Magnetic compensation, field-dependent magnetization reversal, and complex magnetic ordering in ${\mathrm{Co}}_2{\mathrm{TiO}}_4$

The complex nature of magnetic ordering in the spinel $\mathrm{C}{\mathrm{o}}_2\mathrm{Ti}{\mathrm{O}}_4$ is investigated by analyzing the temperature and magnetic field dependence of its magnetization ($M$), specific heat ($C_{\mathrm{p}}$), and ac magnetic susceptibilities ${\chi }^{\prime }$ and ${\chi }^{″}$. X-ray diffraction of the sample synthesized by the solid-state reaction route confirmed the spinel structure whereas x-ray photoelectron spectroscopy shows its electronic structure to be $\mathrm{C}{\mathrm{o}}_2\mathrm{Ti}{\mathrm{O}}_4=\left[\mathrm{C}{\mathrm{o}}^{2+}\right]\left[\mathrm{C}{\mathrm{o}}^{3+}\mathrm{T}{\mathrm{i}}^{3+}\right]{\mathrm{O}}_4$. From analysis of the temperature dependence of the dc paramagnetic susceptibility, the magnetic moments $\mu \left(A\right)=3.87{\mu }_{\mathrm{B}}$ and $\mu \left(B\right)=5.19{\mu }_{\mathrm{B}}$ on the $A$ and $B$ sites are determined with $\mu \left(B\right)$ in turn yielding $\mu \left(\mathrm{T}{\mathrm{i}}^{3+}\right)=1.73{\mu }_{\mathrm{B}}$ and $\mu \left(\mathrm{C}{\mathrm{o}}^{3+}\right)=4.89{\mu }_{\mathrm{B}}$. Analysis of the dc and ac susceptibilities combined with the weak anomalies observed in the $C_{\mathrm{p}}$ vs $T$ data shows the existence of a quasi-long-range ferrimagnetic state below $T_{\mathrm{N}}\sim 47.8\mathrm{K}$ and a compensation temperature $T_{\mathrm{comp}}\sim 32\mathrm{K}$, the latter characterized by sign reversal of magnetization with its magnitude depending on the applied magnetic field and the cooling protocol. Analysis of the temperature dependence of $M$ (field cooled) and $M$ (zero field cooled) data and the hysteresis loop parameters is interpreted in terms of large spin clusters. These results in $\mathrm{C}{\mathrm{o}}_2\mathrm{Ti}{\mathrm{O}}_4$, significantly different from those reported recently in isostructural $\mathrm{C}{\mathrm{o}}_2\mathrm{Sn}{\mathrm{O}}_4=\left[\mathrm{C}{\mathrm{o}}^{2+}\right]\left[\mathrm{C}{\mathrm{o}}^{2+}\mathrm{S}{\mathrm{n}}^{4+}\right]{\mathrm{O}}_4$, warrant further investigations of its magnetic structure using neutron diffraction.

Figure 1

XRD patterns together with the Rietveld refined data of (a) $\mathrm{C}{\mathrm{o}}_2\mathrm{Ti}{\mathrm{O}}_4$ and (b) $\mathrm{C}{\mathrm{o}}_2\mathrm{Sn}{\mathrm{O}}_4$. The blue lines at the bottom represent difference between the measured and simulated patterns.

Figure 2

The XPS of $\mathrm{Co}-2p$ peaks of (a) $\mathrm{C}{\mathrm{o}}_3{\mathrm{O}}_4$, (b) $\mathrm{C}{\mathrm{o}}_2\mathrm{Ti}{\mathrm{O}}_4$, and (c) $\mathrm{C}{\mathrm{o}}_2\mathrm{Sn}{\mathrm{O}}_4$.

Figure 3

The XPS of (a) $\mathrm{Ti}-2p$, (b) Sn–$3d$, (c) O–$1s$ peaks of $\mathrm{C}{\mathrm{o}}_2\mathrm{Ti}{\mathrm{O}}_4, \mathrm{C}{\mathrm{o}}_2\mathrm{Sn}{\mathrm{O}}_4$, and $\mathrm{C}{\mathrm{o}}_3{\mathrm{O}}_4$ systems.

Figure 4

Temperature variation of the inverse paramagnetic susceptibility ${{\chi }^{-}}^1\left(T\right)$ of $\mathrm{C}{\mathrm{o}}_2\mathrm{Ti}{\mathrm{O}}_4$ and $\mathrm{C}{\mathrm{o}}_2\mathrm{Sn}{\mathrm{O}}_4$ systems. The solid lines are best fits to the Néel's expression for ferrimagnets discussed in the text.

