Dielectric properties of doping-free $\mathrm{Na}{\mathrm{Mn}}_7{\mathrm{O}}_{12}$: Origin of the observed colossal dielectric constant

The semiconducting $\mathrm{Na}{\mathrm{Mn}}_7{\mathrm{O}}_{12}$ is a doping-free compound with several coexistent properties such as orbital ordering, charge ordering, and magnetic orderings of different types. We investigated its dielectric response by means of frequency impedance measurements in the range from $20\mathrm{Hz}\text{to}1\mathrm{MHz}$. Standard measurements on metallized samples exhibit an apparent colossal dielectric constant (CDC) with an ${ϵ}_R$ value of several thousands at low frequencies, but a careful equivalent circuit analysis allows one to ascribe the observed CDC to the effect of a depletion layer on the metal-semiconductor junctions. We bypass this effect by means of a nonstandard technique employing mica linings: the resulting dielectric behavior exhibits the presence of the charge ordering transition at $T_{\mathit{CO}}=176\mathrm{K}$ and shows a net bulk dielectric constant value ${ϵ}_R\simeq 68$ at room temperature.

Figure 1

Total dielectric response of Au-metallized $\mathrm{Na}{\mathrm{Mn}}_7{\mathrm{O}}_{12}$. Dielectric constant curves are measured from $40\mathrm{K}\text{to}120\mathrm{K}$ in steps of $5\mathrm{K}$; loss tangent curves are shown only at selected temperatures for sake of clarity.

Figure 2

Complex impedance of Au-metallized $\mathrm{Na}{\mathrm{Mn}}_7{\mathrm{O}}_{12}$ at $T=70\mathrm{K}$ for various bias voltage values $V_b$.

Figure 3

Equivalent circuit for Au-metalized $\mathrm{Na}{\mathrm{Mn}}_7{\mathrm{O}}_{12}$.

Figure 4

Least-squares best fit of the total dielectric response of Au-metallized $\mathrm{Na}{\mathrm{Mn}}_7{\mathrm{O}}_{12}$ at $T=82\mathrm{K}$ with applied voltage $V_b=0.335\mathrm{V}$. Best-fit parameters are $G_{0_1}=1.99\times {10}^{-5}$, $C_{{\infty }_1}=5.89\times {10}^{-12}$, $B_1=1.68\times {10}^{-7}$, $s_1=0.36$, $G_{0_2}=5.86\times {10}^{-6}$, $C_{{\infty }_2}=3.15\times {10}^{-13}$, $B_2=2.95\times {10}^{-9}$, and $s_2=0.91$.

Figure 5

Inverse capacitance of electrode junctions with respect to applied bias voltage, as calculated from the best fit described in the text at $T=82\mathrm{K}$ for different frequencies. Values for $n$ exponent of Eq. (5) at single frequencies are given by power-law regression slopes for $V⩾0.145\mathrm{V}$.

Figure 6

Arrhenius plots of the electric conductivity. ●: net $\mathrm{Na}{\mathrm{Mn}}_7{\mathrm{O}}_{12}$ result from the best fit of Au-metallized sample measurements at $526\mathrm{kHz}$ (see text). ▴: net $\mathrm{Na}{\mathrm{Mn}}_7{\mathrm{O}}_{12}$ result from a sample with mica linings. ▵, ◁, ▿: total conductivity of the Au-metallized sample at $1\mathrm{MHz}$, $1\mathrm{kHz}$ and $20\mathrm{Hz}$, respectively. ◇: total dc conductivity of the Au-metallized sample.

Figure 7

$I\text{−}V$ characteristic measured in the temperature range $55\mathrm{K}⩽T⩽295\mathrm{K}$ in steps of $5\mathrm{K}$.

Figure 8

$\mathrm{Na}{\mathrm{Mn}}_7{\mathrm{O}}_{12}$ net dielectric response from sample with mica linings for temperatures in the range from $20\mathrm{K}\text{to}285\mathrm{K}$. Loss tangent points are reported only for those temperatures where it was possible to assess $\tan \delta$.

Figure 9

$\mathrm{Na}{\mathrm{Mn}}_7{\mathrm{O}}_{12}$ dielectric constant plotted as function of temperature. The dashed line marks the charge ordering transition temperature $T=T_{\mathit{CO}}$. ●: dielectric constant at frequency $1\mathrm{MHz}$ resulting from the best-fit procedure applied to metallized $\mathrm{Na}{\mathrm{Mn}}_7{\mathrm{O}}_{12}$ (see text).