Magnetodielectric effects in $A$-site cation-ordered chromate spinels $\mathrm{Li}M\mathrm{C}{\mathrm{r}}_4{\mathrm{O}}_8$ ($M=\mathrm{Ga}$ and In)

We report the occurrence of a magnetodielectric effect and its correlation with structure and magnetism in the $A$-site ordered chromate spinel oxides $\mathrm{Li}M\mathrm{C}{\mathrm{r}}_4{\mathrm{O}}_8$ ($M=\mathrm{Ga}$, In). In addition to magnetic and dielectric measurements, temperature dependent synchrotron and neutron diffraction experiments have been carried out for the Ga compound. The results are compared and contrasted with that of a corresponding conventional $B$-site magnetic chromate spinel oxide, $\mathrm{ZnC}{\mathrm{r}}_2{\mathrm{O}}_4$. Like $\mathrm{ZnC}{\mathrm{r}}_2{\mathrm{O}}_4$, the $A$-site ordered chromate spinels exhibit a magnetodielectric effect at the magnetic ordering temperature ($T_{\mathrm{N}}\sim 13–15\mathrm{K}$), resulting from magnetoelastic coupling through a spin Jahn-Teller effect. While the presence of a broad magnetic anomaly, associated with a short-range magnetic ordering ($T_{\mathrm{SO}}\sim 45\mathrm{K}$) in $\mathrm{ZnC}{\mathrm{r}}_2{\mathrm{O}}_4$, does not cause any dielectric anomaly, a sharp change in dielectric constant has been observed in $\mathrm{LiInC}{\mathrm{r}}_4{\mathrm{O}}_8$ at the magnetic anomaly, which is associated with the opening of a spin gap ($T_{\mathrm{SG}}\sim 60\mathrm{K}$). Contrary to the In compound, a broad dielectric anomaly exists at the onset of short-range antiferromagnetic ordering ($T_{\mathrm{SO}}\sim 55\mathrm{K}$) in $\mathrm{LiGaC}{\mathrm{r}}_4{\mathrm{O}}_8$. The differences in dielectric behavior of these compounds have been discussed in terms of breathing distortion of the $\mathrm{C}{\mathrm{r}}_4$ tetrahedra.

Figure 1

(a, b) Rietveld refinements on the synchrotron XRD pattern of $\mathrm{LiGaC}{\mathrm{r}}_4{\mathrm{O}}_8$ acquired at 298 and 5 K with $\lambda =0.4127$ and 0.4959 Å, respectively. Red open circle and black solid line are the experimental data and calculated patterns, respectively; green vertical bars indicate the nuclear Bragg reflections, and the blue line below is the difference between the experimental and calculated patterns. The first and second green vertical bars in panel (b) correspond to the Bragg reflections for the cubic and tetragonal phases, respectively. Insets of panel (b) show the broadening and splitting of the two cubic Bragg reflections (400) and (800) in the antiferromagnetic state. The XRD patterns shown in the inset are recorded with $\lambda =0.4959\AA$. The suffixes $c$ and $t$ stand for cubic and tetragonal symmetry, respectively. Small unrefined peaks visible in the $2\theta$ range of 7–15 degrees originated from the cryostat.

