy in a band structure derived parameter is comparable to an independent scale, the single-electron charging energy. Effective kinetic-exchange model calculations in (Ga,Mn)As show chemical potential anisotropies consistent with experiment and ab initio calculations in transition metal systems suggest that this generic effect persists to high temperatures in metal ferromagnets with strong spin-orbit coupling.