The phase transition of ThFe_1-xCo_xAsN from superconductor to metallic paramagnet

Figure 1(a) shows the powder X-ray diffraction (PXRD) patterns of ThFe_1-xCo_xAsN ($0.01 \leq x \leq 1$) with nominal composition. All the observed reflections could be indexed based on the tetragonal ZrCuSiAs (space group = P4/nmm) type structure and hence testify the monophasic nature of these compounds. The refined result shows that the c-axis shrinks markedly while the a-axis stretches slightly with the increase of the Co doping amount (fig. 1(c)). Similar phenomena have also been observed in LaFe_1-xCo_xAsO [15], SmFe_1-xCo_xAsO [16] and PrOFe_1-xCo_xAs [17]. The decrease of the c-lattice parameter could be ascribed to Co doping, which belongs to electron doping, making the Coulomb attraction between the [Th₂N₂]²⁺ layer and the [Fe₂As₂]²⁻ layer stronger. The increase of the a-lattice parameter may be due to the larger As-Co-As angle (117.818°) of ThCoAsN than that of As-Fe-As (114.2°). Figure 1(b) shows the powder XRD pattern and its Rietveld refinement profile of ThCoAsN. The XRD pattern could be well indexed with a tetragonal structure of $a = 4.0507\ \text{\AA}$ and $c = 8.1303\ \text{\AA}$. No obvious impurity peak is found. Table 1 lists the refined structural parameters. Figure 1(d) shows that the cell volumes decrease with the increase of Co amount.

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Figure 2(a) shows the temperature dependence of the electrical resistivity in zero field for all samples. In our previous work, ThFeAsN exhibits superconductivity at 30 K. However, for ThFe_1-xCo_xAsN, only samples with $x=0.01$ and 0.03 exhibit superconductivity at 21.7 K and 9.6 K, respectively. With $x \geq 0.05$, its superconductivity vanishes. All samples show metallic behavior. The doping of Co can suppress the superconductivity of ThFeAsN dramatically. Larger doping amount with $x=0.2$, 0.5, and 1 give only metallic behavior. Panel (b) of fig. 2 shows the low-field dc magnetic susceptibility χ of ThFe_0.99Co_0.01AsN. The strong diamagnetic signal observed below 21.7 K is in accordance with the resistivity measurement result. The magnetic shielding fraction at 1.8 K even exceeds 100$\%$, which could be ascribed to the demagnetization effect, indicating it is the bulk superconductivity. To understand the transport behaviour better, we investigate temperature-dependent normal-state resistivity ρ(T). As is known that most of the iron-based superconductors exhibit strong anisotropy, e.g., the resistivity along the c-axis could be two orders of magnitude larger than that of the ab-plane [18], thus, when the current passes through samples composed of polycrystals with random crystal orientation, the current will choose the path of lower resistance route according to Kirchhoff's current law. Thus, the ρ(T) behavior of a polycrystalline sample is mainly determined by the low-resistivity $\rho_{ab}$, which reflects the intrinsic transport property [19,20]. Panels (c) and (d) of fig. 2 show the temperature dependence of electrical resistivity and magnetization of ThFe_0.99Co_0.01AsN and ThCoAsN, respectively. As shown that, the $\rho{\text{-}}T$ curve of ThFe_0.99Co_0.01AsN is smooth and shows well metallic behaviour in the non-superconductive region. The $\rho{\text{-}}T$ curve of ThCoAsN shows well metallic behaviour too. No sign of phase transition is observed in both of them, which coincides with their magnetic results. In addition, the $\rho{\text{-}}T$ curve of ThCoAsN is similar to that of itinerant ferromagnets LaCoAsO and LaCoPO [21].

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As both its crystal structure and transport behaviour are similar to those of itinerant ferromagnets LaCoAsO and LaCoPO, it is expected that ThCoAsN would be a kind of itinerant ferromagnet. The paramagnetic regime is fitted with a modified Curie-Weiss law, $\chi(T)=\chi_0+C/(T-\Theta_{cw}$), in the range of 80 K to 300 K. The fitted effective moment of ThCoAsN is $p_{\textit{eff}} = 1.82\mu_B$ which approximates to the value of 1.3$\mu_B$ of LaCoOAs [21]. The Weiss temperature $\Theta_{cw}$ is 26.1 K. Figure 3(b) shows the isothermal magnetization (M vs. H) curves in the range of 1.8 K to 54 K. No hysteresis loop is observed. Below 30 K, the M shows a convex curvature against H, but it does not show saturating behavior. With increasing temperature, the $M{\text{-}}H$ curve begins to show linear behavior at high field. However, the extrapolation of the high-field slope to zero field yields small but significant remanent magnetization (about 100 emu/mol). The remanent magnetization could also be observed at 300 K as shown in fig. S1 of the Supplementary Material Supplementarymaterial.pdf, which means that its Curie temperature is above 300 K. It may come from a trace amount of ferromagnetic impurity Co_1-xAs_x ($0\leq x \leq 0.0238$) with the Curie temperature of 1336 K [22]. The magnetic behaviour of the impurity could be classified as soft ferromagnetism [23]. The impurity could not be confirmed by the XRD analysis, which may be due to the fact that its amount is too small.

