Odd and Even Numbered Ferric Wheels.

The structurally related odd and even numbered wheels [FeIII 11 ZnII 4 (tea)10 (teaH)1 (OMe)Cl8 ] (1) and [FeIII 12 ZnII 4 (tea)12 Cl8 ] (2) can be synthesized under ambient conditions by reacting FeIII and ZnII salts with triethanolamine (teaH3 ), the change in nuclearity being dictated by the solvents employed. An antiferromagnetic exchange between nearest neighbors, J = -10.0 cm-1 for 1 and J = -12.0 cm-1 for 2, leads to a frustrated S = 1/2 ground state in the former and an S = 0 ground state in the latter.

Fe-Gd Ferromagnetic Cyclic Coordination Cluster [FeIII4GdIII4(teaH)8(N3)8(H2O)] with Magnetic Anisotropy─Theory and Experiment.

The synthesis, structural, and magnetic characterization of [FeIII4LnIII4(teaH)8(N3)8(H2O)] (Ln = Gd and Y) and the previously reported isostructural Dy analogue are discussed. The commonly held belief that both FeIII and GdIII can be regarded as isotropic ions is shown to be an oversimplification. This conclusion is derived from the magnetic data for the YIII analogue in terms of the zero-field splitting seen for FeIII and from the fact that the magnetic data for the new GdIII analogue can only be fit employing an additional anisotropy term for the GdIII ions. Furthermore, the Fe4Gd4 ring shows slow relaxation of magnetization. Our analysis of the experimental magnetic data employs both density functional theory as well as the finite-temperature Lanczos method which finally enables us to provide an almost perfect fit of magnetocaloric properties.

A {Gd12Na6} Molecular Quadruple-Wheel with a Record Magnetocaloric Effect at Low Magnetic Fields and Temperatures.

Reaction of Gd(OAc)3·4H2O, salicylaldehyde and CH3ONa in MeCN/MeOH affords [Gd12Na6(OAc)25(HCO2)5(CO3)6(H2O)12]·9H2O.0.5MeCN (1·9H2O.0.5MeCN), whose structure describes a quadruple-wheel consisting of two {Na3} and two {Gd6} rings. The magnetic properties of 1 reveal very weak antiferromagnetic interactions between the GdIII ions, which give rise to a record magnetocaloric effect at low applied magnetic fields and low temperatures. The magnetic entropy change reaches -ΔSm= 29.3 J kg-1 K-1 for full demagnetization from B = 1 T at T = 0.5 K.

Templating metallocycles with a macrocycle: synthesis, structures and magnetic studies of {Cr11M2} complexes.

Addition of 1,4,8,11-tetrazacyclotetradecane (cyclam) to a reaction that produces octametallic rings when simpler amines are used, produces {Cr11M2} "pretzels" (M = ZnII or CuII) where the cyclam coordinates to the MII ion which then sits at the centre of a twelve-metal macrocycle. Magnetic studies were fitted using the finite-temperature Lanczos method (FTLM), and the results demonstrate that exchange interactions are transferable from previous exchange-coupled CrIII rings.

A graceful break-up: serendipitous self-assembly of a ferromagnetically coupled [NiII14] wheel.

The complex [NiII14(HL2)12(HCOO)14Cl14(MeOH)(H2O)] describes an aesthetically pleasing wheel displaying ferromagnetic nearest neighbour exchange.

Investigation of electron-induced cross-linking of self-assembled monolayers by scanning tunneling microscopy.

Ultrathin membranes with subnanometer pores enabling molecular size-selective separation were generated on surfaces via electron-induced cross-linking of self-assembled monolayers (SAMs). The evolution of p-terphenylthiol (TPT) SAMs on Au(111) surfaces into cross-linked monolayers was observed with a scanning tunneling microscope. As the irradiation dose was increased, the cross-linked regions continued to grow and a large number of subnanometer voids appeared. Their equivalent diameter is 0.5 ± 0.2 nm and the areal density is ≈1.7 × 1017 m-2. Supported by classical molecular dynamics simulations, we propose that these voids may correspond to free volumes inside a cross-linked monolayer.

An [FeIII8] molecular oxyhydroxide.

An [FeIII8] hexagonal bipyramid displays antiferromagnetic exchange between the two capping tetrahedral ions and the six ring octahedral ions resulting in a spin ground state of S = 10.