Figure 2

(a, b) Rietveld refinements on the neutron diffraction pattern of $\mathrm{LiGaC}{\mathrm{r}}_4{\mathrm{O}}_8$ acquired at 4 K with $\lambda =2.4395\AA$ for the whole region and small region, respectively, where red cross and black solid line are the experimental data and calculated patterns, green vertical bars indicate the Bragg reflections and the blue line below is the difference between experimental and calculated pattern. The first series of Bragg reflections correspond to the cubic $F\overline{4}3m$ phase and the second correspond to the tetragonal $I\overline{4}m2$ phase, the third and the fourth series account for the magnetic phases for the cubic phase $k_{\mathrm{c}}=\left(001\right)$ and for the tetragonal phase $k_{\mathrm{t}}=(½½½)$, respectively. (*Aluminum peaks from the cryostat). (c, d) Schematic representation of cubic ($F\overline{4}3m$) and tetragonal ($I\overline{4}m2$) structure of $\mathrm{LiGaC}{\mathrm{r}}_4{\mathrm{O}}_8$ obtained from the Rietveld refinement on neutron diffraction pattern collected at 4 K, where yellow and green tetrahedra contains the $\mathrm{L}{\mathrm{i}}^{+}$ and $\mathrm{G}{\mathrm{a}}^{3+}$ ions, respectively, and blue octahedra contains the $\mathrm{C}{\mathrm{r}}^{3+}$ ions. (e, f) Pyrochlore network consists of $\mathrm{C}{\mathrm{r}}_4$ tetrahedra embedded in the cubic structure and breathing distortion in a three-dimensional network of corner-sharing Cr tetrahedra forming pyrochlore sublattice ($d>d^{\prime }$). (g) The $k_{\mathrm{c}}$ magnetic structure associated with cubic symmetry, with alternating spin chains on the $ab$ plane. Every second $ab$ plane is rotated ${90}^{\circ }$ with respect to the first. (h) The $k_{\mathrm{t}}$ magnetic structure associated with tetragonal symmetry with chains of spins with two-up and two-down arrangement along the [100] and [010] directions.

Figure 3

(a, b) Temperature dependence of dc magnetization data of $\mathrm{LiGaC}{\mathrm{r}}_4{\mathrm{O}}_8$ and $\mathrm{LiInC}{\mathrm{r}}_4{\mathrm{O}}_8$, respectively, under zero-field-cooled (ZFC) and field-cooled (FC) conditions in the presence of a magnetic field of 0.1 kOe. Upper insets of panels (a) and (b) show the temperature dependent FCC and FCW magnetization data at 0.1 kOe, while the bottom insets of panels (a) and (b) show the first order derivative of magnetization with respect to temperature as a function of temperature at 0.1 kOe. (c, d) Temperature dependence of specific heat divided by temperature ($C_p/T$) for $\mathrm{LiGaC}{\mathrm{r}}_4{\mathrm{O}}_8$ and $\mathrm{LiInC}{\mathrm{r}}_4{\mathrm{O}}_8$ across $T_{\mathrm{N}}$, respectively. Insets of panels (c) and (d) show the $C_p/T$ data across short-range antiferromagnetic ordering ($T_{\mathrm{SO}}\sim 55\mathrm{K}$) of the Ga compound and spin-gap opening temperature ($T_{\mathrm{SG}}\sim 60\mathrm{K}$) of the In compound, respectively.

Figure 4

(a, b) Temperature dependence of dielectric constant of $\mathrm{LiGaC}{\mathrm{r}}_4{\mathrm{O}}_8$ and $\mathrm{LiInC}{\mathrm{r}}_4{\mathrm{O}}_8$, respectively, in zero magnetic field at 50 kHz. Inset of panel (a) shows the temperature dependence of dielectric constant of $\mathrm{ZnC}{\mathrm{r}}_2{\mathrm{O}}_4$ in zero magnetic field at 50 kHz. Inset of panel (b) shows the temperature dependent cell volume of the In compound fitted with a function of the type $V_0=V_1+V_2{\theta }_{S1}\mathrm{Coth}\frac{{\theta }_{S1}}{T}$. The experimental data (square symbol) shows a discontinuity from the theoretical fit (blue line) at the spin gap, as well as magnetic and structural transitions (∼13–15 K). (c, d) Temperature dependence of dielectric constant of $\mathrm{LiGaC}{\mathrm{r}}_4{\mathrm{O}}_8$ and $\mathrm{LiInC}{\mathrm{r}}_4{\mathrm{O}}_8$, respectively, in the presence of different magnetic fields at 50 kHz. Insets of panels (c) and (d) show the magnetic field dependence magnetocapacitance (% MC) at 50 kHz for the Ga and In compounds, respectively.