Absence of superconductivity in electron-doped chromium pnictides ThCrAsN_1-xO_x

The XRD patterns of ThCrAsN and its oxygen-doped variants are displayed in Figs. 1(a) and (b). The pattern of ThCrAsN can be indexed well using space group $P4/nmm$, indicating the successful preparation of the parent compound. Element substitutions of oxygen for nitrogen are carried out, ranging from 10% oxygen to 100% oxygen, and the doping step is equal to 10%. With increasing oxygen concentration, the impurity peaks emerge and become conspicuous. The impurities of Th₃As₄ (for $x\geq 0.1$), ThO₂ (for $x\geq 0.4$), and Cr₂As (for $x\geq 0.7$) can be identified, as well as some unknown impurity phase(s) (only for $0.2\leq x\leq 0.4$). However, ThCrAsN_1-xO_x remains the main phase even though the nominal concentration of oxygen is as high as 80%. Even for the pattern of $x=0.9$, the phase of 1111 is conspicuous enough to examine the existence of superconductivity. A simple estimation of the ratio between the 1111 phase and ThO₂ is presented in Supplemental Materials (SM) [32]. With regard to the wholly doped sample, i.e. ThCrAsO, no ZrCuSiAs-type phase can be identified. It’s proper to believe ThCrAsO can not be synthesized under the present synthesis conditions.

In Fig. 1(b), two tilted green bars are sketched to show the monotonic shift of the (111) peaks and (200) peaks, suggesting the unit cell of ThCrAsN_1-xO_x decreases gradually with the increase of oxygen doping. By a least-squares fit for the XRD patterns, the lattice parameters of ThCrAsN_1-xO_x are determined and plotted as functions of nominal oxygen concentration $x$ in Fig. 1(c). Both the $a$-axis and $c$-axis decrease almost linearly with increasing $x$ when $x\leq 0.4$, as indicated by the green bars on the data points. The dependences of cell parameters on $x$ deviate from the green bars gradually when $x\geq 0.5$, indicating the real oxygen concentration is lower than the nominal doping $x$, in line with the increasing impurity of ThO₂ in panel (b). If we take the slopes of $a(x)$ and $c(x)$ ($x\leq 0.4$) as reference, the real oxygen concentration for the sample of ThCrAsN_0.1O_0.9 is about 0.75, inferred from its cell parameters. It is worth noting that the change of the $c$-axis is about 1.75% from $x=0$ to 0.9, while the $a$-axis only shrinks by 1.13%. That the $c$-axis changes much faster than the $a$-axis is consistent with the enhanced inter-layer coupling by electron doping.

A Rietveld refinement was carried out using the collected XRD data shown in Fig. 1(a). The refinement yields a weighted reliable factor of $R_{\mathrm{wp}}=7.41\%$ and a goodness-of-fit of $S=1.54$, indicating reliability of the refinement. The resulting crystallographic data were summarized in Table 1, and compared with the selected structural parameters of LaCrAsO. The axial ratio $c/a$ of ThCrAsN is smaller than that of LaCrAsO, implying ThCrAsN bears stronger internal chemical pressure along the $c$-axis. Similar reduction of $c/a$ was also observed in other siblings Th$M$AsN and La$M$AsO ($M$ = Mn, Fe, Ni, Co) [24, 28, 27, 33]. Other structural parameters of ThCrAsN, such as the height of As from Cr plane and As$-$Cr$-$As bond angle, are not distinct from those of LaCrAsO, which accounts for their close properties.

The resistivity data ($\rho(T)$) for ThCrAsN_1-xO_x are plotted in Fig. 2. As seen in Fig. 2(a), $\rho(T)$ curves show a similar metallic behavior, regardless of the doping concentration. The magnitudes of resistivity are about 1 m$\Omega$ cm at room temperature, comparable to that of LaCrAsO [4]. Only the samples of $x$ = 0.8 and 0.9 show a slightly higher resistivity due to the increased impurity proportion. Although the measured values of resistivity are affected by the contacts and impurity, the residual resistivity ratios (RRR) for all samples are between 2 and 3. The data below 20 K for $x=$ 0.2, 0.3, 0.4, 0.5, and 0.7 are enlarged in the inset of Fig. 2(a) so that the curves differentiate from each other. It’s easily noticed that all curves but $x=0.9$ approach to constant values at 2 K. To examine the possibility that superconductivity emerges under lower temperatures, we measured $\rho(T)$ (30 mK $<T<$ 0.8 K) of several selected compounds in the dilution refrigerator, which are displayed in Fig. 2(b). However, the data of $\rho(T)$ are almost constant below 0.8 K and show no signs for superconductivity. Hence, superconductivity can’t be induced in ThCrAsN_1-xO_x even thogh the real electron doping concentration is as high as 0.75 ($n=4.75$), against the prediction of a superconductivity phase at $n>4.2$ [20].

