Weak Interchain Interactions Research Articles

Slow Magnetic Relaxation in CoIICuII Coordination Oligomer Built into Mesoporous Material

AbstractThe ferrimagnetic system CoCu(opba) [opba = ortho‐phenylenebis(oxamato)] was employed to prepare a traditional chain [CoCu(opba)]·4H2O (1) and a nanocomposite by incorporation in porous Vycor glass (PVG). This nanocomposite was made by first anchoring [Bu4N]2[Cu(opba)] on PVG [PVG‐Cu (2)] and then treating it “in situ” with cobalt(II) acetate to obtain the nanomagnet PVG‐CuCo (3). Magnetic measurements show that 1 consists of a one‐dimensional ferrimagnet with strong intrachain antiferromagnetic coupling and weak interchain interactions that result in spin‐glass behavior below 3.5 K. Nanocomposite 3 presents ferrimagnetic chains limited by the nanopore size, which leads to a slow relaxation of the magnetization following Arrhenius' law, frequency dependence for in‐phase and out‐of‐phase susceptibility, and hysteresis below the blocked regime temperature (< 6 K). These features are characteristics of single‐chain magnets (SCM).(© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2008)

A Two-Dimensional Iron(II) Carboxylate Linear Chain Polymer that Exhibits a Metamagnetic Spin-Canted Antiferromagnetic to Single-Chain Magnetic Transition

A two-dimensional iron(II) carboxylate coordination polymer, [Fe(pyoa)2]infinity, where pyoa is 2-(pyridin-3-yloxy)acetate, has been prepared by hydrothermal synthesis. Its crystal structure reveals a single iron(II) site with an elongated octahedral coordination environment containing four equatorial carboxylate oxygens and two axial pyridyl nitrogens; the iron(II) sites are linked by syn-anti micro-carboxylates to form chains along the b axis that have an Fe...Fe separation of 4.910 A. The shortest interchain and interlayer Fe...Fe distances are 6.453 and 11.125 A, respectively. The 4.2-295 K Mössbauer spectra of [Fe(pyoa) 2] infinity consist of a single paramagnetic high-spin iron(II) quadrupole doublet. The axial Fe-N bond direction defines the Jahn-Teller axis at an iron(II) site and, consequently, the orientation of the single-ion magnetic anisotropy. Thus, along the b axis in a given chain, the spins are collinear and parallel to the Jahn-Teller axis. The Jahn-Teller axes of adjacent intralayer chains have different orientations with an angle of 79.2 degrees between the axes in adjacent chains in a bc layer. [Fe(pyoa)2]infinity exhibits field-induced metamagnetic behavior such that, in an applied field smaller than the critical field, the iron(II) spin-canted moments experience intrachain ferromagnetic interactions and weak interchain antiferromagnetic interactions; the spin canting yields weak ferromagnetism. In an applied field larger than the critical field, the weak antiferromagnetic interchain interactions are overwhelmed to yield superparamagnetic-like slow-magnetic relaxation with an energy barrier of 23(3) K. Single-crystal magnetic studies reveal a quasi-uniaxial magnetic anisotropy with the a axis as the easy-magnetic axis and the b axis as the hard-magnetic axis; the susceptibility measured along the easy a axis may be fit with the Glauber model to yield an effective intrachain exchange coupling constant of 2.06(8) K. A dynamic analysis of the susceptibility yields a 6.3(1) K energy barrier for intrachain domain wall creation. The observed field-assisted superparamagnet-like behavior is consistent with the dynamics of a single-chain magnet. Thus, [Fe(pyoa)2]infinity is best considered as a "metamagnetic-like" single-chain magnet.

