Revisiting the influence of Fe excess in the synthesis of ${\mathrm{BaFe}}_2{\mathrm{S}}_3$

${\mathrm{BaFe}}_2{\mathrm{S}}_3$ is a quasi-one-dimensional antiferromagnetic insulator that becomes superconducting under hydrostatic pressure. The magnetic ordering temperature $T_N$, as well as the presence of superconductivity have been found to be sample dependent. It has been argued that the Fe content may play a decisive role, with the use of 5 mol% ($\delta =0.1$) excess Fe being reportedly required during the synthesis to optimize the magnetic ordering temperature and the superconducting properties. However, it is yet unclear whether a Fe off-stoichiometry is actually present in the samples, and how it affects the structural, magnetic, and transport properties. Here, we present a systematic study of compositional, structural, and physical properties of ${\mathrm{BaFe}}_{2+\delta }{\mathrm{S}}_3$ as a function of the nominal Fe excess $\delta$. As $\delta$ increases, we observe the presence of an increasing fraction of secondary phases but no systematic change in the average composition or crystal structure of the main phase. Magnetic susceptibility curves are influenced by the presence of magnetic secondary phases. While a small excess Fe (2.5 mol%, i.e., $\delta =0.05$) can slightly increase $T_N$ and decrease the temperature of the resistivity anomaly at $T^{*}$, a range of $T_N^{\prime }\mathrm{s}/T^{*}$'s is observed within each batch. This result strongly contrasts with the previously reported maximum of $T_N$ at $\delta =0.1$. Rather than with the value of $\delta$, $T_N$ and $T^{*}$ seem to correlate with the broadening in the logarithmic derivative of the resistivity around $T_N$ that could be an indicator of the level of disorder in the samples. Finally, we show that crystals free of ferromagnetic secondary phases can be obtained by remelting samples with nominal $\delta =0.05$ in a Bridgman-like process based on optical heating.

Figure 1

(a) Secondary electron SEM image of ${\mathrm{BaFe}}_{2+\delta }{\mathrm{S}}_3$ for $\delta =0$. Back-scattered electron SEM images for (b) $\delta =0$ and for inclusions of (c) a Si-rich phase for $\delta =0.05$ (remelted), (d) Fe for $\delta =0.05$, (e) other ternary phases containing Ba, Fe, and S for $\delta =0.1$, and (f) FeS for $\delta =0.2$.

Figure 2

(a) Powder x-ray diffraction pattern of ${\mathrm{BaFe}}_{2+\delta }{\mathrm{S}}_3$ for nominal $\delta =0$, 0.05, 0.1, and 0.2. Vertical lines indicate the positions of the most intense reflections for the secondary phases. The patterns are vertically shifted for clarity and the intensity is normalized. (b) Rietveld analysis of the powder x-ray diffraction pattern for $\delta =0.05$.

Figure 3

Weight fraction of the phases ${\mathrm{BaFe}}_2{\mathrm{S}}_3$, ${\mathrm{Ba}}_2{\mathrm{Fe}}_4{\mathrm{S}}_5$, FeS, and ${\mathrm{SiO}}_2$ as a function of the nominal Fe composition. The dotted lines are guides to the eye.

Figure 4

Crystal structure of orthorhombic ${\mathrm{BaFe}}_2{\mathrm{S}}_3$ obtained for $\delta =0$ from single crystal x-ray diffraction measurements. Samples with other $\delta$ values exhibit a very similar structure, see Tables 3, 4, and 5.

Figure 5

(a) Magnetization of ${\mathrm{BaFe}}_{2+\delta }{\mathrm{S}}_3$ as a function of temperature for crystals with different nominal Fe content. The arrows indicate the Néel temperature as defined in the inset. The circles are the susceptibility obtained from $M(H$) for fields above 4 T. The color indicates the value of $\delta$. Measurements for two samples of the same batch are shown for $\delta =0.1$. (b) Field dependence of the magnetization for the same samples of (a) for $T=250\mathrm{K}$. $\mathrm{\Delta }M$ indicates the contribution of extrinsic magnetic inclusions for $\delta =0.05$. Inset: Definitions of the characteristic temperatures for the case of $\delta =0$.

Figure 6

Correlation between $T_{\text{min}}$ and $T_N^M$. The different data points for the same value of $\delta$ correspond to measurements of different samples of the same batch, with the exception for the case of $\delta =0.05$ where data from two different batches are presented in yellow. The dotted lines are guides to the eye to indicate a linear and nonlinear dependence. Inset: $T_{\text{min}}-T_N^M$ as a function of $\mathrm{\Delta }M$ for $T$ = 250 K.

Figure 7

(a) Normalized resistivity as a function of the inverse temperature for different nominal values of $\delta$ for ${\mathrm{BaFe}}_{2+\delta }{\mathrm{S}}_3$. The curves are vertically shifted for clarity. (b) Temperature dependence of the derivative of the logarithmic of the resistivity with respect to the inverse temperature for $\delta =0.1$ and 0. $T_N^{\rho }$ and $T^{*}$ are indicated with an arrow for $\delta =0.1$. The horizontal segments indicate the broadening of the curves around $T_N^{\rho }$, computed as the width of the curves at half of the distance from their maximum to the value of $\mathrm{\Delta }$. Inset: Value of the energy gap for $T<T_N^{\rho }$ as a function of the nominal Fe content.

Figure 8

(a) Dependence of $T_N^{\rho }$ and $T^{*}$ with the nominal Fe content for ${\mathrm{BaFe}}_{2+\delta }{\mathrm{S}}_3$. $T_{\text{min}}$, $T_N^M$, and $T_N^{\rho }$ correspond to the Néel temperature obtained from magnetization [inset of Fig. 5] and resistivity measurements (Fig. 7), respectively. For each value of $\delta$, data from several samples are presented. For comparison, $T_N$ and $T^{*}$ extracted from reference [16] are also included. The dotted lines are guides to the eye. (b) $T_N^{\rho }$ and $T^{*}$ as a function of the broadening of $d\ln \rho /d(1/T$) around $T_N^{\rho }$ as defined in Fig. 7. The dotted lines are guides to the eye. The background color indicates the change from thermal activated behavior to variable range hopping. Samples from two batches are presented for the case of $\delta =0.05$ in addition to the remelted samples.