Microwave investigation of the phase diagram of hexagonal multiferroic ${\text{HoMnO}}_3$

Using a microwave cavity perturbation technique at 16.5 GHz, we have investigated the complex dielectric and magnetic susceptibilities of the hexagonal multiferroic manganite ${\text{HoMnO}}_3$. The $c$-axis and $ab$-plane magnetic susceptibilities both appear to be dominated by the contribution of the ${\text{Ho}}^{3+}$ moments below 100 K. Along the same crystal orientations, Debye relaxation effects are found on the dielectric and magnetic-susceptibility functions above 100 K in a temperature range where unconventional magnetic fluctuations associated to the ${\text{Mn}}^{3+}$ moments are known to exist. At low temperatures, anomalies at the various phase transitions are observed on both susceptibility functions. These were investigated in magnetic fields up to 16 T and an $H\text{−}T$ phase diagram is deduced for the two crystal directions. Along the $c$ axis, the diagram is compared with the one found in the literature.

Figure 1

(Color online) Temperature dependence of the dielectric function in zero magnetic field at 16.5 GHz along the $c$ axis (upper panel) and the $ab$ plane (lower panel).

Figure 2

(Color online) Temperature dependence of the magnetic susceptibility in zero magnetic field at 16.5 GHz along the $c$ axis (upper panel) and the $ab$ plane (lower panel).

Figure 3

(Color online) Phase diagram of ${\text{HoMnO}}_3$ for a magnetic field oriented along the $c$ axis. Inset: details of the low-temperature part; the gray lines indicate where hysteresis is found.

Figure 4

(Color online) Magnetic field dependence of the susceptibility ${\chi }_c$ at three different temperatures. Curves of increasing field, red and blue (gray), and decreasing field, black. Arrows indicate the phase boundaries.

Figure 5

(Color online) Phase diagram of ${\text{HoMnO}}_3$ for a magnetic field oriented along the $ab$ plane. Temperature sweeps (△), field sweeps (◻); ${ϵ}_c$ (red or dark gray), ${\chi }_c$ (blue or black), and ${\chi }_{ab}$ (light gray). The lines indicate the region where hysteresis is found on field sweeps, the solid one indicating the maximum value.

Figure 6

(Color online) Temperature dependence of ${ϵ}_c^{″}$ at different magnetic field (tesla) oriented along the $ab$ plane.

Figure 7

(Color online) Magnetic field dependence of ${\chi }_{ab}^{″}$ at 10 and 22 K: field oriented along the $ab$ plane; curves for increasing and decreasing field, red (gray) and blue (black).