Tetragonal polymorph of ${\mathrm{BaFe}}_2{\mathrm{S}}_2\mathrm{O}$ as an antiferromagnetic Mott insulator

We report a tetragonal polymorph of ${\mathrm{BaFe}}_2{\mathrm{S}}_2\mathrm{O}$ synthesized under high pressures. This $\beta \text{−}{\mathrm{BaFe}}_2{\mathrm{S}}_2\mathrm{O}$ phase is structurally characterized by two-dimensional ${\mathrm{Fe}}_2\mathrm{O}$ square nets that are sandwiched by sulfur atomic layers. The electrical, magnetic, and thermodynamic measurements indicate that it is an antiferromagnetic insulator with a Néel temperature of 121 K. A successive magnetic transition at $\sim 40\mathrm{K}$ is observed, possibly associated with spin canting due to Dzyaloshinskii-Moriya interactions. Density functional theory based calculations reveal Mott localization driven by the on-site electron-electron Coulomb repulsion. The calculations also suggest a noncollinear ${\mathrm{Fe}}^{2+}$-spin structure with two-$\mathbf{k}$ [${\mathbf{k}}_{\mathbf{1}}=(1/2,0,1/2)$ and ${\mathbf{k}}_{\mathbf{2}}=(0,1/2,1/2)$] propagation vectors, primarily due to the magnetocrystalline anisotropy as well as the next-nearest-neighbor superexchange interactions mediated by oxygen and sulfur anions, respectively.

Figure 1

Powder x-ray diffraction at room temperature and its Rietveld refinement profile of $\beta \text{−}{\mathrm{BaFe}}_2{\mathrm{S}}_2\mathrm{O}$. The crystal structure of $\beta \text{−}{\mathrm{BaFe}}_2{\mathrm{S}}_2\mathrm{O}$ is shown in the inset.

Figure 2

Temperature dependence of resistivity for the $\beta \text{−}{\mathrm{BaFe}}_2{\mathrm{S}}_2\mathrm{O}$ polycrystalline sample. The inset shows the plot of $\ln \rho$ vs 1/$T$. The red line is the fit with the Arrhenius equation.

Figure 3

Temperature dependence of magnetic susceptibility of $\beta \text{−}{\mathrm{BaFe}}_2{\mathrm{S}}_2\mathrm{O}$ measured at a 3-T field in field-cooling (FC) and zero-field-cooling (ZFC) protocols. The red solid line is the Curie-Weiss (CW) fit, and the pink dashed line is the extrapolation. Deviations from the extrapolated CW formula are plotted in the inset. The antiferromagnetic Néel temperature is marked.

Figure 4

[(a)–(c)] Temperature dependence of magnetic susceptibility of $\beta \text{−}{\mathrm{BaFe}}_2{\mathrm{S}}_2\mathrm{O}$ measured at different magnetic fields in field-cooling (FC) and zero-field-cooling (ZFC) protocols. (d) Field dependence of the characteristic temperatures, $T_1$, $T_2$, and $T_{\mathrm{N}}$, all of which are marked in (a)–(c).

Figure 5

Magnetic field dependence of magnetization at fixed temperatures for $\beta \text{−}{\mathrm{BaFe}}_2{\mathrm{S}}_2\mathrm{O}$. The upper-left inset is a close-up of the initial $M\left(H\right)$ curves, in which the metamagnetic-like transitions at $H_{\mathrm{mm}}$ are marked by arrows. The lower-right inset plots $H_{\mathrm{mm}}$ and the coercive force $H_{\mathrm{cov}}$ as functions of temperature. Both inset plots employ a logarithmic scale for the horizontal axes.

Figure 6

Temperature dependence of specific heat for $\beta \text{−}{\mathrm{BaFe}}_2{\mathrm{S}}_2\mathrm{O}$. The solid red line is the fitted data with combined Einstein and Debye models. The inset shows the released magnetic entropy associated with the long-range magnetic ordering.

Figure 7

Correlations between the Néel temperature, $T_{\mathrm{N}}$, and the interatomic distances of $\mathrm{Fe}\text{−}\mathrm{O}$ (a) and $\mathrm{Fe}\text{−}Ch$ (b) in the oxychalcogenides with ${\mathrm{Fe}}_2\mathrm{O}C{h}_2$ ($Ch=$ Se, S) layers. The dashed lines are guides to the eye. The data of $\beta \text{−}{\mathrm{BaFe}}_2{\mathrm{S}}_2\mathrm{O}$ are displayed with blue solid diamonds.

Figure 8

Possible in-plane magnetic structures in $\beta \text{−}{\mathrm{BaFe}}_2{\mathrm{S}}_2\mathrm{O}$ for the DFT-based calculations. FM (a), S-AFM (b), C-AFM (c), and $2\mathbf{k}$-AFM (d) represent ferromagnetic, striped AFM, Néel-type AFM, and the noncollinear AFM, respectively. The ${\mathrm{Fe}}^{2+}$ spins tend to align along the $\mathrm{Fe}\text{−}\mathrm{O}$ bond direction due to spin-orbit coupling effect. Three intralayer magnetic exchange parameters, the nearest-neighbor $J_1$ and the next-nearest-neighbor $J_2$ and $J_2^{\prime }$, are marked in (d).

Figure 9

Energy-dispersive density of states (DOS) projected on each atom for $\beta \text{−}{\mathrm{BaFe}}_2{\mathrm{S}}_2\mathrm{O}$. (a) shows the nonpolarized calculation result without plus $U$. (b)–(d) are based on $2\mathbf{k}$-AFM order with $U=0$, 1, and 2 eV, respectively. The insets display the close-ups showing the DOS around the Fermi level, $E_{\mathrm{F}}=$ 0.