An [FeIII30] molecular metal oxide.

Dissolution of FeBr3 in a mixture of acetonitrile and 3,4-lutidine in the presence of an amine results in the formation of an [Fe30] molecular metal oxide containing alternating layers of tetrahedral and octahedral FeIII ions. Mass spectrometry suggests the cluster is formed quickly and remains stable in solution, while magnetic measurements and DFT calculations reveal competing antiferromagnetic exchange interactions.

[Fe15]: a frustrated, centred tetrakis hexahedron.

The combination of two different FeIII salts in a solvothermal reaction with triethanolamine results in the formation of a high symmetry [FeIII15] cluster whose structure conforms to a centred, tetrakis hexahedron.

Rational Design of a Confacial Pentaoctahedron: Anisotropic Exchange in a Linear ZnII FeIII FeIII FeIII ZnII Complex.

The first confacial pentaoctahedron comprised of transition metal ions namely ZnII FeIII A FeIII B FeIII A ZnII has been synthesized by using a dinucleating nonadentate ligand. The face-sharing bridging mode enforces short ZnII ⋅⋅⋅FeIII A and FeIII A ⋅⋅⋅FeIII B distances of 2.83 and 2.72 Å, respectively. Ab-initio CASSCF/NEVPT2 calculations provide significant negative zero-field splittings for FeIII A and FeIII B with |DA |>|DB | with the main component along the C3 axis. Hence, a spin-Hamiltonian comprised of anisotropic exchange, zero-field, and Zeeman term was employed. This allowed by following the boundary conditions from the theoretical results the simulation in a theory-guided parameter determination with Jxy =+0.37, Jz =-0.32, DA =-1.21, EA =-0.24, DB =-0.35, and EB =-0.01 cm-1 supported by simulations of high-field magnetic Mössbauer spectra recorded at 2 K. The weak but ferromagnetic FeIII A FeIII B interaction arises from the small bridging angle of 84.8° being at the switch from anti- to ferromagnetic for the face-sharing bridging mode.

NiII 36 -Containing 54-Tungsto-6-Silicate: Synthesis, Structure, Magnetic and Electrochemical Studies.

The 36-NiII -containing 54-tungsto-6-silicate, [Ni36 (OH)18 (H2 O)36 (SiW9 O34 )6 ]6- (Ni36 ) was synthesized by a simple one-pot reaction of the Ni2 -pivalate complex [Ni2 (µ-OH2 )(O2 CCMe3 )4 (HO2 CCMe3 )4 ] with the trilacunary [SiW9 O34 ]10- polyanion precursor in water and structurally characterized by a multitude of physicochemical techniques including single-crystal XRD, FTIR, TGA, elemental analysis, magnetic and electrochemical studies. Polyanion Ni36 comprises six equivalent {NiII 6 SiW9 } units which are linked by Ni-O-W bridges forming a macrocyclic assembly. Magnetic studies demonstrate that the {Ni6 } building blocks in Ni36 remain magnetically intact while forming a hexagonal ring with antiferromagnetic exchange interactions between adjacent {Ni6 } units. Electrochemical studies indicate that the first reduction is reversible and associated with the WVI/V couple, whereas the second reduction is irreversible attributed to the NiII/0 couple.

The Synthesis and Characterisation of a Molecular Sea-Serpent: Studies of a {Cr24 Cu7 } Chain.

A finite chain of thirty-one paramagnetic centers is reported, synthesized by reaction of hydrated chromium fluoride, copper carbonate and pivalic acid in the presence of 1,4,7,10-tetrazacyclododecane (cyclen). Magnetic studies show predominantly anti-ferromagnetic exchange leading to a high density of low-lying spin states and large saturation field.

Magnon Crystallization in the Kagome Lattice Antiferromagnet.

We present numerical evidence for the crystallization of magnons below the saturation field at nonzero temperatures for the highly frustrated spin-half kagome Heisenberg antiferromagnet. This phenomenon can be traced back to the existence of independent localized magnons or, equivalently, flatband multimagnon states. We present a loop-gas description of these localized magnons and a phase diagram of this transition, thus providing information for which magnetic fields and temperatures magnon crystallization can be observed experimentally. The emergence of a finite-temperature continuous transition to a magnon crystal is expected to be generic for spin models in dimension D>1 where flatband multimagnon ground states break translational symmetry.

