Origin of natural and magnetic field induced polar order in orthorhombic $\mathrm{Pr}{\mathrm{Fe}}_{1/2}{\mathrm{Cr}}_{1/2}{\mathrm{O}}_3$

Here, we report the possible origin of natural and magnetic field induced polar order near room temperature (RT) in $\mathrm{Pr}{\mathrm{Fe}}_{1/2}{\mathrm{Cr}}_{1/2}{\mathrm{O}}_3$. The temperature-dependent Raman spectroscopy (RS) and synchrotron x-ray diffraction experiments disregard any change in the structure at low temperatures, which is not compatible with the emergence of natural ferroelectricity in this sample. Further, inelastic neutron scattering, neutron Compton scattering, neutron resonance transmission analysis and magnetic field-dependent RS experiments, suggest an increase in the delocalization of ${\mathrm{Pr}}^{3+}$ ions in $\mathrm{Pr}{\mathrm{Fe}}_{1/2}{\mathrm{Cr}}_{1/2}{\mathrm{O}}_3$ with respect to the parent compound $\mathrm{PrFe}{\mathrm{O}}_3$. The evaluation of the present results reveals that more delocalized ${\mathrm{Pr}}^{3+}$ ions and strong spin-phonon coupling in $\mathrm{Pr}{\mathrm{Fe}}_{1/2}{\mathrm{Cr}}_{1/2}{\mathrm{O}}_3$ seem to be a driving force for the observed natural and magnetic field induced switchable polar order in $\mathrm{Pr}{\mathrm{Fe}}_{1/2}{\mathrm{Cr}}_{1/2}{\mathrm{O}}_3$. The present results provide a significant contribution in understanding the ferroelectric polarization and progress in the search for RT magnetodielectric materials.

Figure 1

Temperature dependence of the direct current magnetization variation for polycrystalline $\mathrm{Pr}{\mathrm{Fe}}_{1/2}{\mathrm{Cr}}_{1/2}{\mathrm{O}}_3$. Insets corresponding to $T_{\mathrm{N}1}$ and $T_{\mathrm{N}2}$ represent the magnetic transition and spin reorientation temperature. Low temperature ascribed as $T_{\mathrm{N}3}$ is due to the ordering of ${\mathrm{Pr}}^{3+}$ ions.

Figure 2

(a) The Raman shift for the ${\mathrm{B}}_2$_g (7) mode and Fe-O symmetric stretching Raman mode as a function of temperature. (b) The variation of the Raman line width for ${\mathrm{B}}_2$_g (1) mode fitted by the Balkanski model. The deviation from normal anharmonic behavior suggests the presence of strong spin-phonon coupling/magneto-elastic coupling.

Figure 3

The variation of Raman spectra as a function of the applied magnetic field. The inset of the figure represents the spin-phonon coupling induced magneto-expansion effect with the application of a magnetic field.

Figure 4

The low-temperature Raman spectra (90 K) related to (a) Pr atomic vibrations and (b) Fe atomic vibrations recorded with and without the application of a very small magnetic field (30 Gauss). The Raman shift at 90 K with the magnetic field applied is maximized for heavier Pr atomic vibrations, suggesting the involvement of Pr atomic displacements in observed polar order. (c) and (d) The variation of Raman shift as a function of temperature for ${\mathrm{B}}_{2}g$ (1) and ${\mathrm{A}}_g$ (7) modes with the application of the magnetic field. The changes of the Raman shift of ${\mathrm{B}}_2$_g Raman mode with the application of magnetic field reveal that the field induced polar order at low temperatures has a direct relationship with the displacement of Pr atoms. (e) The variation of $\mathrm{\Delta }w$ (variation in Raman shift with the application of magnetic field) vs Δε (variation in dielectric constant due to the presence of hyperfine interactions).

Figure 5

Neutron Compton scattering (NCS) spectrum for (a) Cr-substituted $\mathrm{PrFe}{\mathrm{O}}_3$ and (b) $\mathrm{PrFe}{\mathrm{O}}_3$, both recorded at 10 K. Black points show the sum (over all backward scattering detectors) of the recorded data. A solid red curve indicates the sum (over all backward scattering detectors) of the fits of the recorded data. The sum of the fits is dissected into sums (over all backward detectors) of fits to individual recoil lines of Pr (solid green line), Fe (solid navy blue line), Cr (solid orange line), aluminum sample container (magenta), and O (solid blue line). (c) Inelastic neutron scattering (INS) spectra of Cr-substituted $\mathrm{PrFe}{\mathrm{O}}_3$ (solid blue line) and $\mathrm{PrFe}{\mathrm{O}}_3$ (solid black line). The contribution from the sample aluminum container has been subtracted, and the resultant spectra were normalized/scaled in such a way that the integrated area between 10 and $4000\mathrm{c}{\mathrm{m}}^{-1}$ is equal to 1.

Figure 6

(a) Neutron resonance transmission analysis (NRTA) spectra of Pr141 resonances of $\mathrm{Pr}{\mathrm{Fe}}_{1/2}{\mathrm{Cr}}_{1/2}{\mathrm{O}}_3$ and $\mathrm{PrFe}{\mathrm{O}}_3$ recorded at $T=10$ K. (b) NRTA spectra of Pr141 resonances of $\mathrm{Pr}{\mathrm{Fe}}_{1/2}{\mathrm{Cr}}_{1/2}{\mathrm{O}}_3$ and $\mathrm{PrFe}{\mathrm{O}}_3$ recorded at $T=300$ K. See text for details.

Figure 7

Neutron resonance transmission analysis (NRTA) spectra of Pr141 resonances of $\mathrm{Pr}{\mathrm{Fe}}_{1/2}{\mathrm{Cr}}_{1/2}{\mathrm{O}}_3$ and $\mathrm{PrFe}{\mathrm{O}}_3$ recorded at (a) $T=10$ K and (b) $T=300$ K together with fits. See text for details.

Figure 8

(a) The temperature dependence of dielectric constant variation at 1 MHz. The inset of the figure represents the first derivative of dielectric constant with temperature. The anomaly near 280 K is attributed to the presence of magnetodielectric coupling. (b) The linear variation between the Δε and $M^2\left(T\right)$. The deviation of normal linear behavior could be attributed to internal magnetic hyperfine interactions.

Figure 9

The variation of capacitance as a function of the magnetic field.