Raman spectroscopic evidence for multiferroicity in rare earth nickelate single crystals

The rare earth nickelates $\mathrm{R}\mathrm{Ni}{\mathrm{O}}_3$ are metallic at high temperatures and insulating and magnetically ordered at low temperatures. The low temperature phase has been predicted to be type II multiferroic, i.e., ferroelectric and magnetic order are coupled and occur simultaneously. Confirmation of those ideas has been inhibited by the absence of experimental data on single crystals. Here we report on Raman spectroscopic data of $\mathrm{R}\mathrm{Ni}{\mathrm{O}}_3$ single crystals (R = Y, Er, Ho, Dy, Sm, Nd) for temperatures between 10 and 1000 K. Entering the magnetically ordered phase we observe the appearance of a large number of additional vibrational modes, implying a breaking of inversion symmetry expected for multiferroic order.

Figure 1

(a) Image of a $\mathrm{Dy}\mathrm{Ni}{\mathrm{O}}_3$ single crystal inside the cryostat. (b) Typical Raman spectra recorded on $\mathrm{Dy}\mathrm{Ni}{\mathrm{O}}_3$ at temperatures in the antiferromagnetic-insulating phase (blue curve, dashed line is a factor 5 magnification of the blue curve), the paramagnetic-insulating phase (orange curve), and the metallic paramagnetic phase (red curve). The purple curve is close to the melting point of the material. The curves have been given vertical offsets to avoid clutter. Raman modes appearing in the antiferromagnetic phase are marked by arrows. (c) Colormap of the Raman response in the full temperature range from 12.5 to 1911 K. Metal-insulator and magnetic transitions are labeled as red symbols.

Figure 2

Evolution with temperature of the frequency of the Raman modes. Black symbols: Modes already present above $T_{MI}$. Orange symbols: Additional modes below $T_{MI}$. Blue symbols: Additional modes below $T_N$. Red symbols: Antiferromagnetic resonance. Gray symbols for $\mathrm{Er}\mathrm{Ni}{\mathrm{O}}_3$ and $\mathrm{Dy}\mathrm{Ni}{\mathrm{O}}_3$: Additional modes appearing halfway $T_{MI}$ and $T_N$. Green symbols ($\mathrm{Nd}\mathrm{Ni}{\mathrm{O}}_3$): Bimagnon bound state (tentative; see Discussion).

Figure 3

Raman spectra of an $\mathrm{Y}\mathrm{Ni}{\mathrm{O}}_3$ single crystal (a) in the paramagnetic-insulating phase (180 K) and (b) in the antiferromagnetic-insulating phase (14 K). Orange triangles: Raman modes of the paramagnetic phase. Blue triangles: Additional modes in the magnetic phase. Red: Antiferromagnetic resonance. (c) Simulated Raman spectrum of $\mathrm{Y}\mathrm{Ni}{\mathrm{O}}_3$ in the paramagnetic-insulating phase (orange) and the insulating antiferromagnetic phase (blue), where it is assumed that all dipole-active phonons ($b$ axis, black; $ac$ plane, red) have become Raman active as a result of inversion symmetry breaking. The calculation of the phonon frequencies is described in Appendix pp2. The modes have a Lorentz line-shape with a full width at half-maximum of 4 ${\mathrm{cm}}^{-1}$. The amplitudes $f_j$ of the Raman modes [see Eq. (A3)] were all given the same value and the amplitudes of all polar modes 1/5 of those of the Raman modes.

Figure 4

Multiferroicity of (a) $T$-type and (b) $S$-type antiferromagnetic order [39]. Coordinate axes are labeled according to $P{2}_1/n$ setting. Dotted squares indicate the alignment of the planes stacked along [0,0,1]. Labels for up/down spin and long-/short-bond Ni are given in the top right.

Figure 5

Scheme of the spontaneous inversion symmetry breaking. Labels for up/down spin and long-/short-bond Ni are indicated at the right-hand side. To avoid clutter, oxygen atoms (at the corners of the squares) and rare earth atoms (in the open spaces) are not indicated. Top: The Ni ions occupy inversion-symmetric positions. Bottom: The electric fields induced by the T-type or S-type antiferromagnetic order (see Fig. 4) push the Ni ions to low-symmetry positions, which has two main effects: (i) It contributes a net electric dipole moment. (ii) Since these positions lack inversion symmetry, modes of any polarization are simultaneously Raman active and dipole active. Vibrations around the rest position are symbolized by double-headed arrows.

Figure 6

Images of (a) $\mathrm{Y}\mathrm{Ni}{\mathrm{O}}_3$, (b) $\mathrm{Er}\mathrm{Ni}{\mathrm{O}}_3$, (c) $\mathrm{Ho}\mathrm{Ni}{\mathrm{O}}_3$, (d) $\mathrm{Dy}\mathrm{Ni}{\mathrm{O}}_3$, (e) $\mathrm{Sm}\mathrm{Ni}{\mathrm{O}}_3$, and (f) $\mathrm{Nd}\mathrm{Ni}{\mathrm{O}}_3$ single crystals inside the cryostat and the associated raw Raman spectra in the high-temperature metallic state (red curve) and in the low-temperature antiferromagnetic state (blue curve). Temperature of each spectrum is indicated on the curve. Scale bar is identical for all samples.

Figure 7

Colormap of Raman intensity for (a) $\mathrm{Y}\mathrm{Ni}{\mathrm{O}}_3$, (b) $\mathrm{Er}\mathrm{Ni}{\mathrm{O}}_3$, (c) $\mathrm{Ho}\mathrm{Ni}{\mathrm{O}}_3$, (d) $\mathrm{Dy}\mathrm{Ni}{\mathrm{O}}_3$, (e) $\mathrm{Sm}\mathrm{Ni}{\mathrm{O}}_3$, and (f) $\mathrm{Nd}\mathrm{Ni}{\mathrm{O}}_3$ samples. Horizontal axis is the Raman shift in ${\mathrm{cm}}^{-1}$, vertical axis is the temperature in K on a log scale, and color defined the intensity of the signal in a logarithmic scale. White triangles indicate the temperatures of metal to insulator (high temperature) and magnetic ordering (low temperature). When present, the soft-mode frequency from the spectral fit is marked with a dashed gray line. Gray regions are averaging windows used for the temperature dependence of the Raman electronic background. Dotted horizontal lines indicate the temperatures of the spectra above 700 K used for the colorplot.The temperature mesh below 700 K is too dense to indicate this way.

Figure 8

Raman spectrum of $\mathrm{Dy}\mathrm{Ni}{\mathrm{O}}_3$ shown together with a multioscillator fit obtained by adjusting the temperature, the oscillator parameters of Eq. (A3), a background, and the zero of frequency.