Possible spin-Peierls transition in La2RuO5

The semiconductor–semiconductor transition of La₂RuO₅ is studied by means of augmented spherical wave (ASW) electronic structure calculations as based on density functional theory and the local density approximation. This transition has lately been reported to lead to orbital ordering and a quenching of the local spin magnetic moment. Our results give strong hints for a different orbital ordering scenario than the one previously proposed. In our type of ordering the local S = 1 moment at the Ru sites is preserved in the low-temperature phase. The unusual magnetic behaviour is interpreted by the formation of spin ladders resulting from the structural transformations occurring at the transition. The spin ladders are characterized by antiferromagnetic coupling along the rungs. The loss of the total spin moment is attributed to a spin-Peierls transition.     

Vom einfachen Komplex zum komplexen Gitter: Metallo‐supramolekulare Chemie

Supramolecular structures and metal‐complexes play a dominant role in the functionality of biomolecules. Taking nature as an example a major goal of metallo‐supramolecular chemistry is the extension of the traditional coordination chemistry towards supramolecular architectures, utilizing complex ligand systems. Herein we describe a wide range of different geometries such as helicates, linear rod‐like polymers, ladders, racks or grids, which are realized by the combination of supramolecular ligands and coordinating metal ions on the basis of self‐assembly and self‐recognition processes. Besides the pure beauty of the structures, the electro‐, photochemical and magnetic properties of the materials might open avenues to applications as smart coatings, catalysts or optical devices.     

Constructing single-chain magnets by supramolecular π-π stacking and spin canting: a case study on manganese(III) corroles

A single‐chain magnet (SCM) was constructed from manganese(III) 5,10,15‐tris(pentafluorophenyl)corrole complex [Mn^III(tpfc)] through supramolecular π–π stacking without bridging ligands. In the crystal structures, [Mn(tpfc)] molecules crystallized from different solvents, such as methanol, ethyl acetate, and ethanol, exhibit different molecular orientations and intermolecular π–π interaction or weak Mn ??? O interaction to form a supramolecular one‐dimensional motif or dimer. These three complexes show very different magnetic behaviors at low temperature. Methanol solvate 1 shows obvious frequency dependence of out‐of‐phase alternating‐current magnetic susceptibility below 2 K and a magnetization hysteresis loop with a coercive field of 400 Oe at 0.5 K. It is the first example of spin‐canted supramolecular single‐chain magnet due to weak π–π stacking interaction. By fitting the susceptibility data χ_MT (20–300 K) of 1 with the spin Hamiltonian expression ${\overrightarrow{H}}A single-chain magnet (SCM) was constructed from manganese(III) 5,10,15-tris(pentafluorophenyl)corrole complex [Mn(III) (tpfc)] through supramolecular π-π stacking without bridging ligands. In the crystal structures, [Mn(tpfc)] molecules crystallized from different solvents, such as methanol, ethyl acetate, and ethanol, exhibit different molecular orientations and intermolecular π-π interaction or weak Mn???O interaction to form a supramolecular one-dimensional motif or dimer. These three complexes show very different magnetic behaviors at low temperature. Methanol solvate 1 shows obvious frequency dependence of out-of-phase alternating-current magnetic susceptibility below 2?K and a magnetization hysteresis loop with a coercive field of 400?Oe at 0.5?K. It is the first example of spin-canted supramolecular single-chain magnet due to weak π-π stacking interaction. By fitting the susceptibility data χ(M) T (20-300?K) of 1 with the spin Hamiltonian expression H = -2J Σ(i=1)(n-1) S(Ai) S(Ai+1) + D Σ(i) S((iZ)(2)), the intrachain magnetic coupling parameter transmitted by π-π interaction of -0.31?cm(-1) and zero field splitting parameter D of -2.59?cm(-1) are obtained. Ethyl acetate solvate 2 behaves as an antiferromagnetic chain without ordering or slow magnetic relaxation down to 0.5?K. The magnetic susceptibility data χ(M) T (20-300?K) of 2 was fitted by assuming the spin Hamiltonian H = -2JΣ(i=1)(n-1) S(Ai) S(Ai+1), and the intrachain antiferromagnetic coupling constant of -0.07?cm(-1) is much weaker than that of 1. Ethanol solvate 3 with a dimer motif shows field-induced single-molecule magnet like behavior below 2.5?K. The exchange coupling constant J within the dimer propagated by π-π interaction is -0.14?cm(-1) by fitting the susceptibility data χ(M) T (20-300?K) with the spin Hamiltonian H = -2J S(A) S(B) + β(S((A)g(A)) + S((B)g(B)))H. The present studies open a new way to construct SCMs from anisotropic magnetic single-ion units through weak intermolecular interactions in the absence of bridging ligands.     

