Three-dimensional Ising ferrimagnetism of Cr-Fe-Cr trimers in $\mathrm{Fe}{\mathrm{Cr}}_2{\mathrm{Te}}_4$

We carried out a comprehensive study of magnetic critical behavior in single crystals of ternary chalcogenide $\mathrm{Fe}{\mathrm{Cr}}_2{\mathrm{Te}}_4$ that undergoes a ferrimagnetic transition below $T_c\sim$ 123 K. Detailed critical behavior analysis and scaled magnetic entropy change indicate a second-order ferrimagnetic transition. Critical exponents $\beta =0.30\left(1\right)$ with $T_c=122.4\left(5\right)\mathrm{K}, \gamma =1.22\left(1\right)$ with $T_c=122.8\left(1\right)\mathrm{K}$, and $\delta =4.24\left(2\right)$ at $T_c\sim 123\mathrm{K}$ suggest that the spins approach the three-dimensional Ising ($\beta =0.325, \gamma =1.24$, and $\delta =4.82$) model coupled with attractive long-range interactions between spins that decay as $J\left(r\right)\approx r^{-4.88}$. Our results suggest that the ferrimagnetism in $\mathrm{Fe}{\mathrm{Cr}}_2{\mathrm{Te}}_4$ is due to itinerant ferromagnetism among the antiferromagnetically coupled Cr-Fe-Cr trimers.

Figure 1

Synchrotron powder x-ray diffraction (XRD) data and structural model refinements. The data are shown by $+$ and $\circ$; structural model fits at 300 and 105 K are shown by red and blue solid lines, respectively. The difference curves are given by green solid lines, offset for clarity. The vertical tick marks represent Bragg reflections of the $I2/m$ space group and up to 4% of FeTe impurity. The inset shows the single-crystal XRD pattern of $\mathrm{Fe}{\mathrm{Cr}}_2{\mathrm{Te}}_4$ at room temperature.

Figure 2

(a) Crystal structure and results of EDS analysis on $\mathrm{Fe}{\mathrm{Cr}}_2{\mathrm{Te}}_4$. (b) Room-temperature Fe $2p$, Cr $2p$, and Te $3d$ core-level XPS and (c) normalized Cr and Fe $K$-edge XANES spectra. (d) and (e) Fe and Cr $K$-edge EXAFS oscillations and (f) and (g) Fourier transform magnitudes of EXAFS data measured at room temperature. The experimental data are shown as blue symbols alongside the model fit plotted as a red line. The corresponding first coordination shells of Fe and Cr are shown in the insets.

Figure 3

(a) Temperature-dependent dc magnetic susceptibility $\chi \left(T\right)$ in zero-field cooling (ZFC) and field-cooling (FC) modes taken at ${\mu }_{0}H=0.1\mathrm{T}$ for ${\mu }_{\mathbf{0}}\mathbf{H}\parallel \mathbf{c}$ and ${\mu }_{\mathbf{0}}\mathbf{H}\parallel \mathbf{ab}$ (inset), respectively. (b) $1/\chi \left(T\right)$ taken at ${\mu }_{0}H=0.1\mathrm{T}$ along with the Curie-Weiss fit from 150 to 300 K. (c) Field dependence of magnetization for $\mathrm{Fe}{\mathrm{Cr}}_2{\mathrm{Te}}_4$ measured at $T=2\mathrm{K}$. (d) The ac susceptibility real part $m^{\prime }\left(T\right)$ measured with an oscillating ac field of 3.8 Oe and frequency of 499 Hz. The chosen experimental parameters (field and frequency) allow for a well-defined moment and adequate frequency resolution.

Figure 4

(a) Typical initial isothermal magnetization curves from 100 to 150 K with a temperature step of 2 K for the $\mathrm{Fe}{\mathrm{Cr}}_2{\mathrm{Te}}_4$ single crystal. (b) Arrott plot ($\beta =0.5, \gamma =1$) and (c) the modified Arrott plot with the optimum exponents $\beta =0.32$ and $\gamma =1.21$. (d) Temperature-dependent magnetic entropy change $-\mathrm{\Delta }{S}_M\left(T\right)$ at various fields.

Figure 5

(a) Temperature dependence of the spontaneous magnetization $M_s$ (left) and the inverse initial susceptibility ${\chi }_0^{-1}$ (right) with solid fitting curves. The inset shows ${\log }_{10}M$ vs ${\log }_{10}\left({\mu }_{0}H\right)$ collected at $T_c$ = 123 K with a linear fitting curve. (b) Kouvel-Fisher plots of $M_s{(d{M}_s/dT)}^{-1}$ (left axis) and ${\chi }_0^{-1}{(d{\chi }_0^{-1}/dT)}^{-1}$ (right axis) with solid fitting curves. (c) Scaled magnetization $m$ vs scaled field $h$ below and above $T_c$ for $\mathrm{Fe}{\mathrm{Cr}}_2{\mathrm{Te}}_4$. (d) The rescaling of the $M\left({\mu }_{0}H\right)$ curves by $M{\left({\mu }_{0}H\right)}^{-1/\delta }$ vs $\varepsilon {\left({\mu }_{0}H\right)}^{-1/\left(\beta \delta \right)}$.

Figure 6

(a) The antiferromagnetic structures used in the first-principles total energy calculations. Atom-resolved density of states (b) in the nonmagnetic state and (c) in the ferrimagnetic state where the Cr and Fe atoms have opposite spin orientations, which are shown in the ratio of two Cr ions to one Fe ion.