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

TL;DR

This study reveals that the metal-organic framework Na[Mn(HCOO)$_3$] exhibits geometric frustration phenomena characteristic of a trillium lattice, with experimental observations well explained by a simple Heisenberg model, linking it to classical spin liquids and magnetocaloric effects.

Contribution

It provides the first experimental realization of a Heisenberg antiferromagnet on the trillium lattice and establishes a mapping to the Shastry-Sutherland model, connecting geometric frustration to magnetocaloric properties.

Findings

Suppressed Néel transition below magnetic interaction strength

Persistent short-range magnetic order above Néel temperature

Pseudo-plateau in magnetic susceptibility at 1/3 saturation

Abstract

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