High-pressure crystalline polyethylene studied by x-ray diffraction andab initiosimulations

Crystalline polyethylene was investigated under pressure between 0 and $40\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, up to $280\phantom{\rule{0.2em}{0ex}}\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$, by means of synchrotron x-ray powder diffraction and ab initio calculations. A rich polymorphism was unveiled, consisting of two new high-pressure monoclinic phases, in addition to the well-known orthorhombic one, which appear reversibly, although with strong hysteresis, upon increasing pressure above $6\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ ($P{2}_{1}∕m$, ${Z}_{\text{chain}}=1$) and $14--16\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ ($A2∕m$, ${Z}_{\text{chain}}=2$), respectively. The equation of state was determined for the three solid phases. We find that polyethylene is characterized by a sharp separation between strong covalent intrachain and weaker interchain interactions up to the maximum investigated pressure, which, in turn, places the ultimate chemical stability limit of polyethylene far beyond these thermodynamic conditions.

Theory of ordering in three-dimensional polymer systems with local orientational-deformational interactions

The spontaneous ordering of a three-dimensional polymer system composed of flexible segments with a fixed mean-square length in the presence of local intra- and interchain orientational-deformational interactions was considered. The fixation of the segment chain length on average is possible only during relatively weak interchain interactions or at high temperatures, i.e., in the isotropic state. The three-dimensional model, unlike its two-dimensional version, suggests the existence of the critical point at which a second-order phase transition from the isotropic state to an ordered state takes place. The critical behavior of the multichain model is described by the spherical approximation for an anisotropic Heisenberg ferromagnetic. The dependence of the critical point and the parameters of short- and long-range dipole and quadrupole orientational orders on the chain rigidity and magnitude of interchain interactions was determined. In the isotropic state, orientation correlations of segments decline according to the Ornstein-Zernike law, as in the 3D model of Gaussian subchains without fixation of their mean-square length. In the ordered state, the correlation functions tend to a finite limiting value corresponding to the presence of long-range order, as in the case of the multichain model of rigidchain segments in the strong-order approximation. A comparison of the short-range and long-range orders in the model of chains composed of segments with a fixed mean-square length and undeformable (rodlike) elements in the mean-field approximation, on the one hand, and multichain models, on the other hand, showed their equivalence, especially at high degrees of ordering.

Interpretation of experimental results of spin chains with weak interchain interaction

Experimental results concerning magnetic susceptibility and heat capacity of the CuSb 2 O 6 crystal, where the Cu 2 + ions form chains interacting with strong short range antiferromagnetic (AF) intrachain and weak AF interchain interactions, can be interpreted in terms of small rings to which the large chains are split and rejoined. The weak interchain interaction causes a small energy gap between the ground and the first excited states of CuSb 2 O 6 . The agreement between theory and experiment is remarkable. The fitting of the theoretical to the experimental results, permits the determination of the coupling constants of the Heisenberg Hamiltonian and the Lande factors along the symmetry axes of the crystal.

Renormalization of ferrimagnetic alternating spin chains

The linear real space renormalization group is applied to study alternating spin(1/2,1) chains. The temperature dependences of the specific heat and spin–spin correlationfunctions for the quantum easy-axis mixed-spin chain are found. The role of single-ionanisotropy is discussed. The phase diagram of Ising spin chains with antiferromagneticintrachain interactions and weak ferromagnetic interchain interactions is presented. As oneexpects, the weak interchain coupling leads to antiferrimagnetic long-range order in severalchains. The threshold value of single-ion anisotropy below which the system does notexhibit a phase transition is found.

Self-Assembly of Dithiolene-based Coordination Polymers of Mercury(II): Dithioether versus Thiocarbonyl Bonding

The reactions of 4,5-bis(methylthio)-1,3-dithiole-2-thione (L) with mercury(II) halides allowed the isolation and structural characterization of three novel coordination polymers, [HgX2L]n (X = I, 1; X = Br, 2; X = Cl, 3). In all cases, the complexation of L on HgX2 occurs via the thiocarbonyl function. The strength of this Hg–S bond decreases from X = I to X = Cl, as indicated by the increasing Hg–S bond distances (2.583(4) 1; 2.668(4) 2; 2.815(5) A 3). The 1D polymeric structures result from bridging halide interactions and a combination of π–π and S···S interactions between the sulfur rich ligands. The coordination around the Hg center is distorted tetrahedral in 1, whereas the geometry around the mercury in 3 is better described as distorted square pyramidal. In addition, weak interchain interactions are observed in the crystalline state. The preference of HgI2 for thiocarbonyl bonding instead of a chelating dithioether bonding was also studied by means of ab initio calculations.