Figure 5

Temperature dependence of dc magnetic susceptibility $\chi \left(T\right)\left[=M/H_{\mathrm{dc}}\left(T\right)\right]$ for $\mathrm{C}{\mathrm{o}}_2\mathrm{Ti}{\mathrm{O}}_4$ measured under both ZFC and FC conditions recorded at various magnetic fields in the range $50\mathrm{Oe}\le H_{\mathrm{dc}}\le 10\mathrm{kOe}$.

Figure 6

High-field $(5\mathrm{kOe}\le H_{\mathrm{dc}}\le 40\mathrm{kOe})$ magnetization ($M$) vs temperature ($T$) data for $\mathrm{C}{\mathrm{o}}_2\mathrm{Ti}{\mathrm{O}}_4$ measured under both the ZFC and FC conditions.

Figure 7

Temperature dependence of dc magnetic susceptibility $\chi \left(T\right)\left[=M/H_{\mathrm{dc}}\left(T\right)\right]$ for $\mathrm{C}{\mathrm{o}}_2\mathrm{Sn}{\mathrm{O}}_4$ measured under both ZFC and FC conditions recorded at various magnetic fields.

Figure 8

(a) Temperature variation of the ac magnetic susceptibility (a) ${\chi }^{\prime }\left(T\right)$, and (b) ${\chi }^{″}\left(T\right)$ for $\mathrm{C}{\mathrm{o}}_2\mathrm{Ti}{\mathrm{O}}_4$ measured at 2 Hz in $h_{\mathrm{ac}}=4\mathrm{Oe}$ with superposed dc bias fields $H_{\mathrm{dc}}=0$, 10, 20, and 30 Oe.

Figure 9

Temperature dependence of ac magnetic susceptibilities (a) ${\chi }^{\prime }\left(T\right)$ and (b) ${\chi }^{″}\left(T\right)$ of $\mathrm{C}{\mathrm{o}}_2\mathrm{Ti}{\mathrm{O}}_4$ measured at various frequencies between 0.17 and 1202 Hz under warming conditions using $h_{\mathrm{ac}}=4\mathrm{Oe}$ and $H_{\mathrm{dc}}=0\mathrm{Oe}$.

Figure 10

The best fit of the relaxation times to the Vogel-Fulcher law in $\mathrm{C}{\mathrm{o}}_2\mathrm{Ti}{\mathrm{O}}_4$.

Figure 11

Plots of hysteresis loops ($M$ vs $H$) in $\mathrm{C}{\mathrm{o}}_2\mathrm{Ti}{\mathrm{O}}_4$ are shown at selected temperatures of (a) 10 K, (b) 20 K, (c) 30 K, and (d) 50 K recorded under ZFC condition. The insets show the zoomed view of $M-H$ loops near origin showing the asymmetry in the loops.

Figure 12

The hysteresis loops ($M$ vs $H$) measured at low temperatures 5, 6, 7, 8, and 9 K under ZFC condition. The insets show the asymmetry in the $M-H$ loops measured at 5 K under FC (20 kOe) condition.

Figure 13

The temperature variation of (a) coercive field $H_{\mathrm{C}}\left(T\right)$ and remanence magnetization $M_{\mathrm{R}}$ and (b) exchange bias $H_{\mathrm{EB}}\left(T\right)$ and high field $(H\sim 90\mathrm{kOe})$ magnetization $M_{\max }$ measured under both ZFC and FC (20 kOe) conditions in $\mathrm{C}{\mathrm{o}}_2\mathrm{Ti}{\mathrm{O}}_4$. The lines connecting the data points are visual guides.

Figure 14

Temperature variations of (a) exchange bias $H_{\mathrm{EB}}$ and (b) coercivity $H_{\mathrm{C}}$ in $\mathrm{C}{\mathrm{o}}_2\mathrm{Sn}{\mathrm{O}}_4$ for the ZFC and FC (@ 10 kOe) cases. The lines connecting the data points are visual guides.

Figure 15

The temperature variation of specific heat $C_{\mathrm{p}}\left(T\right)$ for the $\mathrm{C}{\mathrm{o}}_2\mathrm{Ti}{\mathrm{O}}_4$ sample recorded at various magnetic fields ($H_{\mathrm{dc}}=0$, 10, and 50 kOe). The insets show the zoomed view across the ferrimagnetic Néel temperature $\left(T_{\mathrm{N}}\right)$ and compensation temperature $\left(T_{\mathrm{comp}}\right)$.

Figure 16

The temperature dependence of $C_{\mathrm{p}}{T}^{-1}$ for the $\mathrm{C}{\mathrm{o}}_2\mathrm{Ti}{\mathrm{O}}_4$ sample using the data of Fig. 15.