Magnetic and structural phase transitions in the spinel compound ${\mathrm{Fe}}_{1+x}$${\mathrm{Cr}}_{2-x}$$O_4$

Neutron and x-ray diffraction, magnetic susceptibility, and specific heat measurements have been used to investigate the magnetic and structural phase transitions of the spinel system ${\mathrm{Fe}}_{1+x}$${\mathrm{Cr}}_{2-x}$$O_4$ ($0.0$ $\le$ $x$ $\le$ $1.0$). The temperature versus Fe concentration ($x$) phase diagram features two magnetically ordered states and four structural states below 420 K. The complexity of the phase diagram is closely related to the change in the spin and orbital degrees of freedom induced by substitution of Fe ions for Cr ions. The systematic change in the crystal structure is explained by the combined effects of Jahn-Teller distortion, spin-lattice interaction, ${\mathrm{Fe}}^{2+}$${\mathrm{-Fe}}^{3+}$ hopping, and disorder among ${\mathrm{Fe}}^{2+}$, ${\mathrm{Fe}}^{3+}$, and ${\mathrm{Cr}}^{3+}$ ions.

Figure 1

The temperature dependence of magnetic susceptibilities and specific heat for ${\mathrm{Fe}}_{1+x}$${\mathrm{Cr}}_{2-x}$$O_4$ (0.0 $\le$ $x$ $\le$ 0.8). Black and red lines are the results of the field-cooled (FC) and zero-field-cooled (ZFC) measurements, respectively. The blue line represents the specific heat data. For $x\le$ 0.3, $T_{S_2}$ is close to $T_C$; for 0.3$\le x\le$ 0.8, $T_{S_1}$ is close to $T_C$. Insets present the enlarged view of the specific heat data around $T_{S_1}$ and $T_C$.

Figure 2

The temperature dependence of magnetic susceptibilities for ${\mathrm{Fe}}_{1+x}$${\mathrm{Cr}}_{2-x}$$O_4$ [$x=0.9$ (a) and 1.0 (b)]. Black and red lines are the results of FC and ZFC measurements, respectively. The insets are the related temperature derivative of the ZFC susceptibilities and the arrows mark the peak positions in temperature.

Figure 3

The 2$\theta$ dependence of the (004) Bragg peak of ${\mathrm{Fe}}_{1+x}$${\mathrm{Cr}}_{2-x}$$O_4$ [$x=0.4$ (a) and 0.9 (b)] as a function of temperature by XPD. The XPD data around the cubic (004) Bragg position of $x=0.4$ (c) and 0.9 (d) at selected temperatures. Inset shows the width (open circle) and integrated intensity (filled square) of the (004) Bragg reflections of $x$ = 0.9 by XPD.

Figure 4

The NPD data around the cubic (004) Bragg position for different compositions at 5 K.

Figure 5

The neutron diffraction data of ${\mathrm{Fe}}_{1+x}$${\mathrm{Cr}}_{2-x}$$O_4$ upon warming. The paramagnetic-to-collinear ferrimagnetic transitions of $x=0.4$ (a) and 1.0 (b) are presented by the integrated intensities of (111) Bragg peaks, and the integrated intensities of the incommensurate reflection at 19.197${}^{\circ }$ presents the collinear-to-conical ferrimagnetic transitions of $x=0.4$ (c) and 0.2 (d), respectively.

Figure 6

Plots of raw NPD data (black dots) for ${\mathrm{Fe}}_{1.2}$${\mathrm{Cr}}_{1.8}$$O_4$ measured at $T=5$, 75, and 150 K for $2\theta \le {120}^{\circ }$. Solid lines are results of Rietveld refinements described in the main text. Differences between observed and calculated intensities are shown directly below the respective patterns. The stars indicate an incommensurate phase.

Figure 7

Plots of NPD data (black dots) for ${\mathrm{Fe}}_{1+x}$${\mathrm{Cr}}_{2-x}$$O_4$($x=0.3$, 0.6, 0.8, and 1.0) measured at $T=5$ K for $2\theta \le {120}^{\circ }$. Solid lines are results of Rietveld refinements described in the main text. Differences between observed and calculated intensities are shown below the respective patterns. The stars indicate an incommensurate phase and the gray arrows are the signal from Al-can.

Figure 8

The temperature versus Fe content ($x$) phase diagram of ${\mathrm{Fe}}_{1+x}$${\mathrm{Cr}}_{2-x}$$O_4$. $T_C$ is the paramagnetic-to-collinear ferrimagnetic phase transition temperature (black lines and dots), $T_N$ is the collinear-to-conical ferrimagnetic phase transition temperature (red lines and dots), $T_{S_1}$ is the cubic-to-tetragonal lattice transition temperature (olive line with open squares), and $T_{S_2}$ is the tetragonal-to-orthorhombic lattice transition temperature (blue line with open squares). The solid lines display the structural and magnetic transitions, while the dashed lines display the possible structural distortions.