Figure 3(a) shows the $\chi(T)$ curve for the parent compound ThCrAsN under the magnetic field 1 T and there is no difference between zero-field-cooling and field-cooling data. Below 160 K, the susceptibility shows a Curie-Weiss-like tail, which may be caused by trace amount of paramagnetic impurity. Above 160 K, the susceptibility increases with the temperature monotonically and shows a gentle slope around 850 K, suggesting ThCrAsN is an antiferromagnet. The $\chi(T)$ behavior of ThCrAsN is reminiscent of the cases for polycrystalline SrCr₂As₂, which also shows no Curie-Weiss behavior below 900 K and no clear AFM transition [7]. In addition, LaCrAsO only shows a smooth maximum at $520\sim 570$ K [4]. The behaviors of $\chi(T)$ for these Cr₂As₂-based materials are considered as the character of a two-dimensional (2D) antiferromagnet, which means that strong 2D AFM correlations may set in well above the ordering temperature ($T_{N}$) [4]. Since the actual $T_{N}$ could be notably lower than the maximum in the susceptibility for 2D AFM compounds, here we use the derivative $\mathrm{d}(\chi T)/\mathrm{d}T$ to extract $T_{N}$ of ThCrAsN, as plotted in the inset [34, 35, 7]. $\mathrm{d}(\chi T)/\mathrm{d}T$ shows an AFM transition peak at about 630 K, indicating $T_{N}$ of ThCrAsN is fall on same level with most Cr₂As₂-based materials [7, 23, 36, 4, 37].

$\chi(T)$ for ThCrAsN_0.9O_0.1 under 1 T is displayed in Fig. 3(b), which is quite akin to that of ThCrAsN. Yet the AFM order wasn’t suppressed by the oxygen doping. As shown in the inset of Fig. 3(b), $T_{N}$ of ThCrAsN_0.9O_0.1 is determined to be $\sim 820$ K from $\mathrm{d}(\chi T)/\mathrm{d}T$, even higher than the parent. In addition, the susceptibility maximum of ThCrAsN_0.9O_0.1 appears at higher temperature than ThCrAsN, indicative of stronger 2D correlations. $\chi(T)$ curves for other ThCrAsN_1-xO_x samples are shown in Fig. S2 in SM [32]. Unfortunately, the susceptibility data for other samples are not informative because of the strong background from the robust magnetic impurities. Nevertheless, we can still draw the conclusion that the susceptibility data show no sign of Meissner effect in ThCrAsN_1-xO_x.

To determine the magnetic structure of ThCrAsN and its oxygen-doped derivatives, we examined the magnetic energies ($E_{m}$) for several possible AFM structures by performing DFT calculations. $E_{m}$ is defined as the energy difference between the spin-polarized state and nonmagnetic state. The selected spin configurations are presented in Fig. 4, as well as the corresponding $E_{m}$ and Cr spin moments. $E_{m}$ and Cr spin moments are calculated for both ThCrAsN and ThCrAsO, in spite of the failure of synthesis for the latter.

As shown in Fig. 4(a), all magnetic orders lower the total energy of ThCrAsN, compared to the nonmagnetic state. Among them G-type AFM order is the most stable magnetic structure, yet C-type spin configuration has a pretty close energy. The similar $E_{m}$ values for G-type and C-type AFM orders demonstrate the interplane spin coupling for ThCrAsN is weak, consistent with the characteristic of 2D AFM order. Note that the calculated $E_{m}$ of G-type and C-type AFM orders for LaCrAsO are also reported to be close [4]. And the spin structure of LaCrAsO is experimentally determined to be G-type. Based on the comparable behaviors of $\chi-T$ and results of $E_{m}$ calculations, it’s plausible to anticipate that ThCrAsN has a G-type order, like LaCrAsO. In addition, the G-type AFM order were found to be the ground state for Cr-based 122-type coumpouds like BaCr₂As₂, BaCr₂P₂, SrCr₂As₂, EuCr₂As₂, Sr₂Cr₃As₂O₂, and Sr₂Cr₂AsO₃ [23, 7, 6, 38, 8, 11], which also supports our speculation of the magnetic structure of ThCrAsN.

To gain a deeper insight into the magnetic ordering of ThCrAsN, we calculate the exchange interactions between the Cr neighbors in light of a simple Heisenberg model [39]. The magnetic energies of C-type, G-type and S-type AFM orderings can be expressed as

where $S$ is the local spin, and $J_{1}/J_{2}/J_{c}$ refer to the interactions of in-plane nearest-neighbor, in-plane next-nearest-neighbor, out-of-plane nearest-neighbor, respectively. The values of energies for ThCrAsN could be found in the Table S2 in the SM [32]. Solutions of the equations are

Assuming the Cr spin moment of ThCrAsN is 2.5 $\mu_{B}$ ($S=1.25$, according to Fig. 4(a)), the resulting interactions are $J_{1}$ = 187.9 meV, $J_{2}$ = 62.1 meV, $J_{c}$ = 0.66 meV, consistent with the stability conditions of G-type AFM order that $J_{1}>0$, $J_{1}>2J_{2}$, and $J_{c}>0$. The small positive $J_{c}$ value confirms the AFM coupling between the adjacent Cr₂As₂ layers is weak, in good agreement with the $\chi(T)$ behavior. The large positive values of $J_{1}$ and $J_{1}/J_{2}$ indicate that in-plane Cr–Cr direct interaction is dominant, thus the high Neel temperature and robust G-type AFM order is explicit. We also notice that the calculated energies $E_{\mathrm{C}}$, $E_{\mathrm{G}}$, and $E_{\mathrm{S}}$ for ThCrAsN, as well as the Cr moment, are all close to the values for LaCrAsO [4]. Hence the resultant $J_{1}$ and $J_{2}$ are almost the same as the interactions for ThCrAsN.

