Probing magnetic anisotropy and spin-reorientation transition in the three-dimensional antiferromagnet Ho0.5Dy0.5FeO3|Pt using spin Hall magnetoresistance

Orthoferrites ($R{\mathrm{FeO}}₃$) containing rare-earth ($R$) elements are 3D antiferromagnets (AFMs) that exhibit characteristic weak ferromagnetism originating due to slight canting of the spin moments and display a rich variety of spin-reorientation transitions in the magnetic field ($H$)-temperature ($T$) parameter space. We present spin Hall magnetoresistance (SMR) studies on a $b$ plate ($\mathit{ac}$ plane) of crystalline ${\mathrm{Ho}}_0.5{\mathrm{Dy}}_0.5{\mathrm{FeO}}₃|\mathrm{Pt}$ hybrid at various $T$ in the range 11--300 K. In the room temperature ${\mathrm{\ensuremath{\Gamma}}}₄$ phase, the switching between two degenerate domains occurs at fields above a critical value, ${H}_{\text{c}}\ensuremath{\approx}713$ Oe. Under $H>{H}_{\text{c}}$, the angular dependence of SMR ($\ensuremath{\alpha}$ scan) yielded a highly skewed curve with a sharp change (sign-reversal) along with a rotational hysteresis around the $\mathit{a}$ axis. Notably, at $H<{H}_{\text{c}}$, the $\ensuremath{\alpha}$-scan measurements on the single degenerate domain exhibited an anomalous sinusoidal signal of periodicity ${360}^{\ensuremath{\circ}}$. Low-$T$ evolution of the SMR curves ($H$ = 2.4 kOe) suggests weakening of the anisotropy possibly due to the $T$ evolution of Fe-$R$ exchange coupling. Below 25 K, the SMR modulation showed an abrupt change around the $\mathit{c}$ axis, marking the presence of a ${\mathrm{\ensuremath{\Gamma}}}₂$ phase. We have employed a simple Hamiltonian and computed SMR to examine the observed skewed SMR modulation. In summary, SMR is found to be an effective tool to probe magnetic anisotropy as well as a spin reorientation in ${\mathrm{Ho}}_0.5{\mathrm{Dy}}_0.5{\mathrm{FeO}}₃$. Our spin-transport study highlights the potential of ${\mathrm{Ho}}_0.5{\mathrm{Dy}}_0.5{\mathrm{FeO}}₃$ for future AFM spintronic devices.