Ferroelectricity and weak ferromagnetism of hexagonal $\mathrm{ErFe}{\mathrm{O}}_3$ thin films

Hexagonal $\mathrm{ErFe}{\mathrm{O}}_3$ thin films fabricated by a pulsed laser deposition method were investigated by x-ray diffraction (XRD) and transmission electron microscopy. No structural phase transition was observed between 20 and 900 K. Ferroelectric $D-E$ hysteresis loops were obtained at room temperature using the double-wave method, and the magnitude of spontaneous polarization was determined to be $200\mathrm{nC}/\mathrm{c}{\mathrm{m}}^2$. The existence of superlattice reflections in the XRD indicates that the space group of $\mathrm{ErFe}{\mathrm{O}}_3$ thin film is the polar hexagonal $P{6}_{3}cm$. This result also supports the ferroelectricity at room temperature. Magnetic properties were examined by a superconducting quantum interference device and Mössbauer spectroscopy. Below the Néel temperature of 120 K $\left(T_{\mathrm{N}}\right)$, a weak ferromagnetism appears along the $c$ axis due to the canting of $\mathrm{F}{\mathrm{e}}^{3+}$ magnetic moments. Around $T_{\mathrm{N}}$, the imaginary part of dielectric constant shows an anomaly. These results prove $h-\mathrm{ErFe}{\mathrm{O}}_3$ thin films to be multiferroic below 120 K.

Figure 1

XRD profiles of the $h-\mathrm{ErFe}{\mathrm{O}}_3$ thin film deposited on the YSZ (111) substrate. (a) $\theta -2\theta$ profile showing the $\left[0001\right]$ oriented growth; (b) and (c) correspond to the $\varphi$ scan of YSZ 110 and the $h-\mathrm{ErFe}{\mathrm{O}}_{3}30\overline{3}8$ reflections, respectively. (d) The $\theta -2\omega$ profile of the $h-\mathrm{ErFe}{\mathrm{O}}_3$ thin film. Two superlattice reflections of the $\mathrm{ErFe}{\mathrm{O}}_3$ thin film are observed around ${35}^{\circ }$ and ${74}^{\circ }$ together with main reflections from $h-\mathrm{ErFe}{\mathrm{O}}_3$ and the YSZ substrate.

Figure 2

(a) HRTEM image of the $h-\mathrm{ErFe}{\mathrm{O}}_3$ thin film deposited on the YSZ substrate. No amorphous phase is observed at the interface between the $h-\mathrm{ErFe}{\mathrm{O}}_3$ thin film and YSZ substrate, as observed in the $h-\mathrm{YbFe}{\mathrm{O}}_3$ thin films [24]. (b) SAED pattern of the $h-\mathrm{ErFe}{\mathrm{O}}_3$ thin film, showing that the thin film is $c$ axis oriented.

Figure 3

Temperature dependences of lattice constants of the $h-\mathrm{ErFe}{\mathrm{O}}_3$ thin film and YSZ substrate. (a) Result in the low temperature and (b) in the high temperature. Red solid diamonds indicate the $h-\mathrm{ErFe}{\mathrm{O}}_3$ lattice constant, and blue open squares indicate the YSZ lattice constant. Left axis corresponds to the $h-\mathrm{ErFe}{\mathrm{O}}_3$ lattice constant and right axis to that of YSZ. No anomaly corresponding to the structural phase transition is observed in this temperature range within the experimental error.

Figure 4

(a) Temperature dependences of the dielectric constant of the $h-\mathrm{ErFe}{\mathrm{O}}_3$ thin film measured at 10 kHz. Blue solid and red open squares correspond to the real $\left({\varepsilon }^{\prime }\right)$ and imaginary part $\left({\varepsilon }^{\prime \prime }\right)$ of the dielectric constant, respectively. ${\varepsilon }^{\prime }$ is graphed against the $y$ axis scale on the left edge of the graph and ${\varepsilon }^{\prime \prime }$ on the right edge. ${\varepsilon }^{\prime \prime }$ exhibits a hump around 140 K. (b) Resistivity of the $h-\mathrm{ErFe}{\mathrm{O}}_3$ thin film at room temperature. (c) $D-E$ hysteresis loops of the $\mathrm{ErFe}{\mathrm{O}}_3$ thin film measured at room temperature under different amplitudes of the electric field. The magnitude of spontaneous polarization is estimated to be around $200\mathrm{nC}/\mathrm{c}{\mathrm{m}}^2$. The asymmetric form of the loops shows the existence of internal field in the thin film.

Figure 5

Temperature dependence of the magnetization of the $h-\mathrm{ErFe}{\mathrm{O}}_3$ thin film. The magnetic field is applied parallel to the $c$ axis of the $h-\mathrm{ErFe}{\mathrm{O}}_3$ thin film for (a) and (b). In the inset graph of (b), the magnetic field (500 Oe) is applied perpendicular to the $c$ axis. The magnitudes of the magnetic field are 100 Oe and 10 kOe for (a) and (b), respectively. Blue open diamonds represent the ZFC process, and red solid squares correspond to the FC process. The inverse susceptibility is shown as an inset in (a). It obeys the Curie-Weiss law above 200 K.

Figure 6

Magnetic hysteresis loops measured at 30 K (blue square), 50 K (green triangle), 100 K (orange cross), and 130 K (red diamond). The magnetic field is applied parallel to the $c$ axis of the $h-\mathrm{ErFe}{\mathrm{O}}_3$ thin film. Hysteresis loops are observed at 30, 50, and 100 K.

Figure 7

Mössbauer spectra measured at (a) 291, (b) 110, (c) 100, (d) 79, and (e) 16 K. Open diamonds represent the experimental data, and the solid red line corresponds to the fitting result.

Figure 8

The relationship between the crystallographic axes $\left(abc\right)$, the EFG axes $\left(xyz\right)$, and the hyperfine field $H_{\mathrm{hf}}$. The incident direction of $\gamma$ ray is parallel to the $c$ axis. ${\theta }_H$ and ${\phi }_H$ are the Euler angles of the hyperfine filed with respect to the principle axis of the EFG.

Figure 9

The Mössbauer parameters as a function of temperature. The isomer shift (solid diamond) and quadrupole coupling constant (open square) are shown in (a). The $y$ axis scale of the isomer shift and quadrupole coupling constant are on the left and right side of the graph, respectively. (b) Line width (solid diamond) and hyperfine field (open square); scales are on the left and right edge of the graph, respectively.

Figure 10

Magnetic hysteresis loops at several temperatures after subtracting the linear component $\chi H$. Red diamonds correspond to 100 K, orange crosses to 75 K, green triangles to 50 K, and blue squares to 30 K, respectively. They exhibit ferromagnetic behaviors at this temperature range.

Figure 11

The possible spin configurations of the $\mathrm{F}{\mathrm{e}}^{3+}$ site. Large solid circles represent the Er ion. Small open circles and solid circles represent the Fe ion at $c=z$ and $c=z+1/2$ sites, respectively. The arrow indicates the direction of the magnetic moment. The open arrow is canted from the $ab$ plane towards the $+c$ axis, and the solid arrow represents the canting towards the $-c$ axis. (a) The $\alpha$ model with $\phi =0^{\circ }$; (b) the $\beta$ model with $\phi =0^{\circ }$ [37, 38].