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In order to confirm the expected itinerant ferromagnetism, the Arrott plots are drawn. Figure 3(c) shows the M² vs. H/M plots from 1.8 K to 54 K. Generally, T_c could be determined from M(T, H)² vs. H/M(T, H) plots [24]. For a homogeneous itinerant ferromagnet, M(T, H) obeys the law $M(T,\,H)^2 =M_s(T)^2+\zeta \cdot H/M(T,\,H)$, where ζ is the coefficient independent of temperature around T_c. As M_s(T) is zero at T_c, then T_c would be the temperature at which a linear line passes the origin $M(T_c,\,H)^2 = \zeta \cdot H/M(T_c,\,H)$. Then, the T_c can be determined by the Arrott plots. A good example of using Arrott plots to determine T_c is shown by fig. 4(b) of ref. [25]. However, for our Arrott plots, M² does not show a linear behavior but a convex curvature against H/M (as shown by fig. 3(c)). In contrast, its M⁴ vs. H/M plots show a good linear behavior (as shown by fig. 3(d)). In this case, the critical temperature T_c should still be estimated by the low-field data of the isothermal Arrott plots [26]. However, no Arrott plots have the tendency to pass through the zero point which makes it impossible to get T_c from the Arrott plots directly. Then the expected itinerant ferromagnetism cannot be confirmed. However, the behaviour of M² vs. H/M and M⁴ vs. H/M curves is similar to that of the paramagnetic metal phase of FeGa_3-yGe_y [26].

For the $M{\text{-}}H$ curve of ThCoAsN at 1.8 K, it shows the Brillouin function-like paramagnetic behaviour. To check it, the modified Brillouin function is used to fit the curve [27–30],

$$\begin{eqnarray} M&= xNg\mu_{B}JB_{J}(y),\quad y=\frac{g\mu_{B}JH}{k_{B}(T-\theta)},\quad \end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray} B_{J}(y)&= \frac{2J+1}{2J}\textrm{coth}\biggl(\frac{2J+1}{2J}y\biggr)-\frac{1}{2J}\textrm{coth}\frac{1}{2J}y.\quad \end{eqnarray} \tag{ 2 }$$

Before fitting, the magnetization contribution from CoAs impurity has been subtracted. Here, N is the number of Co²⁺ ion contained in the system; g is the Landé g-factor (here $g=1.33$), $\mu_B$ is the Bohr magnetron; B_J(y) is the so-called Brillouin function; J is the total angular momentum quantum number (here $J=9/2$); H is the applied magnetic field; k_B is the Boltzmann constant; T is the temperature; θ is a parameter shown to be related to an internal effective field within the mean-field approach [28]. The fitted parameters are as follows: $x =0.87$ and $\theta = 1.45\ \text{K}$. Figure 4 shows the $M{\text{-}}H$ curve of ThCoAsN at 1.8 K. The solid line represents the Brillouin function fitting. It could be observed that the fitted line coincides well with the experimental data. The $M{\text{-}}H$ curve of ThCoAsN shows paramagnetic behaviour even at 1.8 K. All the experimental data point to the fact that ThCoAsN is a kind of paramagnet. As a summary, fig. 5 shows the phase diagram of ThFe_1-xCo_xAsN.

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In our previous work [13], by another way of electron doping, substitution of O for N in the -ThN- layer, a second superconductive phase is observed, while it is not observed in this work. The possible reasons are as follows. As is known that for ThFeAsN, the -FeAs- layer is the conductive layer. The substitution of Co for Fe not only produces extra electrons directly, but also brings much disorder in the -FeAs- layer directly. Substitution of O for N in the -ThN- layer can also produce extra electrons for the -FeAs- layer, but it brings less disorder in this layer. The reemergence of superconductivity with higher dopings only occurs for O doping in ThFeAsN, which may be due to the fact that its second phase of superconductivity is much sensitive to disorder. As the family members of [Th₂N₂]²⁺ block layer based "1111" type compounds are becoming complete, the influence of [La₂O₂]²⁺ and [Th₂N₂]²⁺ block layers on the physical property of "1111" type compounds could be compared now. Table 2 shows the physical property comparation of "1111" type compounds with different block layers. It could be concluded that compared with the famous [La₂O₂]²⁺ layer, the [Th₂N₂]²⁺ layer has its own special influence on the physical property of "1111" type compounds.

Table 2:.  Physical property comparation of "1111" type compounds with [La₂O₂]²⁺ and [Th₂N₂]²⁺ block layer, respectively. AFM: antiferromagnetic.

Materials	Property
LaFeAsO	SDW-type AFM transition
	around 150 K [31]
ThFeAsN	superconductor with $T_c = 30\ \text{K}$ [32]
LaMnAsO	AFM semiconductor/insulator
	with $T_N =317\ \text{K}$ [33]
ThMnAsN	two AFM transition around
	300 K and 52 K, respectively [34]
LaCoAsO	weakly itinerant ferromagnet
	with $T_c = 66\ \text{K}$ [21]
ThCoAsN	metallic paramagnet above 1.8 K
	(this work)
LaNiAsO	superconductor with $T_c = 2.75\ \text{K}$ [35]
ThNiAsN	superconductor with $T_c = 4.3\ \text{K}$ [14]
LaMnPO	AFM insulator with $T_N= 375\ \text{K}$ [36]
ThMnPN	two AFM transition around
	300 K and 36 K, respectively [34]