Computer simulation of quantum dynamics in a classical spin environment

In this paper, a formalism for studying the dynamics of quantum systems coupled to classical spin environments is reviewed. The theory is based on generalized antisymmetric brackets and naturally predicts open-path off-diagonal geometric phases in the evolution of the density matrix. It is shown that such geometric phases must also be considered in the quantum–classical Liouville equation for a classical bath with canonical phase space coordinates; this occurs whenever the adiabatics basis is complex (as in the case of a magnetic field coupled to the quantum subsystem). When the quantum subsystem is weakly coupled to the spin environment, non-adiabatic transitions can be neglected and one can construct an effective non-Markovian computer simulation scheme for open quantum system dynamics in classical spin environments. In order to tackle this case, integration algorithms based on the symmetric Trotter factorization of the classical-like spin propagator are derived. Such algorithms are applied to a model comprising a quantum two-level system coupled to a single classical spin in an external magnetic field. Starting from an excited state, the population difference and the coherences of this two-state model are simulated in time while the dynamics of the classical spin is monitored in detail. It is the author’s opinion that the numerical evidence provided in this paper is a first step toward developing the simulation of quantum dynamics in classical spin environments into an effective tool. In turn, the ability to simulate such a dynamics can have a positive impact on various fields, among which, for example, nanoscience.     

Sapphyrin Supramolecules through C−H⋅⋅⋅S and C−H⋅⋅⋅Se Hydrogen Bonds—First Structural Characterization of meso- Arylsapphyrins Bearing Heteroatoms

An unprecedented coupling reaction of heteroatom-containing tripyrranes leads to the formation of core-modified sapphyrins 1 and 2 , which self-assemble in the solid state to form supramolecular ladders. Weak C−H⋅⋅⋅S and C−H⋅⋅⋅Se hydrogen-bonding interactions in addition to C−H⋅⋅⋅N hydrogen bonds are responsible for the observed structures.     

Spin relaxation in isolated molecules and clusters: the interpretation of Stern-Gerlach experiments

Intramolecular spin relaxation may occur in isolated molecules or clusters provided that the density of rovibrational eigenstates is sufficiently high to serve as an energy bath and angular momentum is conserved. In the coupled, zero-field limit, total angular momentum (J) is the sum of spin (S) and rotational (N) momenta such that J and M(J) are good angular momentum quantum numbers. In the coupled limit, transitions between Zeeman levels (Delta M(J)++0) cannot occur in the absence of an external torque. However, in the high-field limit, J and M(J) are no longer good quantum numbers, as N and S are decoupled and only their projections on the z axis defined by the external field are invariant. In this case M(N) and M(S) remain as good quantum numbers so that angular momentum conserving transitions can occur subject to the selection rule Delta M(N)=-Delta M(S). Determination of the magnetic moments of isolated molecules and clusters via a thermodynamics-based analysis requires that their magnetizations are measured at sufficiently large fields that spin-rotation effects become negligible and the Zeeman level structure approaches the free-spin case.     