Dynamics of quasi-1D topological soliton in 2D strongly anisotropic crystal

We investigate a 2D strongly anisotropic crystal: 2D system of coupled linear chains of particles with strong intrachain and weak interchain interactions: a generalization of the Frenkel–Kontorova (FK) model giving better approximation to polymer crystals consisting of all moving chains. We study shape and dynamics of topological solitons located mainly on one chain of the crystal. It turns out that at weak interactions between chains there exist exact propagating soliton-like solutions. We have found that the upper boundary of their velocity spectrum is less than unity (the upper boundary of soliton velocity spectrum in the corresponding FK model). The reason of this new restriction is appearance of Cherenkov-type radiation emitted by the kinks moving at higher velocities. In the case of stronger interchain interactions the exact soliton-like solutions are absent. Kinks emit phonons at any velocity. This emission originates from resonances between the kink and phonon modes touched in the second or the third Brillouin zones and so this effect is a pure result of discreteness of the crystal. Deceleration of kink falls exponentially with its velocity (as in the FK model) at medium velocities and is nonzero constant at low velocities (contrary to the FK model where deceleration at low velocities is zero), so at all velocities there is no generally expected direct proportion between deceleration and velocity. Spatial pattern of phonons emitted proves to be in accordance with the conception that kink emits packets of corresponding resonant phonons in direction of their group velocities.

Survival condition for low-frequency quasi-one-dimensional breathers in a two-dimensional strongly anisotropic crystal

We investigate a two-dimensional s2Dd strongly anisotropic crystal s2D SACd on substrate: 2D system of coupled linear chains of particles with strong intrachain and weak interchain interactions, each chain being subjected to the sine background potential. Nonlinear dynamics of one of these chains when the rest of them are fixed is reduced to the well known Frenkel-KontorovasFKd model. Depending on strengh of the substrate, the 2D SAC models a variety of physical systems: polymer crystals with identical chains having light side groups, an array of inductively coupled long Josephson junctions, anisotropic crystals having light and heavy sublattices. Continuum limit of the FK model, the sine-Gordon ssGd equation, allows two types of soliton solutions: topological solitons and breathers. It is known that the quasi-one-dimensional topological solitons can propagate also in a chain of 2D system of coupled chains and even in a helix chain in a three-dimensional model of polymer crystal. In contrast to this, numerical simulation shows that the long-living breathers inherent to the FK model do not exist in the 2D SAC with weak background potential. The effect changes scenario of kink-antikink collision with small relative velocity: at weak background potential the collision always results only in intensive phonon radiation while kink-antikink recombination in the FK model results in long-living low-frequency sG breather creation. We found the survival condition for breathers in the 2D SAC on substrate depending on breather frequency and strength of the background potential. The survival condition bears no relation to resonances between breather frequency and frequencies of phonon band—contrary to the case of the FK model.

Criticality of the uniform magnetic order in a ferromagnetic-antiferromagnetic random alternating quantum spin chain

An $S=1/2$ ferromagnetic (F) - antiferromagnetic (AF) random alternating Heisenberg quantum spin chain model is investigated in connection to its realization compound: (CH$_3$)$_2$CHNH$_3$Cu(Cl$_x$Br$_{1-x}$)$_3$. The exchange interaction bonds have alternating strong F-AF random bonds and weak uniform AF bonds. Using the quantum Monte Carlo method we have found that the excitation energy gap closes and the uniform AF order becomes critical in the intermediate concentration region. This finding explains the experimental observation of the magnetic transition by considering weak interchain interactions. Present results suggest that the uniform AF order survives even in the presence of randomly located ferromagnetic bonds. This may be a new quantum effect.

