High-field phase diagram and phase transitions in hexagonal manganite $\mathrm{ErMn}{\mathrm{O}}_3$

We report high-field magnetization study on the complex spin system $h\text{−}\mathrm{ErMn}{\mathrm{O}}_3$ and propose an explanation for the $c$-axis phase transitions observed at 0.8, 12, and 28 T based on an analysis of the magnetization jumps, the complete $H\text{−}T$ phase diagram and the irreducible representations of the $\mathrm{E}{\mathrm{r}}^{3+}$ ($2a$ and $4b$) spin structure. Our measurements reveal that magnetic reorientation of the representation ${\mathrm{\Gamma }}_2$ induces the magnetic transition at 12 T, i.e., from a one-third plateau phase to a fully polarized phase. The magnetic transition at 0.8 T and the anomaly at 28 T can be understood by magnetic reorientations of ${\mathrm{\Gamma }}_1\to {\mathrm{\Gamma }}_2$ and a reflection of the $\mathrm{M}{\mathrm{n}}^{3+}$ moments triggered by the $\mathrm{E}{\mathrm{r}}^{3+}$ spins in strong magnetic fields. These scenarios are in good agreement with the magnetization process perpendicular to the $c$ axis and the magnetic susceptibility results. These findings are helpful for a complete understanding of the magnetic phase transitions and the underlying physics in this family compounds.

Figure 1

Crystallographic geometry and magnetic structures of $h\text{−}\mathrm{ErMn}{\mathrm{O}}_3$. (a) The projection along the $c$ axis showing the actual arrangements of Er and Mn ions in the $ab$ plane. (b) Four possible magnetic structures (${\mathrm{\Gamma }}_1$ to ${\mathrm{\Gamma }}_4$) of the $\mathrm{E}{\mathrm{r}}^{3+}$ $2a$ and $4b$ lattices. The corresponding symmetry (space group) is also enclosed. Symmetry analysis shows that all emerging magnetic orders of the $R^{3+}$ moments can be expressed by six irreducible representations ${\mathrm{\Gamma }}_1$ to ${\mathrm{\Gamma }}_6$. Among them, ${\mathrm{\Gamma }}_1$ to ${\mathrm{\Gamma }}_4$ are one dimensional, corresponding to the $R^{3+}$ moments aligned along the $c$ axis, while ${\mathrm{\Gamma }}_5$ and ${\mathrm{\Gamma }}_6$ are two dimensional and the $R^{3+}$ moments lie in the $ab$ plane. Therefore, ${\mathrm{\Gamma }}_5$ and ${\mathrm{\Gamma }}_6$ should be excluded because they cannot explain the $c$-axis phase transitions. We also do not show the $\mathrm{M}{\mathrm{n}}^{3+}$ spin structures because they strictly orient in the $ab$ plane and less susceptible to the field along the $c$ axis. The details of the $\mathrm{M}{\mathrm{n}}^{3+}$ and $\mathrm{E}{\mathrm{r}}^{3+}$ (${\mathrm{\Gamma }}_5$, ${\mathrm{\Gamma }}_6$) representations can be referred in Ref. [12].

Figure 2

Temperature dependence of the magnetization $M\left(T\right)$ with applied magnetic field along the $c$ axis. The symbols denote magnetic anomalies with increasing fields. The dashed (black) lines show the Curie-Weiss fitting in the temperature range of 150–300 K. Inset: $1/M$ versus $T$ for $H=0.1\mathrm{T}$.

Figure 3

High-field magnetization processes measured at 1.4 K for $H\parallel c$ and $H\perp c$, where f.u. denotes the formula unit. Inset: magnetization data at 2 K for $H\parallel c$ measured by SQUID. The arrows indicate the magnetic transitions. The dashed lines show linearly extrapolating the magnetization data to zero fields. The magnetization jump at $H_{\mathrm{C}1}(\mathrm{\Delta }{M}_{\mathrm{C}1}=0.45{\mu }_{\mathrm{B}})$ is much smaller than that at $H_{\mathrm{C}2}(\mathrm{\Delta }{M}_{\mathrm{C}2}=2.3{\mu }_{\mathrm{B}})$. The transition at $H_{\mathrm{C}2}$ is a magnetic reorientation from a one-third plateau phase to a fully polarized phase, whereas $H_{\mathrm{C}1}$ corresponds to a magnetic transition of ${\mathrm{\Gamma }}_1\to {\mathrm{\Gamma }}_2$ as we proposed in this paper. The magnetization jump at $H_{\mathrm{C}0}$ is not a real phase transition but a change from multidomains to a single domain in applied fields [12].

Figure 4

(a) The magnetization measured up to 52 T and (b) The derivative $dM/dH$ as a function of $H$ in temperature range of 1.4–20 K for $h\text{−}\mathrm{ErMn}{\mathrm{O}}_3$. A small magnetization jump is observed at $H_{\mathrm{C}3}$, which is clearly shown in the $dM/dH$ curves. (c) The magnetization processes for $h\text{−}\mathrm{YbMn}{\mathrm{O}}_3$ in pulsed fields up to 58 T. (d) The $dM/dH$ curves from 1.5–15 K for $h\text{−}\mathrm{YbMn}{\mathrm{O}}_3$. The dashed lines indicate the evolution of the magnetic transitions with temperatures.

Figure 5

The resulting high-field phase diagram of $h\text{−}\mathrm{ErMn}{\mathrm{O}}_3$. The experimental results by Yen et al. and Meier et al. (Refs. [11] and [12]) are shown for a comparison. Five magnetic ordered phases I-V are distinguished by the phase boundaries. The dashed lines are guides for eyes. The phase V has a ferromagnetic (FM) $\mathrm{E}{\mathrm{r}}^{3+}$ order. The boundary near 25 T is attributed to a magnetic reorientation in the $ab$ plane where $\mathrm{M}{\mathrm{n}}^{3+}$ spins are triggered by the mutual induction of the $\mathrm{E}{\mathrm{r}}^{3+}$ spins. Symmetry analysis is shown in the Appendix.