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=5/2) occupy the nodes of a "trillium" net. We show that the system is strongly magnetically frustrated: 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 magnetization. A simple model of nearest-neighbor Heisenberg antiferromagnetic and dipolar interactions accounts quantitatively for all observations, including an unusual 2-k magnetic ground state. We show that the relative strength of dipolar interactions is crucial to selecting this particular ground state. Geometric frustration within the classical spin liquid regime gives rise to a large magnetocaloric response at low applied fields that is degraded in powder samples as a consequence of the anisotropy of dipolar interactions.

A quantum liquid of magnetic octupoles on the pyrochlore lattice.

Spin liquids are highly correlated yet disordered states formed by the entanglement of magnetic dipoles1. Theories define such states using gauge fields and deconfined quasiparticle excitations that emerge from a local constraint governing the ground state of a frustrated magnet. For example, the '2-in-2-out' ice rule for dipole moments on a tetrahedron can lead to a quantum spin ice2-4 in rare-earth pyrochlores. However, f-electron ions often carry multipole degrees of freedom of higher rank than dipoles, leading to intriguing behaviours and 'hidden' orders5-6. Here we show that the correlated ground state of a Ce3+-based pyrochlore, Ce2Sn2O7, is a quantum liquid of magnetic octupoles. Our neutron scattering results are consistent with a fluid-like state where degrees of freedom have a more complex magnetization density than that of magnetic dipoles. The nature and strength of the octupole-octupole couplings, together with the existence of a continuum of excitations attributed to spinons, provides further evidence for a quantum ice of octupoles governed by a '2-plus-2-minus' rule7-8. Our work identifies Ce2Sn2O7 as a unique example of frustrated multipoles forming a 'hidden' topological order, thus generalizing observations on quantum spin liquids to multipolar phases that can support novel types of emergent fields and excitations.

Long-range magnetic order in the porous metal-organic framework Ni(pyrazine)[Pt(CN)4].

A combined study involving DFT calculations, neutron scattering, heat capacity and magnetic measurements at very low temperatures demonstrates the long-range magnetic ordering of Ni(pyrazine)[Pt(CN)4] below 1.9 K, describing its antiferromagnetic spin arrangement. This compound belongs to the family of porous coordination polymers M(pyrazine)[Pt(CN)4] (M = divalent metal), renowned for showing interesting combinations of porosity and magnetic properties. The possibility of including long-range magnetic ordering, one of the most pursued functional properties, opens new perspectives for the multifunctionality of this class of compounds.

Coulomb spin liquid in anion-disordered pyrochlore Tb2Hf2O7.

The charge ordered structure of ions and vacancies characterizing rare-earth pyrochlore oxides serves as a model for the study of geometrically frustrated magnetism. The organization of magnetic ions into networks of corner-sharing tetrahedra gives rise to highly correlated magnetic phases with strong fluctuations, including spin liquids and spin ices. It is an open question how these ground states governed by local rules are affected by disorder. Here we demonstrate in the pyrochlore Tb2Hf2O7, that the vicinity of the disordering transition towards a defective fluorite structure translates into a tunable density of anion Frenkel disorder while cations remain ordered. Quenched random crystal fields and disordered exchange interactions can therefore be introduced into otherwise perfect pyrochlore lattices of magnetic ions. We show that disorder can play a crucial role in preventing long-range magnetic order at low temperatures, and instead induces a strongly fluctuating Coulomb spin liquid with defect-induced frozen magnetic degrees of freedom.Experimental studies of frustrated spin systems such as pyrochlore magnetic oxides test our understanding of quantum many-body physics. Here the authors show experimentally that Tb2Hf2O7 may be a model material for investigating how structural disorder can stabilize a quantum spin liquid phase.

Candidate Quantum Spin Liquid in the Ce3+ Pyrochlore Stannate Ce2Sn2O7.

We report the low-temperature magnetic properties of Ce2Sn2O7, a rare-earth pyrochlore. Our susceptibility and magnetization measurements show that due to the thermal isolation of a Kramers doublet ground state, Ce2Sn2O7 has Ising-like magnetic moments of ∼1.18 µ_{B}. The magnetic moments are confined to the local trigonal axes, as in a spin ice, but the exchange interactions are antiferromagnetic. Below 1 K, the system enters a regime with antiferromagnetic correlations. In contrast to predictions for classical ⟨111⟩-Ising spins on the pyrochlore lattice, there is no sign of long-range ordering down to 0.02 K. Our results suggest that Ce2Sn2O7 features an antiferromagnetic liquid ground state with strong quantum fluctuations.

[Mn(III)(Schiff base)]3[Re(IV)(CN)7], highly anisotropic 3D coordination framework: synthesis, crystal structure, magnetic investigations, and theoretical analysis.

