Critical behavior in the itinerant ferromagnet $\mathrm{AsNC}{\mathrm{r}}_3$ with tetragonal-antiperovskite structure

Herein, we have systematically reported the synthesis, structure, magnetism, and electrical/thermal transport properties of $\mathrm{AsNC}{\mathrm{r}}_3$. Tetragonal-antiperovskite metallic $\mathrm{AsNC}{\mathrm{r}}_3$ exhibits a second-order ferromagnetic (FM)-paramagnetic (PM) transition around 243 K, where the resistivity and specific heat also show a related change. Based on the obtained parameters from basic physical properties, the nature of weak electron-electron correlation was confirmed by both the Kadowaki-Woods ratio and Wilson ratio. Moreover, the value of the Rhodes-Wolfarth ratio (1.312) is larger than 1, suggesting an itinerant ferromagnetism in $\mathrm{AsNC}{\mathrm{r}}_3$. To further clarify the magnetic interaction of the $\mathrm{AsNC}{\mathrm{r}}_3$ system, the study of critical behavior around the FM-PM transition has been performed. The critical exponents ($\beta$, $\gamma$, and $\delta$) of $\mathrm{AsNC}{\mathrm{r}}_3$ obtained from different methods are very close to the theoretical values of the mean-field model ($\beta =0.5$, $\gamma =1.0$, and $\delta =3.0$), indicating the existence of a long-range FM interaction. Besides, the exchange interaction distance $J\left(r\right)\sim r^{-4.3}$ for $\mathrm{AsNC}{\mathrm{r}}_3$ decreases more slowly than that of mean-field model $J\left(r\right)\sim r^{-4.5}$, further confirming the long-range magnetic coupling in our system. The strong hybridization between Cr-$3d$ and N-$2p$ states as well as between Cr-$3d$ and As-$4p$ states confirmed by our theoretical calculations results in the itinerant characterization of carriers and the long-range FM interaction in tetragonal-antiperovskite $\mathrm{AsNC}{\mathrm{r}}_3$.

Figure 1

(a) Rietveld refined powder XRD patterns at room temperature for $\mathrm{AsNC}{\mathrm{r}}_3$. The vertical marks (blue line) stand for the position of Bragg peaks, and the solid line (green line) at the bottom correspond to the difference between experimental and calculated intensities. (b) EDS information on $\mathrm{AsNC}{\mathrm{r}}_3$. (c) Sketches of crystal structure with different directions for $\mathrm{AsNC}{\mathrm{r}}_3$.

Figure 2

(a) Temperature-dependent magnetization $M\left(T\right)$ curves under ZFC and FC processes and inverse susceptibility ${{\chi }^{-}}^1\left(T\right)$ (ZFC) curves of $\mathrm{AsNC}{\mathrm{r}}_3$ at a magnetic field of 1 kOe between 5 and 300 K. (b) $M\left(H\right)$ curves at 5 and 300 K. The left and right inset show the enlargement of $M\left(H\right)$ curve at 5 and 300 K with low magnetic fields. (c) Temperature dependence of resistivity $\rho \left(T\right)$ at 0 and 5 T for $\mathrm{AsNC}{\mathrm{r}}_3$. The left inset presents the lower-$T\rho \left(T\right)$ data plotted as $\rho \left(T\right)$ vs $T^2$. The right inset reveals the MR effect around FM-PM transition. (d) Temperature-dependent heat capacity $C_P\left(T\right)$ at zero magnetic field between 5 and 300 K for $\mathrm{AsNC}{\mathrm{r}}_3$. Inset displays the plot of $C_P\left(T\right)/T$ vs $T^2$ below 10 K and the solid line represents the linear fitting results according to Eq. (3).

Figure 3

(a) The initial isothermal magnetization around $T_C$. (b) The Arrott plot of $H/M$ vs $M^2$.

Figure 4

(a) The temperature-dependent spontaneous magnetization $M_{\mathrm{S}}$ and inverse initial susceptibility ${\chi }_0^{-1}$ with the fitting solid curves. (b) KF plots for $M_S\left(T\right)$ and ${{\chi }_0}^{-1}\left(T\right)$. The solid lines are fitted. (c) Scaling plots around $T_C$ using the values of $\beta$ and $\gamma$ determined by the KF method. (d) The critical isotherm analysis at $T_C$. The inset presents the plot on ${log}_{10}\text{−}{log}_{10}$ scale with a fitted solid line.

Figure 5

(a) The ${(H/M)}^{1/\gamma }$ vs $M^{1/\beta }$ using the critical exponents obtained by the KF method. (b) Temperature-dependent modified coefficients $A^{\prime }$ and $B^{\prime }$.

Figure 6

(a) Total and (b) atom-orbital-projected density of states of $\mathrm{AsNC}{\mathrm{r}}_3$ with cubic-antiperovskite structure ($Pm\text{−}3m$); (c) Total and (d) atom-orbital-projected DOS of $\mathrm{AsNC}{\mathrm{r}}_3$ with tetragonal-antiperovskite structure ($I4/mcm$). The positive and negative values represent the DOS of up and down spins, respectively. The Fermi level is set to be 0 eV.