Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Realising square and diamond lattice $S=1/2$ Heisenberg antiferromagnet
  models in the $\alpha$ and $\beta$ phases of the coordination framework,
  KTi(C$_2$O$_4$)$_2\cdot$\textit{x}H$_2$O   We report the crystal structures and magnetic properties of two
psuedo-polymorphs of the $S=1/2$ Ti$^{3+}$ 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$^{3+}$ ions. Magnetometry and specific heat measurements
reveal weak antiferromagnetic interactions, with $J_1\approx7$ K and
$J_2/J_1=0.11$ indicating a slight frustration of nearest- and
next-nearest-neighbor interactions. Below $1.8$ K, $\alpha$ 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$^{3+}$ in $\alpha$ 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\cdot$2H$_2$O, on the
other hand, realises a three-dimensional diamond-like magnetic network of
Ti$^{3+}$ moments within a hexagonal $P6_222$ structure. An antiferromagnetic
exchange coupling of $J\approx54$ K -- an order of magnitude larger than in
$\alpha$ -- is extracted from magnetometry and specific heat data. $\beta$
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\cdot$2H$_2$O as close to ideal model $S=1/2$
Heisenberg square and diamond lattice antiferromagnets, respectively.

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