A new highly anisotropic coordination heterobimetallic polymer [Mn(III)(Schiff-base)]3[Re(IV)(CN)7] was synthesized and characterized structurally and magnetically. The single crystal X-ray analysis has revealed that this is the first framework among the complexes composed of homoleptic cyanometallate and Mn(III) complex of the tetradentate Schiff base ligand. A formation of 3D assembly is possible due to both the pentagonal bipyrimidal geometry of the cyanometallate unit and suitable size of constituents: [Re(CN)7](3-) and [Mn(III)(acacen)](+), where acacen = N,N'-ethylenebis(acetylacetoneiminato). The powder and crystal magnetic studies show that the compound undergoes an antiferromagnetic ordering of a complicated character below Neel temperature of 13 K, and exhibits a metamagnetic behavior and strong magnetic anisotropy similar to those observed in related 3D Mn(II)-[Mo(CN)7](4-) systems. Unusual magnetic properties of [Mn(III)(acacen)]3[Re(IV)(CN)7] (1) originate from an interplay of Re-Mn anisotropic spin coupling and ZFS effect of Mn(III) ions with a noncollinear orientation of the local magnetic axes in the cyano-bridged 3D network. A theoretical model of anisotropic spin coupling between orbitally degenerate [Re(IV)(CN)7](3-) complexes and Mn(III) ions is developed, and specific microscopic mechanisms of highly anisotropic spin coupling in Re(IV)-CN-Mn(III) linkages in complex 1 are analyzed in detail.

Highly anisotropic rhenium(IV) complexes: new examples of mononuclear single-molecule magnets.

The rhenium(IV) complex (NBu4)2[ReBr4(ox)] (1) (ox = oxalate and NBu4(+) = tetra-n-butylammonium cation) has been prepared and its crystal structure determined by X-ray diffraction. The structure is made up of discrete [ReBr4(ox)](2-) anions and bulky NBu4(+) cations. Each [ReBr4(ox)](2-) anion is surrounded by six NBu4(+) cations, which preclude any significant intermolecular contact between the anionic entities, the shortest rhenium···rhenium distance being 9.373(1) Å. Variable temperature dc and ac magnetic susceptibility measurements and field-dependent magnetization experiments on polycrystalline samples of 1 reveal the occurrence of highly anisotropic magnetically isolated Re(IV) centers (S(Re) = 3/2), which exhibit slow relaxation of the magnetization at very low temperatures in a dc field. Ac measurements conducted on a polycrystalline sample of the complex (NBu4)2[ReCl4(ox)] (2) [compound isostructural to 1 whose structure and dc magnetic susceptibility study were previously reported in Tomkiewicz, A.; Bartczak, T. J.; Kruszynski, R.; Mrozinski, J. J. Mol. Struct. 2001, 595, 225] show a similar behavior, both complexes thus constituting new examples of mononuclear single-molecule magnets. High-frequency and -field electron paramagnetic resonance on polycrystalline samples of 1 and 2 and on single crystals of 2 allowed for the determination for the first time of the negative sign and confirmed a significant magnitude and rhombicity (E/D) of the zero-field splitting tensor of the [ReCl4(ox)](2-) and [ReBr4(ox)](2-) centers, originating from a combination of spin-orbit coupling and low molecular symmetry. D and E values of 1 and 2 were estimated through magnetization measurements and theoretically calculated through complete active space and density functional theory methodologies.

Rational enantioselective design of chiral heterobimetallic single-chain magnets: synthesis, crystal structures and magnetic properties of oxamato-bridged M(II)Cu(II) chains (M=Mn, Co).

A new series of neutral oxamato-bridged M(II)Cu(II) chiral chains of general formula [MCuL(x)(S)(m)(H(2)O)(n)]·aS·bH(2)O [L(1)=(M)-1,1'-binaphthalene-2,2'-bis(oxamate) with M=Mn (1a) and Co (1b); L(2)=(P)-1,1'-binaphthalene-2,2'-bis(oxamate) with M=Mn (2a) and Co (2b)] and the analogous racemic chains of formula [MCuL(3)(S)(m)(H(2)O)(n)]·aS·bH(2)O [L(3)=1,1'-binaphthalene-2,2'-bis(oxamate) with M=Mn (3a) and Co (3b)] have been prepared by reaction of the corresponding dianionic oxamatocopper(II) complex [Cu(L(x))](2-) with Mn(2+) or Co(2+) cations in either dimethylformamide (DMF) or dimethyl sulfoxide (DMSO). Solid circular dichroism (CD) spectra of the bimetallic chain compounds were recorded to establish their chiral and enantiomeric nature. They exhibit maximum positive and negative Cotton effects, each pair of enantiomeric chains being non-superimposable mirror images. The crystal structures of the Mn(II)Cu(II) (1a-3a) and the Co(II)Cu(II) (1b and 2b) chain compounds were solved by single-crystal X-ray diffraction methods. Our attempts to obtain X-ray quality crystals of 3b were unsuccessful. The values of the shortest interchain Mn···Mn and Co···Co distances are indicative of a good isolation of neighbouring chains in the crystal lattice, which is caused by the bulky aromatic ligand. Although all the Mn(II)Cu(II) and Co(II)Cu(II) chains exhibit ferrimagnetic behaviour (-J(MnCu)=18.9-26.6 cm(-1) and -J(CoCu)=19.5-32.5 cm(-1)), only the enantiopure Co(II)Cu(II) chains (1b and 2b) show slow magnetic relaxation at low temperatures (T(B)=0.6-1.8 K), which is a characteristic of single-chain magnets (SCMs) and is related to the magnetic anisotropy of the high-spin Co(II) ion. Analysis of the SCM behaviour of 1b and 2b, based on Glauber's theory for an Ising one-dimensional system, shows a thermally activated mechanism for the magnetic relaxation (Arrhenius law dependence). The energy barriers (E(a)) to reverse the magnetisation direction are 8.2 (1b) and 8.1cm(-1) (2b), whereas the pre-exponential factor (τ(0)) is 1.9×10(-8) (1b) and 6.0×10(-9) s (2b). Interestingly, the racemic Co(II)Cu(II) chain analogue, 3b, showed no evidence of SCM behaviour.