$E_{m}$ and Cr spin moments of ThCrAsO ($3d^{5}$ for Cr, one electron more compared to ThCrAsN) with the same magnetic structures as ThCrAsN are shown in Fig. 4(b). The calculation indicates that G-type order is still the ground state of ThCrAsO, although its $E_{m}$ is significantly lower than ThCrAsN. And the corresponding Cr spin moment is reduced slightly to be 2.43 $\mu_{\mathrm{B}}$. That is to say, AFM order of ThCrAsN is to a certain extent suppressed by electron doping. However, the G-type magnetic order remains for the end member ThCrAsO.

Here we would like to point out that $J_{1}$ and $J_{2}$ values for LaFeAsO both are about 50 meV/$S^{2}$, which are close and conspicuously smaller than the values for ThCrAsN [40]. The competition of exchange interactions in FeSCs lead to the collinear (or bicollinear) AFM order, contrary to the case for ThCrAsN. And the next-nearest-neighbor interaction $J_{2}$ is generally believed to play an important role in the electron pairing mechanism of FeSCs [41, 42]. The magnetic structures and exchange interactions clearly point to the distinction between Cr₂As₂-based materials and FeSCs.

The total density of states (DOS) of G-type AFM ordered ThCrAsN and ThCrAsO are calculated and plotted in Fig. 5, as well as their projected density of states (PDOS) of Cr-3$d$ orbitals. Both ThCrAsN and ThCrAsO show a relatively large DOS at the Fermi energy ($E_{\mathrm{F}}$), coinciding with the typical metallic behavior of ThCrAsN_1-xO_x. As shown in Fig. 5(a), the DOS of ThCrAsN around $E_{\mathrm{F}}$ is mainly contributed by Cr-3$d$ and As-4$p$ orbitals. And it is easy to recognize the modest hybridizations between Cr-3$d$ and As-4$p$ in the inset. The $d-p$ hybridizations account for the itinerant magnetism and the reduced Cr-3$d$ magnetic moment of ThCrAsN (theoretically 4 $\mu_{\mathrm{B}}$ for Cr²⁺).

DOS of ThCrAsO is shown in Fig. 5(d). DOSs for ThCrAsN and ThCrAsO are largely comparable, and $E_{\mathrm{F}}$ of ThCrAsO shifts to higher position due to its nominal Cr-3$d^{5}$ electron configuration. The similarities of DOSs can be seen better in other panels about PDOS of Cr. Cr-3$d$ electrons still dominate the states around $E_{\mathrm{F}}$ of ThCrAsO, but the hybridizations between Cr-3$d$ and As-4$p$ is negligible compared to ThCrAsN.

To compare the PDOS of Cr-3$d$ orbitals for ThCrAsN and ThCrAsO more clearly, we divide the orbitals into two groups and present the curves in Figs. 5(b)(e) ($d_{xy}$, $d_{yz}+d_{xz}$) and (c)(f) ($d_{z^{2}}$, $d_{x^{2}-y^{2}}$), respectively. The itinerant magnetism of ThFeAsN and ThFeAsO is confirmed by the broad energy bands. We notice that the orbital occupations of Cr for both ThCrAsN and ThCrAsO are highly spin-polarized, indicating the crystal field splitting energy is small so that Hund’s rule is followed. The high-spin state is also observed for LaCrAsO and LaMnAsO, while the spin polarization for LaFeAsO is much weaker [4, 40]. For ThCrAsN, the PDOS at $E_{\mathrm{F}}$ comes from all five 3$d$ orbitals, and the $d_{x^{2}-y^{2}}$ and $d_{yz}+d_{xz}$ contribute substantially. The heavy proportion of $d_{x^{2}-y^{2}}$ orbital means enhanced direct exchange at $E_{\mathrm{F}}$, consistent with the G-type AFM order that is favored by the nearest Cr–Cr interactions. After the replacement of nitrogen by oxygen, the DOS of $d_{x^{2}-y^{2}}$ and $d_{xy}$ decline sharply, meanwhile the contributions from $d_{z^{2}}$ increase significantly, preceded only by $d_{yz}+d_{xz}$. Whether for ThCrAsN or ThCrAsO, there is a heavy mixing of the $t_{2}$ and $e$ orbitals at $E_{\mathrm{F}}$, which is deemed detrimental to high-$T_{c}$ superconductivity in some theoretical work [43].