Antiferromagnetism and the emergence of frustration in the sawtooth lattice chalcogenide olivines ${\mathrm{Mn}}_2{\mathrm{SiS}}_{4-x}{\mathrm{Se}}_x$ ($x=0–4$)

The magnetism in the sawtooth lattice of Mn in the olivine chalcogenides, ${\mathrm{Mn}}_2{\mathrm{SiS}}_{4-x}{\mathrm{Se}}_x$ ($x=1–4$), is studied in detail by analyzing their magnetization, specific heat, and thermal conductivity properties and complemented with density functional theory calculations. The air-stable chalcogenides are antiferromagnets and show a linear trend in the transition temperature $T_N$ as a function of Se content ($x$), which shows a decrease from $T_N\approx 86\mathrm{K}$ for ${\mathrm{Mn}}_2{\mathrm{SiS}}_4$ to 66 K for ${\mathrm{Mn}}_2{\mathrm{SiSe}}_4$. Additional magnetic anomalies are revealed at low temperatures for all the compositions. Magnetization irreversibilities are observed as a function of $x$. The specific heat and the magnetic entropy indicate the presence of short-range spin fluctuations in ${\mathrm{Mn}}_2{\mathrm{SiS}}_{4-x}{\mathrm{Se}}_x$. A spin-flop antiferromagnetic phase transition in the presence of applied magnetic field is present in ${\mathrm{Mn}}_2{\mathrm{SiS}}_{4-x}{\mathrm{Se}}_x$, where the critical field for the spin flop increases from $x=0$ towards 4 in a nonlinear fashion. Density functional theory calculations show that an overall antiferromagnetic structure with ferromagnetic coupling of the spins in the $ab$ plane minimizes the total energy. The band structures calculated for ${\mathrm{Mn}}_2{\mathrm{SiS}}_4$ and ${\mathrm{Mn}}_2{\mathrm{SiSe}}_4$ reveal features near the band edges similar to those reported for Fe-based olivines suggested as thermoelectrics; however the experimentally determined thermal transport data do not support superior thermoelectric features. The transition from long-range magnetic order in ${\mathrm{Mn}}_2{\mathrm{SiS}}_4$ to short-range order and spin fluctuations in ${\mathrm{Mn}}_2{\mathrm{SiSe}}_4$ is explained using the variation of the Mn-Mn distances in the triangle units that constitutes the sawtooth lattice upon progressive replacement of sulfur with selenium. Overall, the results presented here point towards the role played by magnetic anisotropy and geometric frustration in the antiferromagnetic state of the sawtooth olivines.

Figure 1

(a)–(e) The PXRD patterns of ${\mathrm{Mn}}_2{\mathrm{SiS}}_{4-x}{\mathrm{Se}}_x$ ($x=0–4$) compositions are presented along with the results of structural analysis using the $Pbnm$ space group. The black markers represent experimental data and the red lines are the fit using the Le Bail approach. The blue horizontal line shows the difference curve. In (a) and (d), an asterisk marks a minor impurity phase, $\alpha$-MnS ($\approx 2\mathrm{wt}.\%$).

Figure 2

(a) The specific heat of ${\mathrm{Mn}}_2{\mathrm{SiS}}_{4-x}{\mathrm{Se}}_x$ ($x=0–4$) obtained at 0 T and 3 T are plotted together, showing no significant influence of the external magnetic field on $T_N$. (b) Shows the $C_p\left(T\right)$ of ${\mathrm{Mn}}_2{\mathrm{SiS}}_4$ (red circles) along with the curve fit using the Einstein model (solid line). The inset of (a) shows the magnetic specific heat, $C_{\mathrm{m}}$. The top inset in (b) shows that, with increasing $x$, the $T_N$ decreases from 86 K to 66 K, while the entropy, $S_{\mathrm{m}}$, is shown in the bottom inset. A significantly low value of entropy compared to $Rln(2S+1)$ is released at the magnetic transition in ${\mathrm{Mn}}_2{\mathrm{SiS}}_{4-x}{\mathrm{Se}}_x$ chalcogenides.

