Field-like Perturbation Enabled Six-state Readout in Triaxial $\alpha$-${\mathrm{F}\mathrm{e}}_2{\mathrm{O}}_3$|Pt Bi-layers

Understanding current-induced spin-orbit torques provides a route for all-electrical control of antiferromagnetic (AFM) order. Here, we demonstrate the reading of six-state memory stabilized by easy-plane triaxial anisotropy in canted antiferromagnetic $\alpha$-${\mathrm{F}\mathrm{e}}_2{\mathrm{O}}_3$|Pt bilayers. The conventional spin Hall magnetoresistance (SMR) readout cannot distinguish states separated by ${180}^{\circ }$, limiting detection to only three states in $\alpha$-${\mathrm{F}\mathrm{e}}_2{\mathrm{O}}_3$. We show that a static field-like perturbation via external field lifts the degeneracy of opposite states in $\alpha$-${\mathrm{F}\mathrm{e}}_2{\mathrm{O}}_3$, enabling unambiguous resolution of all six states in the first-harmonic SMR signal. Our analytical and numerical modeling elucidate the role of spontaneous canting in lifting such degeneracy in $\alpha$-${\mathrm{F}\mathrm{e}}_2{\mathrm{O}}_3$. We demonstrate that dual-modulation SMR measurements (simultaneous current and field excitations) are effective in mitigating thermal drifts in the signals and are essential for reliable readout. Furthermore, our computations of the second-harmonic SMR reveal the interplay of competing interactions governing the decisive lifting of the degeneracy of opposite states. Finally, we propose a two-step current-only protocol for six-state readout in canted AFM $\alpha$-${\mathrm{F}\mathrm{e}}_2{\mathrm{O}}_3$|Pt bilayers.