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 ($S=\frac{5}{2}$) occupy the nodes of a `trillium' hyperkagome net. We show that this material exhibits a variety of behaviour characteristic of geometric frustration: the 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 $\frac{1}{3}$-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.

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• Evidence for spin liquid behavior in the frustrated three-dimensional $S=1/2$ Heisenberg garnet NaCa${}_2$Cu${}_2$(VO${}_4$)${}_3$
• Spin-Chain Incipient Magnetocaloric Effect and Rare-Earth Controlled Switching in the Haldane-Chain System, R2BaNiO5
• Multistage development of short-range spin correlations and weak magnetic order in the two coupled trillium lattices of K2Fe2(MoO4)(PO4)2