Neutron diffraction study of the inverse spinels ${\mathrm{Co}}_2{\mathrm{TiO}}_4$ and ${\mathrm{Co}}_2{\mathrm{SnO}}_4$

We report a detailed single-crystal and powder neutron diffraction study of ${\mathrm{Co}}_2{\mathrm{TiO}}_4$ and ${\mathrm{Co}}_2{\mathrm{SnO}}_4$ between the temperature 1.6 and 80 K to probe the spin structure in the ground state. For both compounds the strongest magnetic intensity was observed for the (111)${}_{\text{M}}$ reflection due to ferrimagnetic ordering, which sets in below $T_{\text{N}}=48.6$ and 41 K for ${\mathrm{Co}}_2{\mathrm{TiO}}_4$ and ${\mathrm{Co}}_2{\mathrm{SnO}}_4$, respectively. An additional low intensity magnetic reflection (200)${}_{\text{M}}$ was noticed in ${\mathrm{Co}}_2{\mathrm{TiO}}_4$ due to the presence of an additional weak antiferromagnetic component. Interestingly, from both the powder and single-crystal neutron data of ${\mathrm{Co}}_2{\mathrm{TiO}}_4$, we noticed a significant broadening of the magnetic (111)${}_{\text{M}}$ reflection, which possibly results from the disordered character of the Ti and Co atoms on the $B$ site. Practically, the same peak broadening was found for the neutron powder data of ${\mathrm{Co}}_2{\mathrm{SnO}}_4$. On the other hand, from our single-crystal neutron diffraction data of ${\mathrm{Co}}_2{\mathrm{TiO}}_4$, we found a spontaneous increase of particular nuclear Bragg reflections below the magnetic ordering temperature. Our data analysis showed that this unusual effect can be ascribed to the presence of anisotropic extinction, which is associated to a change of the mosaicity of the crystal. In this case, it can be expected that competing Jahn-Teller effects acting along different crystallographic axes can induce anisotropic local strain. In fact, for both ions ${\mathrm{Ti}}^{3+}$ and ${\mathrm{Co}}^{3+}$, the $2t_g$ levels split into a lower $d_{xy}$ level yielding a higher twofold degenerate $d_{xz}/d_{yz}$ level. As a consequence, one can expect a tetragonal distortion in ${\mathrm{Co}}_2{\mathrm{TiO}}_4$ with $c/a<1$, which we could not significantly detect in the present work.

Figure 1

Rietveld refinements of the neutron powder diffraction data of ${\mathrm{Co}}_2{\mathrm{TiO}}_4$ collected at (a) 60 and (b) 1.6 K. The crystal structure was refined in the cubic space group $Fd\overline{3}m$. The calculated patterns (red) are compared with the observed one (black circles). In the lower part of each diagram, the difference pattern (blue) as well as the positions of the nuclear reflections of ${\mathrm{Co}}_2{\mathrm{TiO}}_4$ are shown. In the powder pattern collected at 1.6 K, magnetic intensity appears at the position of the reflections 111.

Figure 2

Temperature dependence of nuclear and magnetic Bragg reflections of ${\mathrm{Co}}_2{\mathrm{TiO}}_4$ single crystal. The strongest magnetic intensity shows the reflections 111, which is increasing well above Curie temperature $T_{\text{C}}=50$ K. The presence of the magnetic reflection 200 can be ascribed to an additional weak antiferromagnetic ordering. The strong increase of the 400 indicates the existence of anisotropic change of the mosaicity in the crystal.

Figure 3

The x-ray photoelectron spectra (XPS) of (a) $\mathrm{Co}-2p$, (b) $\text{Ti-2}p$, and (c) $\text{O-1}s$ peaks of single crystal ${\mathrm{Co}}_2{\mathrm{TiO}}_4$ and (d) $\text{Co-2}p$, (e) $\text{Sn-3}d$, and (f) $\text{O-1}s$ peaks of polycrystalline ${\mathrm{Co}}_2{\mathrm{SnO}}_4$.