Inorganic Approach to Stabilizing Nanoscale Toroidicity in a Tetraicosanuclear Fe18Dy6 Single Molecule Magnet.

Cyclic coordination clusters (CCCs) are proving to provide an extra dimension in terms of exotic magnetic behavior as a result of their finite but cyclized chain structures. The Fe18Dy6 CCC is a Single Molecule Magnet with the highest nuclearity among Ln containing clusters. The three isostructural compounds [Fe18Ln6(µ-OH)6(ampd)12(Hampd)12(PhCO2)24](NO3)6·38MeCN for Ln = DyIII (1), LuIII (2), or YIII (3), where H2ampd = 2-amino-2-methyl-1,3-propanediol, are reported. These can be described in terms of the cyclization of six {Fe3Ln(µOH)(ampd)2(Hampd)2(PhCO2)4}+ units with six nitrate counterions to give the neutral cluster. The overall structure consists of two giant Dy3 triangles sandwiching a strongly antiferromagnetically coupled Fe18 ring, leading to a toroidal arrangement of the anisotropy axis of the Dy ions, making this the biggest toroidal arrangement on a molecular level known so far.

Periodic thermodynamics of the Rabi model with circular polarization for arbitrary spin quantum numbers.

We consider a spin s subjected to both a static and an orthogonally applied oscillating, circularly polarized magnetic field while being coupled to a heat bath and analytically determine the quasistationary distribution of its Floquet-state occupation probabilities for arbitrarily strong driving. This distribution is shown to be Boltzmannian with a quasitemperature which is different from the temperature of the bath and independent of the spin quantum number. We discover a remarkable formal analogy between the quasithermal magnetism of the nonequilibrium steady state of a driven ideal paramagnetic material and the usual thermal paramagnetism. Nonetheless, the response of such a material to the combined fields is predicted to show several unexpected features, even allowing one to turn a paramagnet into a diamagnet under strong driving. Thus, we argue that experimental measurements of this response may provide key paradigms for the emerging field of periodic thermodynamics.

An [FeIII 34 ] Molecular Metal Oxide.

The dissolution of anhydrous iron bromide in a mixture of pyridine and acetonitrile, in the presence of an organic amine, results in the formation of an [Fe34 ] metal oxide molecule, structurally characterised by alternate layers of tetrahedral and octahedral FeIII ions connected by oxide and hydroxide ions. The outer shell of the complex is capped by a combination of pyridine molecules and bromide ions. Magnetic data, measured at temperatures as low as 0.4 K and fields up to 35 T, reveal competing antiferromagnetic exchange interactions; DFT calculations showing that the magnitudes of the coupling constants are highly dependent on both the Fe-O-Fe angles and Fe-O distances. The simplicity of the synthetic methodology, and the structural similarity between [Fe34 ], bulk iron oxides, previous FeIII -oxo cages, and polyoxometalates (POMs), hints that much larger molecular FeIII oxides can be made.

Local entanglement and string order parameter in dimerized models.

In this letter, we propose an application of string order parameter (SOP), commonly used in quantum spin systems, to identify symmetry-protected topological phase (SPT) in fermionic systems in the example of the dimerized fermionic chain. As a generalized form of dimerized model, we consider a one-dimensional spin-1/2 XX model with alternating spin couplings. We employ Jordan-Wigner fermionization to map this model to the spinless Su-Schrieffer-Heeger fermionic model (SSH) with generalized hopping signs. We demonstrate a phase transition between a trivial insulating phase and the Haldane phase by the exact analytical evaluation of reconstructed SOPs which are represented as determinants of Toeplitz matrices with the given generating functions. To get more insight into the topological quantum phase transition (tQPT) and microscopic correlations, we study the pairwise concurrence as a local entanglement measure of the model. We show that the first derivative of the concurrence has a non-analytic behaviour in the vicinity of the tQPT, like in the second order trivial QPTs.

Rational Improvement of Single-Molecule Magnets by Enforcing Ferromagnetic Interactions.