Electronic structure ofCaCu2O3: Spin ladder versus one-dimensional spin chain

Quantum chemical calculations on embedded cluster models have been performed to extract accurate estimates of the magnetic coupling $J$ and hopping parameters $t$ of $\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{3}$. It is shown that this copper oxide compound is best described as a quasi-one-dimensional spin chain with weak interchain interactions within and between the ${\mathrm{Cu}}_{2}{\mathrm{O}}_{3}$ planes. This magnetic structure is not reflected in the hopping parameters, since we find a large interplane hopping. Hence, the use of the simple second-order expression that relates $J$, $t$, and the on-site repulsion $U$ $(J=\ensuremath{-}4{t}^{2}∕U)$ is not justified in all cases.

Mixed-valence MnIIIMnIV clusters [Mn7O8(O2SePh)8(O2CMe)(H2O)] and [Mn7O8(O2SePh)9(H2O)]: single-chain magnets exhibiting quantum tunneling of magnetization.

The syntheses, structures, and magnetic properties of two new Mn7 complexes containing phenylseleninate ligands are reported. [Mn7O8(O2SePh)8(O2CMe)(H2O)] (1) and [Mn7O8(O2SePh)9(H2O)] (2) were both prepared by the reaction of 18 equiv of benzeneseleninic acid (PhSeO2H) with [Mn12O12(O2CMe)16(H2O)4] in MeCN. Complex 1 x 6MeCN crystallizes in the triclinic space group P, and complex 2 x 2CH2Cl2 crystallizes in the monoclinic space group P2(1)/m. Both compounds possess an unprecedented [Mn7O8]9+ core comprising a central [MnIII3(micro3-O)4]+ unit attached to [MnIV2(micro-O)2]4+ and [MnIV2(micro-O)(micro3-O)]4+ units on either side. In each cluster, the PhSeO2- groups function as bridging ligands between adjacent Mn centers. The structure reveals strong Se.O intermolecular contacts between Mn7 units to give a one-dimensional chain structure, with weak interchain interactions. Solid-state DC magnetic susceptibility measurements of complexes 1 and 2 reveal that they have very similar properties, and detailed studies on 1 by AC susceptibility measurements confirm an S = 2 ground-state spin value. In addition, out-of-phase AC signals are observed, suggesting slow magnetization relaxation. Magnetization versus DC field sweeps down to 0.04 K reveals hysteresis loops, but the temperature dependence of the coercivity is not what is expected of a single-molecule magnet. Instead, the behavior is due to single-chain magnetism, albeit with weak antiferromagnetic interactions between the chains, with the barrier to relaxation arising from a combination of molecular anisotropy and ferromagnetic intermolecular exchange interactions mediated by the Se...O contacts. An Arrhenius plot was constructed from the magnetization versus time decay data. The thermally activated region at > 0.5 K gave an effective relaxation barrier (Ueff) of 14.2 K. Below approximately 0.1 K, the relaxation is independent of temperature, which is characteristic of magnetization quantum tunneling through the anisotropy barrier. These Mn7 compounds are thus the first single-chain magnets to comprise polynuclear metal clusters and also the first for which the temperature-independent relaxation characteristic of tunneling has been identified. The work also emphasizes that out-of-phase AC signals for ostensibly molecular compounds are not sufficient proof by themselves of a single-molecule magnet.

Structure and Physical Properties of Molecule-Based Magnets Including Transition Metal Complexes of Crown Thioethers

