Dielectric anomalies and spiral magnetic order in ${\mathrm{CoCr}}_2{\mathrm{O}}_4$

We have investigated the structural, magnetic, thermodynamic, and dielectric properties of polycrystalline ${\mathrm{CoCr}}_2{\mathrm{O}}_4$, an insulating spinel exhibiting both ferrimagnetic and spiral magnetic structures. Below $T_c=94\mathrm{K}$ the sample develops long-range ferrimagnetic order, and we attribute a sharp phase transition at $T_S\approx 27\mathrm{K}$ to the onset of long-range spiral magnetic order. Neutron measurements confirm that the structure remains cubic at $80\mathrm{K}$ and at $11\mathrm{K}$; the magnetic ordering by $11\mathrm{K}$ is seen to be rather complex. Density functional theory supports the view of a ferrimagnetic semiconductor with magnetic interactions consistent with noncollinear ordering. Capacitance measurements on ${\mathrm{CoCr}}_2{\mathrm{O}}_4$ show a sharp decrease in the dielectric constant at $T_S$, but also an anomaly showing thermal hysteresis falling between approximately $T=50$ and $57\mathrm{K}$. We tentatively attribute the appearance of this higher-temperature dielectric anomaly to the development of short-range spiral magnetic order, and discuss these results in the context of utilizing dielectric spectroscopy to investigate noncollinear short-range magnetic structures.

Figure 1

(a) Zero-field-cooled (ZFC) and field-cooled (FC) dc magnetization of ${\mathrm{CoCr}}_2{\mathrm{O}}_4$ measured in an applied field of $H=100\mathrm{Oe}$. (b) Real part of the ac susceptibility of ${\mathrm{CoCr}}_2{\mathrm{O}}_4$ measured at $\omega ∕2\pi =10\mathrm{kHz}$. Data below $40\mathrm{K}$ have been shown in an expanded view.

Figure 2

Time-of-flight neutron powder diffraction at (a) 200, (b) 80, and (c) $11\mathrm{K}$. The symbols in each panel are data, the lines are fits using the Rietveld method to the nuclear structure, and the traces at the bottom of each panel are the difference profiles. The peaks in the difference profiles that emerge as the temperature is lowered arise from long-range magnetic ordering. Vertical lines at the top of the plot are expected positions of nuclear reflections. Crystal structure data: space group $Fd\overline{3}m$, $a=8.3294\left(1\right)\mathrm{\AA }$ at $300\mathrm{K}$, $8.3224\left(1\right)\mathrm{\AA }$ at $80\mathrm{K}$, and $8.3211\left(1\right)\mathrm{\AA }$ at $11\mathrm{K}$. Co at $(1∕8,1∕8,1∕8)$, Cr at $(1∕2,1∕2,1∕2)$, and O at $(x,x,x)$ with $x=0.2617\left(1\right)$ at all three temperatures.

Figure 3

Partial densities of $\mathrm{Co}d$ and $\mathrm{Cr}d$ states obtained for (a) $U_{\mathrm{eff}}^{\mathrm{Co}}=U_{\mathrm{eff}}^{\mathrm{Cr}}=0\mathrm{eV}$ (LSDA) and (b) $U_{\mathrm{eff}}^{\mathrm{Co}}=4\mathrm{eV}$ and $U_{\mathrm{eff}}^{\mathrm{Cr}}=2\mathrm{eV}$. Collinear Néel-type magnetic ordering was assumed.

Figure 4

Specific heat measurements on ${\mathrm{CoCr}}_2{\mathrm{O}}_4$ at $H=0$, plotted as $C∕T$ vs $T$.

Figure 5

(a) Dielectric constant of ${\mathrm{CoCr}}_2{\mathrm{O}}_4$ sample $A$ measured at $H=0$ as a function of temperature. (b) Dielectric constant of ${\mathrm{CoCr}}_2{\mathrm{O}}_4$ sample $B$ measured at $H=0$ as a function of temperature. Vertical lines are drawn at 27 and $49\mathrm{K}$ to help locate the dielectric anomalies. All data were acquired at $\omega ∕2\pi =30\mathrm{kHz}$.

Figure 6

(a) Dielectric constant of ${\mathrm{CoCr}}_2{\mathrm{O}}_4$ near $T=50\mathrm{K}$ measured on cooling and warming at $1\mathrm{K}∕\min$. (b) Dielectric constant of ${\mathrm{CoCr}}_2{\mathrm{O}}_4$ near $T=50\mathrm{K}$ measured on cooling and warming at $5\mathrm{K}∕\min$. All data were acquired at $\omega ∕2\pi =30\mathrm{kHz}$.