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

Abstract

In the dense metal-organic framework Na[Mn(HCOO)3], Mn 2+ ions (S = 52 ) occupy the nodes of a 'trillium' hyperkagome net. We show that this material exhibits a variety of behaviour characteristic of geometric frustration: the Néel transition is suppressed well below the characteristic magnetic interaction strength; short-range magnetic order persists far above the Néel temperature; and the magnetic susceptibility exhibits a pseudo-plateau at 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.