Design of molecular ferromagnets

A large variety of molecular ferromagnets have been synthesized since the discovery of the first organic ferromagnets, including pure organic compounds, organometallic charge-transfer complexes, metal complex-organic radical compounds, and transition metal complexes coupled to organic radicals. Besides, there are many reports on the observation of ferromagnetism in polymers and organic matrix composites. Molecular ferromagnets have great potential in different areas of technology such as low frequency magnetic shielding, magnetic imaging, magneto-optics and information storage. We provide a brief review on the current strategies for the design of molecular (organic) ferromagnets. This includes exploiting the inherent advantages of molecular systems, such as the ability to fine-tune the properties at the molecular level, and to control dimensionality, supramolecular structuring and hierarchy of spin interactions etc. for carrying out structural modifications and chemical functionalisations of stable open-shell molecules in order to generate supramolecular structures in which the natural prediction for antiparallel spin alignment (antiferromagnetism) is avoided.     

Spin-Phonon Coupling and Slow-Magnetic Relaxation in Pristine Ferrocenium

We report the spin dynamic properties of non-substituted ferrocenium complexes. Ferrocenium shows a field-induced single-molecule magnet behaviour in DMF solution while cobaltocene lacks slow spin relaxation neither in powder nor in solution. Multireference quantum mechanical calculations give a non-Aufbau orbital occupation for ferrocenium with small first excitation energy that agrees with the relatively large measured magnetic anisotropy for a transition metal S=1/2 system. The analysis of the spin relaxation shows an important participation of quantum tunnelling, Raman, direct and local-mode mechanisms which depend on temperature and the external field conditions. The calculation of spin-phonon coupling constants for the vibrational modes shows that the first vibrational mode, despite having a low spin-phonon constant, is the most efficient process for the spin relaxation at low temperatures. In such conditions, vibrational modes with higher spin-phonon coupling constants are not populated. Additionally, the vibrational energy of this first mode is in excellent agreement with the experimental fitted value obtained from the local-mode mechanism.     

Targeting molecular quantum memory with embedded error correction

The implementation of a quantum computer requires both to protect information from environmental noise and to implement quantum operations efficiently. Achieving this by a fully fault-tolerant platform, in which quantum gates are implemented within quantum-error corrected units, poses stringent requirements on the coherence and control of such hardware. A more feasible architecture could consist of connected memories, that support error-correction by enhancing coherence, and processing units, that ensure fast manipulations. We present here a supramolecular {Cr₇Ni}–Cu system which could form the elementary unit of this platform, where the electronic spin 1/2 of {Cr₇Ni} provides the processor and the naturally isolated nuclear spin 3/2 of the Cu ion is used to encode a logical unit with embedded quantum error-correction. We demonstrate by realistic simulations that microwave pulses allow us to rapidly implement gates on the processor and to swap information between the processor and the quantum memory. By combining the storage into the Cu nuclear spin with quantum error correction, information can be protected for times much longer than the processor coherence.

The implementation of a quantum computer requires protecting of information from noise and the ability to perform quantum gates. We present a molecular architecture providing both these ingredients, via an electronic spin 1/2 processor and a nuclear spin 3/2 memory.     

The mixed-valent manganese [3 x 3] grid [Mn(III)4Mn(II)5(2poap-2H)6](ClO4)10.10 H2O, a mesoscopic spin-1/2 cluster

The magnetic susceptibility and low-temperature magnetization curve of the [3 x 3] grid [Mn(III)4Mn(II)5(2poap-2H)6](ClO4)10.10 H2O (1) are analyzed within a spin Hamiltonian approach. The Hilbert space is huge (4,860,000 states), but the consequent use of all symmetries and a two-step fitting procedure nevertheless allows the best-fit determination of the magnetic exchange parameters in this system from complete quantum mechanical calculations. The cluster exhibits a total spin S = 1/2 ground state; the implications are discussed.     

Spin coupling in the supramolecular structure of a new tetra(quinoline-TEMPO)yttrium(III) complex