Figure 4

Neutron powder patterns of (a) ${\mathrm{Co}}_2{\mathrm{SnO}}_4$ and (b) ${\mathrm{Co}}_2{\mathrm{TiO}}_4$ recorded at two different temperatures 1.6 (blue) and 80 K (red) collected on the instrument E2. Due to the vastly different scattering lengths of the Ti and Sn atoms the intensities of the nuclear reflections of ${\mathrm{Co}}_2{\mathrm{TiO}}_4$ and ${\mathrm{Co}}_2{\mathrm{SnO}}_4$ strongly differ. In contrast, the difference patterns (black) of both compound are very similar indicating that the magnetic ordering is practically the same. The only difference arises through the presence of the magnetic reflection (200)${}_{\text{M}}$ in the powder pattern of ${\mathrm{Co}}_2{\mathrm{TiO}}_4$. The observed and calculated powder patterns of (c) ${\mathrm{Co}}_2{\mathrm{SnO}}_4$ and (d) ${\mathrm{Co}}_2{\mathrm{TiO}}_4$ as obtained from Rietveld refinements are compared in the right part of the figure. The calculated patterns (red) are compared with the observed one (black circles). In the lower part of each diagram, the difference pattern (blue) as well as the positions of the nuclear reflections of ${\mathrm{Co}}_2{\mathrm{TiO}}_4$ are shown. For comparison, the calculated of the pure nuclear part (green) is also shown. The sample of ${\mathrm{Co}}_2{\mathrm{SnO}}_4$ contains a small impurity of ${\mathrm{SnO}}_2$. The positions of the strongest reflections are marked with stars.

Figure 5

Temperature dependence of magnetic moments of the cobalt and titanium atoms in ${\mathrm{Co}}_2{\mathrm{TiO}}_4$. Below the Curie temperature $T_{\text{C}}=50$ K the magnetic moments of Co1 and Ti atoms located at the $B$ sites are coupled antiparallel to the moments of the Co2 atoms located at the $A$ site. During the refinement, we have used a moment ratio $\mu \left({\mathrm{Co}}^{3+}\right)/\mu \left({\mathrm{Ti}}^{3+}\right)=4$ as well as the moment direction parallel to the $a$ axis.

Figure 6

Temperature dependence of ac-magnetic susceptibility of ${\mathrm{Co}}_2{\mathrm{TiO}}_4$ single-crystal (a) real component ${\chi }^{\prime }$($T$) and (b) imaginary ${\chi }^{\prime \prime }$($T$) components measured at various frequencies between 0.17 and 1200 Hz under warming condition using ac-peak-to-peak amplitude $H_{\text{ac}}=3$ Oe without any external dc-magnetic field.

Figure 7

(a) The logarithmic variation of the peak-temperature obtained from ${\chi }^{\prime }$($T$) and ${\chi }^{\prime \prime }$($T$) (i.e., power-law analysis $ln\left[\tau \right]$ vs $ln([T_{\text{P}}-T_{\text{F}}]/T_{\text{F}}$), the solid line represents the best fit to the experimental data. (b) Plots associated with the Vogel-Fulcher law $ln\left[\tau \right]$ vs $[1/(T_{\text{P}}-T_0)]$ using the peak positions in ${\chi }^{\prime }$($T$) and ${\chi }^{\prime \prime }$($T$), the solid lines shows the best-fit to experimental data.

Figure 8

Temperature dependence of ac-magnetic susceptibility (a) real part ${\chi }^{\prime }$($T$) and (b) imaginary ${\chi }^{\prime \prime }$($T$) components of single-crystalline ${\mathrm{Co}}_2{\mathrm{TiO}}_4$ system measured at three different bias fields $H_{\text{dc}}$ (10, 20, and 30 Oe) at a constant frequency of 2 Hz and ac-magnetic field peak-to-peak amplitude of 4 Oe. The inset shows peak splitting in ${\chi }^{\prime }$($T$), which is significant at higher values of $H_{\text{dc}}$.