Unraveling intricate magnetic behavior involving negative magnetization and exchange-bias in ErFe0.5Co0.5O3

In this paper, we present a comprehensive investigation of the distinctive magnetic properties involving the remarkable occurrences of negative magnetization (NM), exchange bias (EB), and spin reorientation (SR) in the $\mathrm{ErF}{\mathrm{e}}_{0.5}{\mathrm{Co}}_{0.5}{\mathrm{O}}_3$ compound. The dc magnetization data, recorded in field-cooled-cooling mode, reveal a net zero magnetization at the compensation temperature $\left(T_{\mathrm{COMP}}\right)$ of 24 K, leading to the NM phenomenon in the compound. Rietveld refinement of the neutron diffraction (ND) patterns over 1.5–300 K elucidates the SR of Fe/Co spins at 100 K $\left(T_{\mathrm{SR}}\right)$ and Er magnetic ordering <4 K $\left(T_{\mathrm{N}}^{\mathrm{Er}}\right)$ resulting in ${\mathrm{\Gamma }}_4\left(G_x\right)$, ${\mathrm{\Gamma }}_{24}(G_z,G_x)$, ${\mathrm{\Gamma }}_2\left(G_z\right)$, and ${\mathrm{\Gamma }}_{257}(G_z;A_y^{\mathrm{Er}}{G}_z^{\mathrm{Er}})$ magnetic structures at T > $T_{\mathrm{SR}}$, $T_{\mathrm{SR}}\ge T>T_{\mathrm{COMP}}$, $T_{\mathrm{N}}^{\mathrm{Er}}<T\le T_{\mathrm{COMP}}$, and $T\le T_{\mathrm{N}}^{\mathrm{Er}}$, respectively. It is, therefore, evident that the SR of Fe/Co moments from ${\mathrm{\Gamma }}_4\left(G_x\right)$ to ${\mathrm{\Gamma }}_2\left(G_z\right)$ gets completed at the $T_{\mathrm{COMP}}$ of 24 K, and the Er magnetic ordering into an unusual ${\mathrm{\Gamma }}_{57}(A_y^{\mathrm{Er}}{G}_z^{\mathrm{Er}})$ spin configuration takes place at $T\le 4$ K. Anomalies in dc magnetization data (coercivity and remanent magnetization) at $T_{\mathrm{SR}}$, $T_{\mathrm{COMP}}$, and $T_{\mathrm{N}}^{\mathrm{Er}}$ are also reflected in the ac susceptibility data. Intriguingly, EB field $\left(H_{\mathrm{EB}}\right)$ in the compound does not change its polarity across $T_{\mathrm{COMP}}$ and remains positive even above $T_{\mathrm{COMP}}$. The observed positive $H_{\mathrm{EB}}$ at T > $T_{\mathrm{COMP}}$ can be attributed to a complex spin arrangement as evident from the ND, whereas for T ≤ $T_{\mathrm{COMP}}$, positive $H_{\mathrm{EB}}$ has its usual explanation within the framework of the Meiklejohn-Beam model. The maximum positive $H_{\mathrm{EB}}$ and a broad hump in $H_{\mathrm{EB}}$ at $T_{\mathrm{COMP}}$ and $T_{\mathrm{SR}}$, respectively, indicate a correlation between the EB and SR in the compound. Additionally, cooling-field dependence of the EB shows a peak value ∼5 kOe; thereafter, an unusual suppression of $H_{\mathrm{EB}}$ up to 70 kOe cooling field is found. The observed NM below $T_{\mathrm{COMP}}$ is elucidated using the Cooke's model, where the polarized Er moment, under the internal magnetic field of the ordered canted antiferromagnetic Fe/Co sublattice, competes with the ferromagnetic Fe/Co moment. This results in a complete cancellation of magnetization at $T_{\mathrm{COMP}}$ and the emergence of NM below $T_{\mathrm{COMP}}$ in the compound. The specific heat data reveal a Schottky anomaly, inferring the dominant polarized nature of the Er moment below $T_{\mathrm{COMP}}$. In this paper, we underscore the pivotal role of Er and Fe/Co exchange coupling in shaping the intriguing and complex magnetic properties—NM and EB—of the compound. These findings highlight the potential utility of the compound in spintronic applications.