The newly synthesized tetra(quinoline-TEMPO)yttrium(III) potassium salt shows interesting structural features at the molecular and supramolecular levels, revealed by the analysis of the X-ray diffraction data. The magnetic susceptibility and EPR data corroborated with structural considerations showed that the exchange and dipolar spin coupling interactions are taking place at the nodes assembling the supramolecular 2D structure. The Y(III) center shows antiprismatic octacoordination, close to the idealized D2 symmetry. The diamagnetic transition metal plays no role in mediating the radical interactions since the TEMPO-type fragments are remote from the chelating moieties of the ligand. In turn, significant interaction occurs on the nodes consisting in the quasi-rectangular coordination of potassium counterions by the spin-bearing TEMPO groups coming from four distinct complex units. The antiferromagnetic susceptibility was consistently modeled by a spin Hamiltonian based on the rectangle topology of four spins S = 1/2. The fitted exchange parameters are Ja = -5.1 cm-1 and Jb = -3.4 cm-1 for the edges, imposing Jd = 0 for the diagonal. These values are in excellent agreement with the ab initio results Ja = -4.83 cm-1, Jb = -3.44 cm-1, Jd = -0.07 cm-1 obtained in a CASSCF(12,8) calculation. Based on the reliability of the ab initio results we were able to select the presented J parameters among several versions of multiple solutions with acceptable goodness of the fit. A methodological caveat about the artifacts of the automatic use of best fit parameters, in the absence of supplementary criteria, in the context of relative blindness of magnetic susceptibility modeling, is raised. The details of the EPR spectrum at 10 K are also consistent, in the frame of dipolar approximation, with the model of four interacting spins at the nodes of the supramolecular assembling.     

An S = 6 cyanide-bridged octanuclear FeIII4NiII4 complex that exhibits slow relaxation of the magnetization

The synthesis and structural and magnetic characterization of an S = 6 cyanide-bridged octanuclear FeIII4NiII4 (1) complex is described. Ac susceptibility and mu-SQUID measurements suggest that fast magnetization relaxation is present in zero-field due to quantum tunneling of the ground spin state (QTM) while application of small magnetic fields induces slow relaxation of the magnetization.     

Effects of the covalent linker groups on the spin transport properties of single nickelocene molecules attached to single-walled carbon nanotubes

The understanding of how the spin moment of a magnetic molecule transfers to a carbon nanotube, when the molecule is attached to it, is crucial for designing novel supramolecular spin devices. Here we explore such an issue by modeling the spin transport of a single-walled carbon nanotube grafted with one nickelocene molecule. In particular we investigate how the electron transport becomes spin-polarized depending on the specific linking group bonding nickelocene to the nanotube. We consider as linkers both aziridine and pyrrolidine rings and the amide group. Our calculations show that, at variance with aziridine, both pyrrolidine and amide, do alter the sp(2) character of the binding site of the nanotube and thus affect the transmission around the Fermi level. However, only aziridine allows transferring the spin polarization of the nickelocene to the nanotube, whose conductance at the Fermi level becomes spin-polarized. This suggests the superiority of aziridine as a linker for grafting magnetic molecules onto carbon nanotubes with efficient spin filtering functionality.     

A supramolecular spin crossover Fe(III) complex and its Cr(III) isomer: stabilization of water-chloride cluster within supramolecular host

The metal complexes, [M(Hdammthiol)(2)]Cl·3H(2)O [M = Cr(III) (1), Fe(III) (2)] [where H(2)dammthiol is the thiol form of the ligand, diacetylmonoxime morpholine N-thiohydrazone] were synthesized by metal template reactions of diacetylemonoxime with morpholine N-thiohydrazide in the presence of CrCl(3)·6H(2)O and FeCl(3)·6H(2)O. Both the complexes (1 and 2) were characterized by single crystal X-ray crystallography, spectroscopic (IR and UV-vis), M?ssbauer and TGA analyses. The single crystal X-ray studies of both complexes show that the supramolecular hosts, constructed by the discrete mononuclear complexes, form supramolecular channels along the c-axis which are filled up by water-chloride clusters. In both complexes, the 1D water-chloride chain with chair-like architecture within the supramolecular hosts presents novelty. The magnetic measurement study of Fe(III) complex shows a spin crossover from S = 1/2 at 2.5 K to S = 5/2 at 300 K. At very low temperature, the presence of strong cooperative hydrogen bonding interactions stabilizes the S = 1/2 state.     

