  A combination of variable-temperature neutron scattering, reverse Monte Carlo
analysis and direct Monte Carlo simulation is used to characterise the
emergence of magnetic order in the metal--organic framework (MOF) Tb(HCOO)$_3$
over the temperature range 100 K to 1.6 K $=T_{\rm N}$. We show that the
magnetic transition at $T_{\rm N}$ involves one-dimensional ferromagnetic
ordering to a partially-ordered state related to the triangular Ising
antiferromagnet. In this phase, the direction of magnetisation of ferromagnetic
chains tends to alternate between neighbouring chains but this alternation is
frustrated and is not itself ordered. In neutron scattering measurements this
partial order gives rise to Bragg-like peaks, which cannot be interpreted using
conventional magnetic crystallography without resort to unphysical spin models.
The existence of low-dimensional magnetic order in Tb(HCOO)$_3$ is stabilised
by the contrasting strength of inter- and intra-chain magnetic coupling, itself
a consequence of the underlying MOF architecture. Our results demonstrate how
MOFs may provide an attractive if as yet under-explored platform for the
realisation and investigation of low-dimensional physics.
