We report the crystal structures and magnetic properties of two psuedo-polymorphs of the $S=1/2$~Ti coordination framework, KTi(C${}_2$O${}_4$)${}_2\cdot$xH${}_2$O. Single-crystal X-ray and powder neutron diffraction measurements on $\alpha$-KTi(C${}_2$O${}_4$)${}_2\cdot$xH${}_2$O confirm its structure in the tetragonal $I4/mcm$ space group with a square planar arrangement of Ti ions. Magnetometry and specific heat measurements reveal weak antiferromagnetic interactions, with $J_1\approx 7$ K and $J_2/J_1=0.11$ indicating a slight frustration of nearest- and next-nearest-neighbor interactions. Below $1.8$~K, $\alpha$-KTi(C${}_2$O${}_4$)${}_2\cdot$xH${}_2$O undergoes a transition to G-type antiferromagnetic order with magnetic moments aligned along the $c$ axis of the tetragonal structure. The estimated ordered moment of Ti in is suppressed from its spin-only value to $0.62(3){\mu }_B$, thus verifying the two-dimensional nature of the magnetic interactions within the system. $\beta$-KTi(C${}_2$O${}_4$)$_2$2H$_2$O, on the other hand, realises a three-dimensional diamond-like magnetic network of Ti moments within a hexagonal $P{6}_{222}$ structure. An antiferromagnetic exchange coupling of $J\approx 54$ K—an order of magnitude larger than in —is extracted from magnetometry and specific heat data. $\beta$-KTi(C${}_2$O${}_4$)$_2$2H$_2$O undergoes N'eel ordering at $T_N=28$ K, with the magnetic moments aligned within the $ab$ plane and a slightly reduced ordered moment of $0.79{\mu }_B$ per Ti${}^{3+}$. Through density-functional theory calculations, we address the origin of the large difference in the exchange parameters between the $\alpha$ and $\beta$ psuedo-polymorphs. Given their observed magnetic behaviors, we propose $\alpha$-KTi(C${}_2$O${}_4$)${}_2\cdot$xH${}_2$O and $\beta$-KTi(C${}_2$O${}_4$)$_2$2H$_2$O as close to ideal model $S=1/2$ Heisenberg square and diamond lattice antiferromagnets, respectively.

中文翻译：

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在配位框架KTi（C2O4）2⋅xH2O的α和β相中实现正方形和菱形晶格S = 1 / 2Heisenberg反铁磁体模型

我们报告了两个假多晶型的晶体结构和磁性 $\mathrm{小号}=\mathrm{1个}/2$〜Ti协调框架，KTi（C${}_2$Ø${}_4$）${}_2\cdot$H${}_2$O.单晶X射线和粉末中子衍射测量 $\alpha$-KTi（碳${}_2$Ø${}_4$）${}_2\cdot$H${}_2$O确认其结构为四方 $\mathrm{一世}4/米C米$Ti离子呈方形平面排列的空间群。磁力计和比热测量显示弱的反铁磁相互作用${Ĵ}_{\mathrm{1个}}\approx 7$ K和 ${Ĵ}_2/{Ĵ}_{\mathrm{1个}}=0.11$表示最近邻居和下一个邻居的交互略有挫败感。下面$1.8$〜K， $\alpha$-KTi（碳${}_2$Ø${}_4$）${}_2\cdot$H${}_2$O经历向G型反铁磁阶跃的转变，其磁矩沿 $C$四边形结构的轴。Ti in的估计有序矩从其自旋值抑制为$0.62（3）{\mu }_{乙}$，从而验证了系统内磁性相互作用的二维性质。 $\beta$-KTi（碳${}_2$Ø${}_4$）$ _ 2$2H$另一方面，_2 $ O实现了六边形内Ti矩的三维类钻石形磁网络 $P{6}_{222}$结构体。的反铁磁交换耦合$Ĵ\approx 54$ 从磁力和比热数据中提取K（比in大一个数量级）。 $\beta$-KTi（碳${}_2$Ø${}_4$）$ _ 2$2H$_2 $ O在接受N'eel订购 ${Ť}_{ñ}=28$ K，磁矩在 $\mathrm{一种}b$ 飞机和稍微减少的有序矩 $0.79{\mu }_{乙}$ 每钛${}^{3+}$。通过密度泛函理论计算，我们解决了之间的交换参数差异很大的根源。$\alpha$ 和 $\beta$假多晶型物。考虑到他们观察到的磁行为，我们建议$\alpha$-KTi（碳${}_2$Ø${}_4$）${}_2\cdot$H${}_2$O和 $\beta$-KTi（碳${}_2$Ø${}_4$）$ _ 2$2H$_2 $ O接近理想模型 $\mathrm{小号}=\mathrm{1个}/2$ 海森堡方形和菱形晶格反铁磁体。