Mechanism of a strongly anisotropic MoIII-CN-MnII spin-spin coupling in molecular magnets based on the [Mo(CN)(7)](4-) heptacyanometalate: a new strategy for single-molecule magnets with high blocking temperatures

Unusual spin coupling between Mo(III) and Mn(II) cyano-bridged ions in bimetallic molecular magnets based on the [Mo(III)(CN)(7)](4-) heptacyanometalate is analyzed in terms of the superexchange theory. Due to the orbital degeneracy and strong spin-orbit coupling on Mo(III), the ground state of the pentagonal-bipyramidal [Mo(III)(CN)(7)](4-) complex corresponds to an anisotropic Kramers doublet. Using a specially adapted kinetic exchange model we have shown that the Mo(III)-CN-Mn(II) superexchange interaction is extremely anisotropic: it is described by an Ising-like spin Hamiltonian JS(z)(Mo) S(z)(Mn) for the apical pairs and by the J(z)S(z)(Mo) S(z)(Mn) + J(xy)(Sx(Mo) Sx(Mn) + Sy(Mo) Sy(Mn)) spin Hamiltonian for the equatorial pairs (in the latter case J(z) and J(xy) can have opposite signs). This anisotropy resulted from an interplay of several Ising-like (Sz(Mo) Sz(Mn)) and isotropic (S(Mo)S(Mn)) ferro- and antiferromagnetic contributions originating from metal-to-metal electron transfers through the pi and sigma orbitals of the cyano bridges. The Mo(III)-CN-Mn(II) exchange anisotropy is distinct from the anisotropy of the g-tensor of [Mo(III)(CN)(7)](4-); moreover, there is no correlation between the exchange anisotropy and g-tensor anisotropy. We indicate that highly anisotropic spin-spin couplings (such as the Ising-like JS(z)(Mo) S(z)(Mn)) combined with large exchange parameters represent a very important source of the global magnetic anisotropy of polyatomic molecular magnetic clusters. Since the total spin of such clusters is no longer a good quantum number, the spin spectrum pattern can differ considerably from the conventional scheme described by the zero-field splitting of the isotropic spin of the ground state. As a result, the spin reorientation barrier of the magnetic cluster may be considerably larger. This finding opens a new way in the strategy of designing single-molecule magnets (SMM) with unusually high blocking temperatures. The use of orbitally degenerate complexes with a strong spin-orbit coupling (such as [Mo(III)(CN)(7)](4-) or its 5d analogues) as building blocks is therefore very promising for these purposes.     

Importance of the O-M-O bridges (M = V5+, Mo6+) for the spin-exchange interactions in the magnetic oxides of Cu2+ ions bridged by MO4 tetrahedra: spin-lattice models of Rb2Cu2(MoO4)3, BaCu2V2O8, and KBa3Ca4Cu3V7O28

The spin-lattice models relevant for the magnetic oxides Rb2Cu2(MoO4)3, BaCu2V2O8, and KBa3Ca4Cu3V7O28 were determined by evaluating the relative strengths of the spin-exchange interactions between their Cu2+ ions on the basis of spin dimer analysis. Our study shows that the O-M-O bridges (M = V5+, Mo6+) between the magnetic ions Cu2+, provided by the MO4 tetrahedra, are crucial for the spin-exchange interactions and hence for deducing the spin-lattice models needed to interpret the magnetic properties of these oxides. The spin-lattice model of Rb2Cu2(MoO4)3 is not a uniform chain but two interpenetrating spin ladders that interact weakly with geometric spin frustration. The spin-lattice model of BaCu2V2O8 is an alternating chain as expected, but the spin-exchange paths responsible for it differ from those expected. With respect to the strongest spin exchange of BaCu2V2O8, the spin exchange of KBa3Ca4Cu3V7O28 is only slightly weaker, but the strongest spin exchange of Rb2Cu2(MoO4)3 is much weaker. This difference in the spin-exchange strengths is caused by the difference in the bridging modes of the MO4 tetrahedra leading to these spin-exchange interactions.     