Abstract A new series of molecule-based magnets, including crown thioether (9S3 = 1,4,7-trithiacyclononane) complexes of transition metals (Ni, Co, Cu), are presented. TCNQ salts [M(9S3)2](TCNQ)2 (M = Ni, Co) are one-dimensional (1D), antiferromagnetic (AF) complexes with an intra-chain interaction J = −3.9 K and −1.3 K for M = Ni and Co, respectively, despite its long intermolecular distance, for which the large spin density on the sulfur atom in the magnetic [M(9S3)2]2+ cation is responsible. The mixed valence salt [M(9S3)2](TCNQ)3 (M = Ni, Co) is a paramagnetic semiconductor. 1D AF magnet [Cu(9S3)Br2] does not undergo any magnetic transition because of the weak inter-chain interaction. Substituting a very small amount (∼5%) of Cu with Ni causes a structural change. The change decreases the distances of inter-chain S–S contacts, resulting in the generation of an AF transition at TN = 4.5 K. [M(9S3)2][Ni(bdt)2]2 (M = Ni, Co; bdt = 1,2-benzenedithiolato) are weak-ferromagnets with TN = 6.2 K and 2.6 K for M = Ni and Co, respectively. In the crystals, [M(9S3)2]2+–[Ni(bdt)2]− alternate chains and [Ni(bdt)2]− uniform chains coexist. The appearance of weak-ferromagnetism is associated with a competition between two kinds of inter-chain AF interactions between [M(9S3)2]2+–[Ni(bdt)2]− alternate chains, where the stronger one is an indirect inter-chain interaction through [Ni(bdt)2]− uniform chains, while the weaker is a direct inter-chain interaction.

Rotational vibration of poly(tetrafluoroethylene) chains by the electron spin resonance method

AbstractTemperature‐dependent electron spin resonance spectra of main‐chain free radicals, CF2(β)C · F(α)CF2(β), in poly(tetrafluoroethylene) (PTFE) were analyzed by the change in the hyperfine splitting due to β‐fluorines, which was a decreasing function of the observation temperature. The results were interpreted in terms of the rotational vibration around the CαCβ bond. The amplitude of the vibration was estimated on the assumption of its harmonic oscillation. The vibration of the PTFE chain was found to have a large amplitude in comparison with that of a polyethylene chain in single crystals. The vibration of the large amplitude was caused by a weak interchain interaction in the PTFE matrices. The amplitude of the vibration in crosslinked PTFE was much larger than that in noncrosslinked PTFE. This result indicated that the free radicals in crosslinked PTFE were trapped in the amorphous region, which had the disordered sites of crosslinking, whereas the free radicals in noncrosslinked PTFE were mainly trapped in the paracrystalline region. The decay reaction of the free radicals in the PTFE matrices was also related to the heterogeneity in the structure and the rotational vibration. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1539–1547, 2004

Antiferromagnetic chains coupled by weak ferromagnetic interchain interactions

The linear-perturbation renormalization-group transformation is used to study $s=\frac{1}{2}$ spin chains with antiferromagnetic intrachain interactions $Jl0$ coupled by weak ferromagnetic interchain interactions ${J}^{\ensuremath{'}}g0$ in the longitudinal external magnetic field H. The field dependence of the specific heat for several models $(XY,$ anisotropic Heisenberg, and Ising) has been found. The specific heat of the one-dimensional models ${(J}^{\ensuremath{'}}=0)$ exhibits a maximum at ${H=H}_{\mathrm{max}}$ which decreases and shifts to higher fields with increasing temperature, and a minimum which disappears for the temperature higher than some characteristic temperature ${T}_{g}.$ For the antiferromagnetic $\mathrm{XY}$ and Ising models the specific-heat maximum is shifted linearly, whereas for the Heisenberg model the shift cannot be fitted to a single power law. For an arbitrary small ferromagnetic interchain interaction ${(J}^{\ensuremath{'}}g0)$ the specific heat as a function of temperature has a singularity characterizing the antiferromagnetic phase transition. From the flow diagram analysis the dependence of the transition temperature on the interchain interaction and the external field has been found.

