Figure 1

Structure of the unit slab for (a) single layered $A{\mathrm{Ga}}_2{\mathrm{S}}_4$ ($A=\mathrm{Ni}$, Fe) and (b) bilayer ${\mathrm{Fe}}_2{\mathrm{Ga}}_2{\mathrm{S}}_5$. Superexchange paths are shown by lines within the diagrams (color online).Reuse & Permissions

Figure 2

(a) Four sublattices (in different colors online) of the buckled honeycomb lattice formed by the Fe-S-Fe straight bonds [yellow path online in Fig. 1b] in the bilayer of ${\mathrm{Fe}}_2{\mathrm{Ga}}_2{\mathrm{S}}_5$. The Fe atoms in the upper triangular lattice layer of the bilayer are shown by open spheres (green online), while the ones in the lower layer by solid black. (b), (c) $ab$ plane and $c$-axis components of $\chi (T)$ for (b) ${\mathrm{NiGa}}_2{\mathrm{S}}_4$ under $B=7\mathrm{T}$, (c) ${\mathrm{FeGa}}_2{\mathrm{S}}_4$ and ${\mathrm{Fe}}_2{\mathrm{Ga}}_2{\mathrm{S}}_5$ under $B=0.1\mathrm{T}$. Both FC (solid symbol) and ZFC results (open symbol) are shown. No in-plane anisotropy was found. Insets: (b) Anisotropy ${\chi }_{ab}/{\chi }_c(T)$ obtained in the FC sequence for ${\mathrm{NiGa}}_2{\mathrm{S}}_4$ (circles), ${\mathrm{FeGa}}_2{\mathrm{S}}_4$ (squares) and ${\mathrm{Fe}}_2{\mathrm{Ga}}_2{\mathrm{S}}_5$ (triangles). The horizontal line indicates the unity for the isotropic case. (c) $\chi (T)$ and $d\chi (T)/dT$ of ${\mathrm{Fe}}_2{\mathrm{Ga}}_2{\mathrm{S}}_5$. The vertical lines indicate the Néel point $T_{\mathrm{N}}$.Reuse & Permissions

Figure 3

(a) Total specific heat divided by temperature $C_P/T$, and their lattice contribution $C_{\mathrm{L}}/T$ (solid line), (b) magnetic part of the specific heat divided by temperature $C_{\mathrm{M}}/T$ (left axis), the entropy $S_{\mathrm{M}}$ (right axis) for ${\mathrm{FeGa}}_2{\mathrm{S}}_4$ (circle) and for ${\mathrm{Fe}}_2{\mathrm{Ga}}_2{\mathrm{S}}_5$ (diamond). The horizontal broken lines indicate $S_{\mathrm{M}}=R\ln 5$ and $R\ln 15$.Reuse & Permissions

Figure 4

Power law behavior of $C_{\mathrm{M}}/T$ for (a) ${\mathrm{NiGa}}_2{\mathrm{S}}_4$, (b) ${\mathrm{FeGa}}_2{\mathrm{S}}_4$, inset of (b) ${\mathrm{Fe}}_2{\mathrm{Ga}}_2{\mathrm{S}}_5$ under various fields along the $c$ axis. Inset of (a): $\Delta (C_{\mathrm{M}}/T){\theta }_{\mathrm{W}}/[R\ln (2S+1)]$ vs $T/{\theta }_{\mathrm{W}}$ for ${\mathrm{NiGa}}_2{\mathrm{S}}_4(S=1,{\theta }_{\mathrm{W}}=80\mathrm{K})$ and ${\mathrm{FeGa}}_2{\mathrm{S}}_4(S=2,{\theta }_{\mathrm{W}}=160\mathrm{K})$ at 0 T in full logarithmic scale.Reuse & Permissions