One-dimensional magnetic order in the metal-organic framework Tb(HCOO)3

Abstract

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 = TN. We show that the magnetic transition at TN 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.Low-dimensional magnets have long provided an important playground for the discovery and exploitation of unconventional physics [1]-from the earliest studies of soliton excitations in CsNiF 3 [2-4] to contemporary research into quantum information transport in spin-chain compounds [5]. The sensitivity of low-dimensional spin systems to small perturbations results in a rich diversity of phase transitions and complex ordering phenomena. By way of example, the Ising spin-chain compound Ca 3 Co 2 O 6 exhibits a variety of equilibrium and non-equilibrium states [6][7][8], characterised by e.g. long-wavelength incommensurate spin density modulations and field-induced magnetisation plateaux reminiscent of Hofstadter fractalisation [9,10]. In the field of low-dimensional magnetism, arguably the strongest scientific interest from both experimental and theoretical perspectives has always been in the limit of strict 1D order [11][12][13][14][15][16]. Yet even in canonical systems such as Ca 3 Co 2 O 6 the divergence of correlation lengths along 1D spin chains is always accompanied by full 3D magnetic order [8,17]. So the realisation and experimental characterisation of genuine partially-ordered low-dimensional spin states remain an important challenge in the field.It was in this context that we chose to study magnetic order in terbium(III) formate, Tb(HCOO) 3 . In metal-organic frameworks (MOFs) such as Tb(HCOO) 3 , magneticallyactive transition-metal or rare-earth ions are connected via organic ligands to form extended 3D framework structures. Because organic ligands can support superexchange interactions that span a broad energy range, and because framework design allows controlled incorporation of low-dimensional structural motifs (e.g. chains, ladders, layers), MOFs are natural candidate hosts for low-dimensional magnetism [18]. Indeed the magnetic response of...

Emergent magnetic order and correlated disorder in formate metal-organic frameworks

“…Using ISODISTORT [51] we have determined the commensurate structure can be described in the P m ′ space group in which there are six independent Tb sites with moments dependant on the global phase, with the lattice parameters a = 3.96860 13 The solution with global phase π/4 results in a modification of the PDA structure in which the k 2 propagation modulates the moment in the chains resulting in couples of large moment Tb chains (±7.68(3) µ B and ±6.19(3) µ B ) anti-ferromagnetically coupled separated by chain with a small moment (±0.74(3) µ B ). For the high temperature magnetic structure this phase choice gives a partially disordered antiferromagnet solution closest to the TIA model proposed, [44] and therefore is our preferred model. The π/6 solution, is a slight modification of the up This is analogous to the emergent charge order observed in the kagome ECO states, [17,52] which has two observed experimental signatures; non-zero entropy and the presence of magnetic diffuse and Bragg-like peaks in the neutron diffraction measurements.…”

“…As reported previously both of these can thought of as conventional crystallographic approximations of the TIA, which only has long range 1D order in the chains. [44] Patterns collected below 1.2 K revealed the presence of additional diffuse reflections at high dspace, the most significant Bragg-like peak can be seen at ≈10.5 Å. The broad nature of these features, comparable to those associated with the TIA phase and the retention of the diffuse suggest these are associated with a state that lacks conventional crystallographic order.…”

“…A clearer transition can be seen at ≈0.5 K indicating more complete, possibly long-range antiferromagnetic order. [9,44] A second large change in the heat capacity is observed below 600 mK, this may be the onset of long-range order but could also be the onset of a hyperfine Schottky anomaly. The interesting physical and magnetic measurements encouraged further investigation, so we have therefore performed neutron diffraction measurements in zero-field of the Ln(DCO 2 ) 3 frameworks.…”

“…[43] Tb(DCO 2 ) 3 is an excellent example of a magnetic MOF with interesting properties at low temperatures and a physical realisation of a stacked triangular lattice, forming chains of Tb ions (Figure 4). The material perfectly combines frustration and 1D magnetic order, [44] making it the ideal model for the triangular lattice with equivalent J coupling between Tb ions, through the formate ligand. The MOF examples discussed so far all have 3D ordered ground states but, for this Ising antiferromagnetic compound, the situation appears to be different.…”

“…The lack of long range 3D order appears to be suppressed by the frustrated interactions between chains leading to the emergence of a triangular Ising antiferromagnetic (TIA) state, with a large number of degenerate ground states. [44] The ferromagnetic correlations and antiferromagnetic frustration that persists, in the paramagnetic state, allow for high entropy changes in small applied magnetic fields contributing to a high efficiency as a magnetocaloric. [9] This dominant ferromagnetic intrachain coupling allow the moments to be more easily aligned with the applied field.…”