Figure 3

The magnetic susceptibility of ${\mathrm{Mn}}_2{\mathrm{SiS}}_{4-x}{\mathrm{Se}}_x$ ($x=0–4$) obtained in 500 Oe field cooled conditions is presented for $x=0$, 1, 4 in panel (a) and $x=2$, 3 in panel (b). The inset of panel (a) shows $T_N$ as a function of Se content ($x$). The insets (1) and (2) in panel (b) show the $1/{\chi }_{\mathrm{dc}}^{\mathrm{fc}}\left(T\right)$ curves of ${\mathrm{Mn}}_2{\mathrm{SiS}}_4$ and ${\mathrm{Mn}}_2{\mathrm{SiSe}}_4$, respectively, along with Curie-Weiss fit (red solid line). (c)–(g) The derivative $dM/dT$ versus temperature showing the multiple anomalies present in each composition.

Figure 4

A schematic of the olivine structure of ${\mathrm{Mn}}_2{\mathrm{SiS}}_4$. The unit cell is outlined in black solid line. The purple spheres are Mn. The sawtooth lattice formed by ${\mathrm{Mn}}^{2+}$ at the two crystallographically inequivalent sites ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$ is shown. The line of ${\mathrm{m}}_1$ atoms forms along the $b$ direction. In the figure, the black spheres are Si and the yellow are S. The figure was created using VESTA [27].

Figure 5

(a)–(e) The dc magnetic susceptibility of ${\mathrm{Mn}}_2{\mathrm{SiS}}_{4-x}{\mathrm{Se}}_x$ ($x=0–4$) obtained in ZFC and FC protocol using an external field of 500 Oe. Large bifurcation in the ZFC and FC arms observed for $x=2$, 3 whereas crossing of the ZFC and FC is seen for $x=4$. (f)–(j) The dc susceptibility in field-cooled mode for 1 T, 3 T, and 5 T for $x=0–4$. Even with the application of 5 T, no significant enhancement of magnetic moment is obtained.

Figure 6

(a) The isothermal magnetization of ${\mathrm{Mn}}_2{\mathrm{SiS}}_{4-x}{\mathrm{Se}}_x$ ($x=0–4$) at 2 K. The inset shows the evolution of the critical field, $H_c$, as a function of Se content, $x$. (b)–(d) The derivative $dM/dH$ versus temperature showing the presence of metamagnetic phase transitions.

Figure 7

The DFT-predicted band structure of (a) ${\mathrm{Mn}}_2{\mathrm{SiS}}_4$ and (b) ${\mathrm{Mn}}_2{\mathrm{SiSe}}_4$. The electronic projected density of states (PDOS) for ${\mathrm{Mn}}_2{\mathrm{SiS}}_4$ and ${\mathrm{Mn}}_2{\mathrm{SiSe}}_4$ is shown in (c) and (d), respectively. The experimentally measured thermal conductivity of (e) ${\mathrm{Mn}}_2{\mathrm{SiS}}_4$ and (f) ${\mathrm{Mn}}_2{\mathrm{SiSe}}_4$. The arrows mark the temperature of the antiferromagnetic phase transition.

Figure 8

A schematic figure showing the sawtooth chain of Mn in ${\mathrm{Mn}}_2{\mathrm{SiS}}_4, {\mathrm{Mn}}_2{\mathrm{SiS}}_2{\mathrm{Se}}_2$, and ${\mathrm{Mn}}_2{\mathrm{SiSe}}_4$. The distance between Mn in the ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$ positions is marked. The Mn triangles tend to form isosceles in all the ${\mathrm{Mn}}_2{\mathrm{SiS}}_{4-x}{\mathrm{Se}}_x$ compositions. The distance between the 2-triangle units (shaded region) along the $b$ direction increases as the Se content increases. The interlayer distances between the sawtooth layers (in the $ab$ plane) also increase with higher Se content.