The anisotropy barrier of polynuclear single-molecule magnets is expected to be higher with less tunneling the better stabilized the spin ground state is so that less MS mixing in the ground state and with excited spin states occur. We have realized this experimentally in two structurally related heptanuclear SMMs: the triplesalen-based [MnIII 6 CrIII ]3+ and the triplesalalen-based *[MnIII 6 CrIII ]3+ . The ligand system triplesalen was developed to enforce ferromagnetic interactions by the spin-polarization mechanism. However, we found weak antiferromagnetic couplings, that we assigned to an inefficient spin-polarization by a heteroradialene formation. To prevent this heteroradialene formation, the triplesalalen ligand H6 talalen t Bu 2 was designed. Here, we present the building block [(talalen t Bu 2 )MnIII 3 ]3+ and its application for the assembly of [{(talalen t Bu 2 )MnIII 3 }2 {CrIII (CN)6 }]3+ (=*[MnIII 6 CrIII ]3+ ). Both the trinuclear and heptanuclear complexes are SMMs. The comparison to the related triplesalen complex [(feld t Bu 2 )MnIII 3 ]3+ proves the absence of heteroradialene character and the enforcement of ferromagnetic MnIII -MnIII interactions in the (talalen t Bu 2 )6- complexes. This results in an increase of the barrier for spin reversal Ueff from 25 K in the triplesalen-based [MnIII 6 CrIII ]3+ SMMs to 37 K in the triplesalalen-based *[MnIII 6 CrIII ]3+ SMM proving the success of our concept. Based on this study, the next step in the rational improvement of our SMMs is discussed.

Order in disorder: solution and solid-state studies of [MM] wheels (MIII = Cr, Al; MII = Ni, Zn).

A family of heterometallic Anderson-type 'wheels' of general formula [MIII2MII5(hmp)12](ClO4)4 (where MIII = Cr or Al and MII = Ni or Zn giving [Cr2Ni5] (1), [Cr2Zn5] (2), [Al2Ni5] (3) and [Al2Zn5] (4); hmpH = 2-pyridinemethanol) have been synthesised solvothermally. The metallic skeleton common to all structures describes a centred hexagon with the MIII sites disordered around the outer wheel. The structural disorder has been characterised via single crystal X-ray crystallography, 1-3D 1H and 13C solution-state NMR spectroscopy of the diamagnetic analogue (4), and solid-state 27Al MAS NMR spectroscopy of compounds (3) and (4). Alongside ESI mass spectrometry, these techniques show that structure is retained in solution, and that the disorder is present in both the solution and solid-state. Solid-state dc susceptibility and magnetisation measurements on (2) and (3) reveal the Cr-Cr and Ni-Ni exchange interactions to be JCr-Cr = -1 cm-1 and JNi-Ni,r = -5 cm-1, JNi-Ni,c = 10 cm-1. Fixing these values allows us to extract JCr-Ni,r = -1.2 cm-1, JCr-Ni,c = 2.6 cm-1 for (1), the exchange between adjacent Ni and Cr ions on the ring is antiferromagnetic and between Cr ions on the ring and the central Ni ion is ferromagnetic.

Suppression of Magnetic Quantum Tunneling in a Chiral Single-Molecule Magnet by Ferromagnetic Interactions.

Single-molecule magnets (SMMs) retain a magnetization without applied magnetic field for a decent time due to an energy barrier U for spin-reversal. Despite the success to increase U, the difficult to control magnetic quantum tunneling often leads to a decreased effective barrier Ueff and a fast relaxation. Here, we demonstrate the influence of the exchange coupling on the tunneling probability in two heptanuclear SMMs hosting the same spin-system with the same high spin ground state St = 21/2. A chirality-induced symmetry reduction leads to a switch of the MnIII-MnIII exchange from antiferromagnetic in the achiral SMM [MnIII6CrIII]3+ to ferromagnetic in the new chiral SMM RR[MnIII6CrIII]3+. Multispin Hamiltonian analysis by full-matrix diagonalization demonstrates that the ferromagnetic interactions in RR[MnIII6CrIII]3+ enforce a well-defined St = 21/2 ground state with substantially less mixing of MS substates in contrast to [MnIII6CrIII]3+ and no tunneling pathways below the top of the energy barrier. This is experimentally verified as Ueff is smaller than the calculated energy barrier U in [MnIII6CrIII]3+ due to tunneling pathways, whereas Ueff equals U in RR[MnIII6CrIII]3+ demonstrating the absence of quantum tunneling.