Magnetization, specific heat, and thermal conductivity of hexagonal ${\mathrm{ErMnO}}_3$ single crystals

We report a study of magnetism and magnetic transitions of hexagonal ${\mathrm{ErMnO}}_3$ single crystals by magnetization, specific heat, and heat transport measurements. Magnetization data show that the $c$-axis magnetic field induces three magnetic transitions at 0.8, 12, and 28 T. The specific heat shows a peak at 2.2 K, which is due to a magnetic transition of ${\mathrm{Er}}^{3+}$ moments. For low-$T$ thermal conductivity $\left(\kappa \right)$, a clear diplike feature appears in the $\kappa \left(H\right)$ isotherm at 1–1.25 T for $H\parallel ab$, while in the case of $H\parallel c$, a steplike increase is observed at 0.5–0.8 T. The transition fields in $\kappa \left(H\right)$ are in good agreement with those obtained from magnetization, and the anomaly of $\kappa$ can be understood by a spin-phonon scattering scenario. The natures of magnetic structures and corresponding field-induced transitions at low temperatures are discussed.

Figure 1

Possible magnetic structures with moments parallel/antiparallel to the $c$ axis for rare-earth sublattice in $h\text{−}R{\mathrm{MnO}}_3$ denoted by four one-dimensional representations ${\mathrm{\Gamma }}_1$ to ${\mathrm{\Gamma }}_4$.

Figure 2

(a) Powder x-ray diffraction of ${\mathrm{ErMnO}}_3$ single crystals. (b),(c) X-ray diffraction pattern of $\left(00h\right)$ plane and the rocking curve of (004) peak. The full width at half maximum (FWHM) of the rocking curve is shown in panel (c).

Figure 3

(a),(b) Temperature dependence of the magnetization and the inverse magnetization of ${\mathrm{ErMnO}}_3$ for magnetic field (0.1 T) applied along the $c$ and $a$ axes. Inset to panel (a): temperature dependence of $dM/dT$. The minimum at 2.2 K indicates the magnetic-order transition of ${\mathrm{Er}}^{3+}(2a)$ moments. In panel (b), the arrow indicates the slope change of $M^{-1}\left(T\right)$ at $\sim 79\mathrm{K}$, which should be corresponding to the Néel temperature of ${\mathrm{Er}}^{3+}(4b)$ and ${\mathrm{Mn}}^{3+}$ moments.

Figure 4

(a)–(g) Temperature dependence of the magnetization of ${\mathrm{ErMnO}}_3$ in the $c$-axis magnetic fields. (h) A comparison among all $M\left(T\right)$ curves. The squares and diamonds indicate two anomalies, respectively, and the dashed lines show the evolution of the anomalies with increasing field, which are in good agreement with previous reports [35, 39]. Besides, the arrow indicates another anomaly of $M\left(T\right)$ in 7 T field. All the anomalies are determined from $dM/dT$.

Figure 5

Temperature dependence of the magnetization of ${\mathrm{ErMnO}}_3$ single crystals in the $a$-axis magnetic fields.

Figure 6

(a),(b) Low-temperature magnetization curves $M\left(H\right)$ of ${\mathrm{ErMnO}}_3$ in magnetic fields along the $c$ and $a$ axes, respectively. (c) A comparison between the $c$- and $a$-axis magnetization. (d) The differential results of $dM/dH$. Inset to panel (a): low-field data of the magnetization at 1.8 K that exhibit a small hysteresis. The arrows indicate the direction of sweeping field. There is not any hysteresis in all other curves.

Figure 7

(a),(c) Low-temperature magnetization curves $M\left(H\right)$ of ${\mathrm{ErMnO}}_3$ obtained in pulsed high magnetic field along the $c$ and $a$ axes. (b),(d) The differential results of $dM/dH$ for the $c$ and $a$ axis $M\left(H\right)$. The arrows in panel (b) indicate three magnetic transitions at 0.8, 12, and 28 T.

Figure 8

Low-temperature specific heat of ${\mathrm{ErMnO}}_3$ single crystals with magnetic fields along the $c$ or $a$ axis. The insets show the low-temperature data.

Figure 9

Temperature dependence of the $a$-axis and $c$-axis thermal conductivities of ${\mathrm{ErMnO}}_3$ single crystals, compared with the results of ${\mathrm{YMnO}}_3,{\mathrm{TmMnO}}_3$, and ${\mathrm{HoMnO}}_3$ [17, 18]. The dashed lines show a $T^2$ temperature dependence.

Figure 10

Temperature dependence of the $a$-axis and $c$-axis thermal conductivities of ${\mathrm{ErMnO}}_3$ single crystals in magnetic fields.

Figure 11

Magnetic-field dependence of thermal conductivity of ${\mathrm{ErMnO}}_3$ single crystals at $T<2$ K.

Figure 12

Magnetic structures of rare-earth moments in ${\mathrm{ErMnO}}_3$ at low temperatures and those in a $c$-axis field.

Figure 13

(a), (c) Low-temperature magnetization curves $M\left(H\right)$ of ${\mathrm{HoMnO}}_3$ obtained in pulsed high magnetic field along the $a$ or $c$ axis. (b),(d) The differential results of $dM/dH$ for the $a$- and $c$-axis $M\left(H\right)$. Inset to panels (b),(d): low-field data of $dM/dH$. The arrows in panels (b),(d) indicate the magnetic transitions. (e),(f) Low-temperature field dependence of ${\kappa }_c$ for field along the $a$ or $c$ axis. Data are taken from Ref. [17].

Figure 14

Magnetic structures of rare-earth moments in ${\mathrm{HoMnO}}_3$ at low temperatures and those in a $c$-axis field.