Geometric frustration on the trillium lattice in a magnetic metal–organic framework

In the dense metal-organic framework Na[Mn(HCOO)$_3$], Mn$^{2+}$ ions ($S=\frac{5}{2}$) occupy nodes of a `trillium' hyperkagome net. We show that this material exhibits variety behaviour characteristic geometric frustration: N\'eel transition is suppressed well below magnetic interaction strength; short-range order persists far above temperature; and susceptibility pseudo-plateau at $\frac{1}{3}$-saturation magnetisation. demonstrate simple nearest-neighbour Heisenberg antiferromagnet model accounts quantitatively for each observation, hence Na[Mn(HCOO)$_3$] first experimental realisation on trillium develop mapping between two-dimensional Shastry-Sutherland lattice, how both link frustration within classical spin liquid regime to strong magnetocaloric response low fields.