Dynamics of electron density, spin-phonon coupling, and dielectric properties of $\mathrm{SmFe}{\mathrm{O}}_3$ nanoparticles at the spin-reorientation temperature: Role of exchange striction

Samarium orthoferrite $\left(\mathrm{SmFe}{\mathrm{O}}_3\right)$ has been the subject of debate on the existence or nonexistence of ferroelectric properties. It has a high spin-reorientation transition temperature $T_{\mathrm{SR}}$ (480 K). Detailed synchrotron x-ray diffraction and Raman spectroscopy dielectric investigations in the 300 to 600 K temperature range of $\mathrm{SmFe}{\mathrm{O}}_3$ nanoparticles $\left(\sim 65\mathrm{nm}\right)$ have been performed. Raman spectroscopy established the existence of strong spin-phonon coupling and magnetostriction in the system. Magnetic measurements showed a spin-reorientation transition region from 480 to 450 K similar to that of a single crystal. The dielectric constant confirmed a clear anomaly around $T_{\mathrm{SR}}$. The signature of unusual relaxor ferroelectric behavior in $\mathrm{SmFe}{\mathrm{O}}_3$ nanoparticles from 380 to 480 K was observed in the dielectric properties. The electron density plots obtained using Rietveld refinement of the synchrotron x-ray diffraction data showed the displacement of the Sm and Fe ions, which can play a key role in the anomalous behavior at $T_{\mathrm{SR}}$. The analysis indicated the presence of magnetoelectric coupling due to the exchange interaction between Sm and Fe spins in $\mathrm{SmFe}{\mathrm{O}}_3$ nanoparticles.

Figure 1

A unit cell of SFO. Here, the red balls denote the oxygen atoms $({\mathrm{O}}_1$ and ${\mathrm{O}}_2)$, the blue balls represent the Sm atoms, and the green balls are used for the Fe atoms. The $\mathrm{Fe}{\mathrm{O}}_6$ octahedra are shaded in light green to indicate the distortion in the Pnma structure.

Figure 2

(a) FESEM micrograph of SFO nanoparticles, (b) EDAX spectrum of SFO nanoparticles, and (c) Rietveld refined synchrotron XRD patterns of SFO nanoparticles at various temperatures of interest.

Figure 3

(a) Lattice constants as a function of temperature, (b) variation of lattice distortion factors with temperature, (c) average tilt angle and orthorhombic strain as a function of temperature, and (d) change in average Sm-O and average Fe-O bond lengths with temperature.

Figure 4

Bond lengths in the $\mathrm{Sm}{\mathrm{O}}_{12}$ dodecahedron and $\mathrm{Fe}{\mathrm{O}}_6$ octahedron at 300 K.

Figure 5

The ED plots for SFO nanoparticles at room temperature (300 K), spin-reorientation temperature (480 K), and below Néel temperature (645 K) for the $yz$ plane, $x$ intercept = 0.5, in column 1; the $xz$ plane, $x$ intercept = 0, in column 2; and the $xz$ plane, $y$ intercept = 0.25, in column 3. The slice of the structure for the corresponding plane is shown in the top row of the figure for the one-to-one correspondence for anion and cations of the SFO system.

Figure 6

(a) Raman spectra of SFO nanoparticles at various temperatures of interest; (b) Raman shift of modes $B_{2g}$(5), $B_{1g}$(3), $B_{1g}$(4), and $A_g$(3) plotted as a function of temperature; and (c) the full-width at half-maximum (FWHM) of modes $B_{2g}$(5), $B_{1g}$(3), $B_{1g}$(4), and $A_g$(3) plotted as a function of temperature.

Figure 7

Model depicting the mechanism of exchange striction responsible for ferroelectric-like behavior in SFO. Since the Sm ions order only at low temperature $\left(\sim 4\mathrm{K}\right)$, their moments are shown as randomly oriented. The Fe ions are AFM coupled below a $T_{\mathrm{N}}$ of $\sim 680\mathrm{K}$ (not to scale).

Figure 8

Temperature dependence of susceptibility measured for FC and FW protocols for SFO nanoparticles showing spin reorientation from ${\mathrm{\Gamma }}_2(G_z,F_x)$ to ${\mathrm{\Gamma }}_4(G_x,F_z)$, corresponding to temperatures of 450 and 480 K, respectively.

Figure 9

(a) Real permittivity vs temperature across the spin reorientation transition, showing the anomaly at $T_{\mathrm{SR}}$ and a relaxor-like behavior (frequency-dependent maxima in real permittivity) below the $T_{\mathrm{SR}}$. (b) A clear discontinuity in the slope across $T_{\mathrm{SR}}=483\mathrm{K}$. Inset in (b) shows relaxation times obtained from the peak frequency (across $\sim 450\mathrm{K})$ following VFT behavior, with finite freezing temperature $T_0=309\mathrm{K}$ and activation energy $E_a=158\mathrm{meV}$.

Figure 10

Loss tangent ($\text{tan}\delta )$ as a function of temperature in the range 350 to 550 K for various frequencies. Inset shows imaginary permittivity $\left({\varepsilon }^{\prime \prime }\right)$ as a function of frequency recorded at various temperatures. Estimated extrinsic contributions to the measured data (tabulated in the inset) are under 6% at the relevant frequencies illustrating the anomaly at $T_{\mathrm{SR}}$ [Fig. 9] and below [Fig. 9].