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Abstract

We report the crystal structures and magnetic properties of two pseudopolymorphs of the $S=1/2 {\mathrm{Ti}}^{3+}$ coordination framework, $\mathrm{K}\mathrm{Ti}{({\mathrm{C}}_{2}{\mathrm{O}}_{4})}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}x{\mathrm{H}}_{2}\mathrm{O}$. Single-crystal x-ray and powder neutron diffraction measurements on $\ensuremath{\alpha}\ensuremath{-}\mathrm{K}\mathrm{Ti}{({\mathrm{C}}_{2}{\mathrm{O}}_{4})}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}x{\mathrm{H}}_{2}\mathrm{O}$ confirm its structure in the tetragonal $I4/mcm$ space group with a square planar arrangement of ${\mathrm{Ti}}^{3+}$ ions. Magnetometry and specific heat measurements reveal weak antiferromagnetic interactions, with ${J}_{1}\ensuremath{\approx}7$ K and ${J}_{2}/{J}_{1}=0.11$ indicating a slight frustration of nearest- and next-nearest-neighbor interactions. Below 1.8 K, $\ensuremath{\alpha}\ensuremath{-}\mathrm{K}\mathrm{Ti}{({\mathrm{C}}_{2}{\mathrm{O}}_{4})}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}x{\mathrm{H}}_{2}\mathrm{O}$ 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 ${\mathrm{Ti}}^{3+}$ in $\ensuremath{\alpha}\ensuremath{-}\mathrm{K}\mathrm{Ti}{({\mathrm{C}}_{2}{\mathrm{O}}_{4})}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}x{\mathrm{H}}_{2}\mathrm{O}$ is suppressed from its spin-only value to $0.62(3)\phantom{\rule{0.28em}{0ex}}{\ensuremath{\mu}}_{B}$, thus verifying the two-dimensional nature of the magnetic interactions within the system. $\ensuremath{\beta}\ensuremath{-}\mathrm{K}\mathrm{Ti}{({\mathrm{C}}_{2}{\mathrm{O}}_{4})}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}2{\mathrm{H}}_{2}\mathrm{O}$, on the other hand, realizes a three-dimensional diamondlike magnetic network of ${\mathrm{Ti}}^{3+}$ moments within a hexagonal $P{6}_{2}22$ structure. An antiferromagnetic exchange coupling of $J\ensuremath{\approx}54$ K---an order of magnitude larger than in $\ensuremath{\alpha}\ensuremath{-}\mathrm{K}\mathrm{Ti}{({\mathrm{C}}_{2}{\mathrm{O}}_{4})}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}x{\mathrm{H}}_{2}\mathrm{O}$---is extracted from magnetometry and specific heat data. $\ensuremath{\beta}\ensuremath{-}\mathrm{K}\mathrm{Ti}{({\mathrm{C}}_{2}{\mathrm{O}}_{4})}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}2{\mathrm{H}}_{2}\mathrm{O}$ 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 $0.79\phantom{\rule{0.28em}{0ex}}{\ensuremath{\mu}}_{B}$ per ${\mathrm{Ti}}^{3+}$. Through density-functional theory calculations, we address the origin of the large difference in the exchange parameters between the $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ pseudopolymorphs. Given their observed magnetic behaviors, we propose $\ensuremath{\alpha}\ensuremath{-}\mathrm{K}\mathrm{Ti}{({\mathrm{C}}_{2}{\mathrm{O}}_{4})}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}x{\mathrm{H}}_{2}\mathrm{O}$ and $\ensuremath{\beta}\ensuremath{-}\mathrm{K}\mathrm{Ti}{({\mathrm{C}}_{2}{\mathrm{O}}_{4})}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}2{\mathrm{H}}_{2}\mathrm{O}$ as close to ideal model $S=1/2$ Heisenberg square and diamond lattice antiferromagnets, respectively.

Topics & Concepts