Thermally assisted and magnetic field driven isostructural distortion of spinel structure and occurrence of polar order in ${\mathrm{CoCr}}_2{\mathrm{S}}_4$

We report appearance of polar order with a ordering temperature $\left(T_C\right)$ at 28 K, which is well below the ferrimagnetic order at 225 K $\left(T_N\right)$ for ${\mathrm{CoCr}}_2{\mathrm{S}}_4$. Intriguingly, the value of spontaneous electric polarization $\left(P\right)$ is $\sim 122 \mu \mathrm{C}/{\mathrm{m}}^2$ at 15 K, which is the second largest value in Cr octahedra-based spinels after ${\mathrm{CdCr}}_2{\mathrm{S}}_4$. Incidentally, the $P$ value is $\sim 60$ times larger than the value of $P$ for the oxide counterpart ${\mathrm{CoCr}}_2{\mathrm{O}}_4$. The significant magnetoelectric coupling is verified from the magnetodielectric response and magnetic field dependent enhancement of $P$. We note that the field-dependent dielectric permittivity scales linearly to the squared magnetization in the low field regime below $\sim 10$ kOe as described by the Ginzburg-Landau theory. Synchrotron diffraction studies over a wide temperature range, $15\text{–}300$ K, illustrate strong magnetoelastic coupling at $T_N$ and isostructural distortion at $T_C$. Analyses of the diffraction patterns reveal that the occurrence of polar order involves expansion of Co tetrahedra and contraction of Cr octahedra of the spinel structure and these distortions are further enhanced driven by the magnetic field. The delicate interplay between magnetoelastic, magnetoelectric, and electroelastic couplings in ${\mathrm{CoCr}}_2{\mathrm{S}}_4$ proposes the system as a potential candidate in multiferroics.

Figure 1

(a) Thermal variation resistivity $\left(\rho \right)$. Inset highlights the low-$T$ region. (b) Real part of ac susceptibility $\left({\chi }^{\prime }\right)$ with $T$. Inset shows $T$ derivative of ${\chi }^{\prime }$ with $T$ in the low-$T$ region. (c) FC-ZFC magnetization with $T$. (d) Magnetic hysteresis loops recorded at various $T$.

Figure 2

Thermal variations of (a) real $\left({\epsilon }^{\prime }\right)$ and (b) imaginary $\left({\epsilon }^{\prime \prime }\right)$ parts of dielectric permittivity at different $f$. Inset of (a) shows the low-$T$ region of $d{\epsilon }^{\prime }/dT$, highlighting the peaks. Arrow indicates no shift of peak position at different frequencies, $f$. (c) Magnetization $\left(M\right)$ curve and magnetodielectric response $[{\epsilon }^{\prime }\left(H\right)/{\epsilon }^{\prime }\left(0\right)-1]$ with $H$. Inset demonstrates thermal variation of ${\epsilon }^{\prime }\left(H\right)/{\epsilon }^{\prime }\left(0\right)-1$. (d) Plot of $M^2$ vs $1-{\epsilon }^{\prime }\left(H\right)/{\epsilon }^{\prime }\left(0\right)$ at 20 and 45 K.

Figure 3

(a) $T$ variation of pyroelectric current $\left(I_p\right)$ at different thermal sweep rates for 2 kV/cm poling field. Thermal variations of (b) electric polarization $\left(P\right)$ for $\pm$ 2 kV/cm poling field, (c) $P$ for different poling fields. Inset shows the plot of $P$ with poling field $\left(E\right)$, and (d) $P$ in $H=0$, 50, and 90 kOe. Inset highlights the low-$T$ data.

Figure 4

Rietveld refinement of x-ray powder diffraction pattern (black symbols) at 300 (a). Solid curve demonstrates the fit. Inset exhibits the fit of (440) diffraction peak. (b) X-ray diffraction patterns at 300, 100, and 15 K. Inset depicts (440) diffraction peak at three temperatures.

Figure 5

Temperature variations of the (a) integrated intensity of (220) peak, (b) S displacement, and (c) lattice constant $\left(a\right)$. Inset of (b) and (c) shows the low-$T$ region of $a$. $T$ variation of (d) $\mathrm{Cr}\text{−}\mathrm{S}$ bond length, (e) $\mathrm{Co}\text{−}\mathrm{S}$ bond length, (f) $\mathrm{Cr}\text{−}\mathrm{S}\text{−}\mathrm{Cr}$, (g) $\mathrm{Cr}\text{−}\mathrm{S}\text{−}\mathrm{Co}$, and (h) $\mathrm{Co}\text{−}\mathrm{S}\text{−}\mathrm{Co}$ bond angles. Vertical lines at 225 and 28 K demonstrate $T_N$ and ferroelectric $T_C$, respectively.

Figure 6

(a) At 45 K x-ray diffraction patterns recorded at $H=0$ and 100 kOe. Inset shows the (440) diffraction peak. (b) $\mathrm{Cr}\text{−}\mathrm{S}$ and $\mathrm{Co}\text{−}\mathrm{S}$ bond lengths with $H$ as obtained from the refinement.

Figure 7

(a) An example of the linkage of ${\mathrm{CoS}}_4$ tetrahedra through a ${\mathrm{CrS}}_6$ octahedron. Schematic representation of (b) expansion of ${\mathrm{CoS}}_4$ tetrahedron and (c) contraction of ${\mathrm{CrS}}_6$ octahedron.