LAUSR

In this work we present the magnetic structures and spin reorientation (SR) transitions of the mixed orthochromite-orthoferrite perovskites $R\mathrm{F}{\mathrm{e}}_{0.5}\mathrm{C}{\mathrm{r}}_{0.5}{\mathrm{O}}_{3}$ ($R=\mathrm{Tb}$, Dy, Ho, Er). Magnetization as a function of temperature and external magnetic field as well as neutron powder diffraction measurements were used to characterize the magnetic transitions, including the SR transitions in the transition metal sublattice and the ordering of the rare earth sublattice. The studied compounds order antiferromagnetically below 270 K in a ${\mathbf{G}}_{\mathbf{x}}$ configuration compatible with the ${\mathrm{\ensuremath{\Gamma}}}_{4}$ representation. As temperature decreases, all the compounds show a SR transition from ${\mathbf{G}}_{\mathbf{x}}$ (${\mathrm{\ensuremath{\Gamma}}}_{4}$) to ${\mathbf{G}}_{\mathbf{z}}$ (${\mathrm{\ensuremath{\Gamma}}}_{2}$). This transition occurs in a wide temperature range, where both magnetic configurations coexist. Below this SR, the behavior in each case depends on the rare earth. $\mathrm{HoF}{\mathrm{e}}_{0.5}\mathrm{C}{\mathrm{r}}_{0.5}{\mathrm{O}}_{3}$ shows $\mathrm{H}{\mathrm{o}}^{3+}$ sublattice ordering at a relatively high temperature (45 K). $\mathrm{DyF}{\mathrm{e}}_{0.5}\mathrm{C}{\mathrm{r}}_{0.5}{\mathrm{O}}_{3}$ and $\mathrm{ErF}{\mathrm{e}}_{0.5}\mathrm{C}{\mathrm{r}}_{0.5}{\mathrm{O}}_{3}$ show a second SR transition of the transition metal sublattice, from ${\mathbf{G}}_{\mathbf{z}}$ (${\mathrm{\ensuremath{\Gamma}}}_{2}$) to ${\mathbf{G}}_{\mathbf{y}}$ (${\mathrm{\ensuremath{\Gamma}}}_{1}$) at low temperatures (15 and 8 K, respectively). Below these temperatures a metamagnetic (MM) transition is observed for these two compounds at an external magnetic field of H \ensuremath{\approx} 7 kOe. The fact that this is only observed for compounds showing ${\mathbf{G}}_{\mathbf{z}}$ (${\mathrm{\ensuremath{\Gamma}}}_{2}$) to ${\mathbf{G}}_{\mathbf{y}}$ (${\mathrm{\ensuremath{\Gamma}}}_{1}$) transition suggests that there is a correlation between the ${\mathbf{G}}_{\mathbf{y}}$ (${\mathrm{\ensuremath{\Gamma}}}_{1}$) order and the MM transition. Finally, $\mathrm{TbF}{\mathrm{e}}_{0.5}\mathrm{C}{\mathrm{r}}_{0.5}{\mathrm{O}}_{3}$ is a peculiar case, since it is the only compound in this family that shows a re-entrant SR to ${\mathbf{G}}_{\mathbf{x}}$ (${\mathrm{\ensuremath{\Gamma}}}_{4}$) at very low temperatures. By combining these results with previous reports on $R\mathrm{Fe}{\mathrm{O}}_{3}$, $R\mathrm{Cr}{\mathrm{O}}_{3}$, and $R\mathrm{F}{\mathrm{e}}_{0.5}\mathrm{C}{\mathrm{r}}_{0.5}{\mathrm{O}}_{3}$, we develop a method to qualitatively estimate the SR temperature and the type of transition. We also propose a complete magnetic phase diagram containing the SR transitions and ${R}^{3+}$ ordering temperatures for all the $R\mathrm{F}{\mathrm{e}}_{0.5}\mathrm{C}{\mathrm{r}}_{0.5}{\mathrm{O}}_{3}$ ($R=\mathrm{Tb}$, Dy, Ho, Er, Tm, Yb, and Lu) compounds.