Theory and spectroscopy of an incarcerated quantum rotor: The infrared spectroscopy,inelastic neutron scattering and nuclear magnetic resonance of H2@C60 at cryogenic temperature

The supramolecular complex, H₂@C₆₀, represents a model of a quantum rotor in a nearly spherical box. In providing a real example of a quantum particle entrapped in a small space, the system cuts to the heart of many important and fundamental quantum mechanical issues. This review compares the predictions of theory of the quantum behaviour of H₂ incarcerated in C₆₀ with the results of infrared spectroscopy, inelastic neutron scattering and nuclear magnetic resonance. For H₂@C₆₀, each of these methods supports the quantization of translational motion of H₂ and the coupling of the translational motion with rotational motion and provides insights to the factors leading to breaking of the degeneracies of states expected for a purely spherical potential. Infrared spectroscopy and inelastic neutron scattering experiments at cryogenic temperatures provide direct evidence of a profound quantum mechanical feature of H₂ predicted by Heisenberg based on the Pauli principle: the existence of two nuclear spin isomers, a nuclear spin singlet (para-H₂) and a nuclear triplet (ortho-H₂). Nuclear magnetic resonance is capable of probing the local lattice environment of H₂@C₆₀ through analysis of the H₂ motional effects on the ortho-H₂ spin dynamics (para-H₂, the nuclear singlet state, is NMR silent). In this review we will show how the information obtained by three different forms of spectroscopy join together with quantum theory to create a complementary and consistent picture which strikingly shows the intrinsically quantum nature of H₂@C₆₀.     

Accurate Determination of the Electronic Structure Parameters of the Spin Ladder Compounds SrCu2O3, Sr2Cu3O5 and CaCu2O3

Ab initio embedded cluster calculations have been employed to calculate a large number of electronic structure parameters of three different spin ladders, namely SrCu₂O₃, CaCu₂O₃ and Sr₂Cu₃O₅. Using the iterative difference dedicated configuration interaction methodology, magnetic couplings J and hopping amplitudes t are determined for first to fourth nearest neighbors. In addition, the four-body cyclic exchange J _ring is extracted and the direct exchange K, the neutral-ionic hopping integral t ₀ and the on-site repulsion U are calculated for first and second nearest neighbor copper ions. The substitution of these parameters in the pertubative superexchange relation J=2K−4t ₀²/U yields magnetic coupling parameters in close agreement with the variational estimates. The spin ladders can be considered as an interpolation between the one-dimensional (1D) spin chains and the 2D antiferromagnets. Hence, results are compared with similar parameters in the spin chain Sr₂CuO₃ and the two-dimensional antiferromagnet La₂CuO₄.     

Theoretical study on spin alignments in ferromagnetic heterospin chains with competing exchange interactions: a generalized ferrimagnetic system containing organic biradicals in the singlet ground state

Spin alignments in heterospin chains are examined from numerical calculations of model spin Hamiltonians. The Hamiltonians of the heterospin chains mimic an open-shell molecular assemblage composed of an organic biradical in a singlet (S = 0) ground state and a doublet (S = 1/2) monoradical, which are coupled by intermolecular ferromagnetic exchange interactions. It is found from numerical calculations of the spin Hamiltonians that the spin value S2 of the ground-state singlet biradical embedded in the exchange-coupled assemblage deviates from zero and contributes to the bulk magnetization. The alternating chain is found to have two kinds of ground spin states, a high- and a low-spin state. All the spins are parallel to each other in the high-spin state, which is characterized by the spin correlation function of (S(i).S(j)) = 0.25. On the other hand, the spin alignment in the low-spin state is found to be dependent on the topology of the intermolecular exchange interactions. The energy preference of the two states depends on the relative amplitude of the exchange interactions in the chain. The intermolecular ferromagnetic couplings are competing in the ground-state singlet biradical with the intramolecular antiferromagnetic interaction. The appearance of the two kinds of ground states is attributed to a quantum spin frustration effect inherent in the triangular motif of the competing interactions. Magnetic properties of a zigzag chain complex composed of a nitronyl nitroxide biradical with a singlet ground state and Cu(hfac)2 are examined on the basis of the theoretical calculations. The vanishing magnetic moments, or the product of susceptibility and temperature chiT, at low temperatures observed for the complex are consistent with those of the low-spin state predicted in the theoretical calculations.