Mechanical behavior of polycyanurate–polyurethane sequential full-interpenetrating polymer networks

Differential scanning calorimetry and dynamic mechanical spectroscopy studies have been performed between 120 and 600 K in a new series of sequential full-interpenetrating polymer networks (full-IPNs) of crosslinked polyurethane and polycyanurate network (PCN), based on dicyanate ester of 1,1 ′-bis-4,cyanatophenyl-ethane. The measurements have revealed the existence of two distinct glass transitions in the thermograms and of relaxation losses given by the overlap of two α a-relaxations in the mechanical spectra whose temperature locations change with changing weight ratio of polymeric component. These observations indicate that the morphology of this new class of full-IPNs is based on double-phase structures characterized by weak interchain interactions. The interpenetration affects markedly the glass transition temperatures revealed in the pure components as a consequence of modifications in the local environments of the relaxing molecular units in the two phases. Below the glass transition, two secondary relaxation losses have been observed which have been ascribed to local molecular transitions within each polymeric component. The analysis of their concentration behaviors leads to a conclusion that the interpenetration process affects markedly the local motion of the PCN component.

Magnetization and specific heat of a ferromagnetic zigzag spin chain compound LaCrOS 2

The magnetization and the specific heat of an oxysulfide LaCrOS 2, in which Cr ions form zigzag spin chains, have been measured. The temperature dependence of the magnetic susceptibility deviates from the Curie–Weiss behavior with the Weiss temperature Θ p =66 K, below 200 K. A peak appears in the low field susceptibility vs. temperature curve at 32 K, which is regarded to signal the ferromagnetic transition. The temperature dependence of the magnetic specific heat shows a broad maximum, which is characteristic of a low dimensional magnetic system. In addition, a small sharp peak is observed at 32 K which is attributed to the three-dimensional ferromagnetic transition. These behaviors are well explained by an effective Ising spin chain model for S=3/2 with a weak interchain interaction.

THEORY OF PHOTOINDUCED PHASE TRANSITION IN THE QUASI-ONE-DIMENSIONAL CHARGE TRANSFER COMPOUND TTF-CA

We theoretically study the photoinduced ionic→neutral phase transition in the quasi-one-dimensional molecular crystal TTF-CA. Our theoretical model includes strong intra-chain Coulomb interactions as well as very weak inter-chain interactions. Within the mean-field picture, we investigate the nonlinear lattice relaxation of a charge transfer exciton, and clarify the adiabatic path from its Franck-Condon state to a macroscopic neutral domain. It is found that the lowest state of such a single charge transfer exciton can not relax down to the neutral domain straightly, but a large excess energy is necessary so that it can overcome a high barrier. The aggregation of two identically shaped neutral domains is also discussed.

Spin dynamics of a one-dimensional spin-1/2 fullyanisotropic Ising-like antiferromagnet in a transverse magneticfield

We consider the one-dimensional Ising-like fully anisotropic S = 1/2 Heisenberg antiferromagnetic Hamiltonian and studythe dynamics of domain wall excitations in the presence ofa transverse magnetic field hx. We obtain dynamical spincorrelation functions along the magnetic field, Sxx(q,ω),and perpendicular to it, Syy(q,ω). It is shown that theline shapes of Sxx(q,ω) and Syy(q,ω) are purelysymmetric at the zone boundary. It is observed inSyy(q,ω) for π/2<q<π that the spectral weight movestoward the low-energy side with the increase of hx. This model isapplicable to the study of the spin dynamics of CsCoCl3 in the presenceof weak interchain interactions.

Structural and magnetic characterization of [Fe(Cp∗) 2]DR-DCNQI, R=Me and Ph

The synthesis and magnetic properties of [Fe(Cp * ) 2 ]DR-DCNQI, R=Me and Ph, are presented and discussed. The crystal structure for the [Fe(Cp * ) 2 ]DMe-DCNQI compound consists of an array of parallel stacks of alternating cations [Fe(Cp * ) 2 ] + and anions DMe-DCNQI', ..D + A - D + A - D + A - ... Strong intrachain DA FM interactions dominate the magnetic behavior of [Fe(Cp * ) 2 ]DMe-DCNQI and the competition between those interactions and weak AFM interchain interactions results in the observation of a metamagnetic behavior at low temperatures, with T N =3 K and H C =2.5 kG, at 1.8 K. In the case of [Fe(Cp * ) 2 ]DPh-DCNQI, weak AFM interactions dominate the magnetic behavior of this compound.