Programmable bias field observed in graded ferromagnetic semiconductor films with broken symmetry

We report on the observation of a field-induced magnetic bias effect in a $\mathrm{G}{\mathrm{a}}_{0.94}\mathrm{M}{\mathrm{n}}_{0.06}\mathrm{A}{\mathrm{s}}_{1\ensuremath{-}y}{\mathrm{P}}_{y}$ thin film with digitally graded phosphorus content. Although phosphorus concentration in the sample is changed in steps from $y\ensuremath{\approx}0.03$ to $y\ensuremath{\approx}0.28$, the magnetometry and magnetotransport data display a coherent magnetic response typical for single-layer in-plane magnetized films with cubic and weak [110] uniaxial anisotropy. Unexpectedly, low-temperature planar Hall resistance loops exhibit remarkable asymmetry tunable by application of strong in-plane initial magnetic field ${H}_{\mathrm{Ini}}$. We discuss this unusual memory effect, resembling the magnetization asymmetry in the exchange biased magnetic bilayers, in terms of a unidirectional bias field ${H}_{b}$ induced by ${H}_{\mathrm{Ini}}$. We show that such bias field defines the delayed or accelerated nucleation of domains with chiral domain walls performing the magnetization reversal.