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Single chain relaxation in Co(NCS)2(4-methoxypyridine)2 proceeds with a single domain wall movement. The origin of the second process is unknown.

Three new hybrid organic-inorganic frameworks employing octacyanidometallates and 4,4'-bypiridine dioxide (4,4'-bpdo) as bridging molecules were prepared and characterized. The three-dimensional coordination frameworks {[Fe

The reaction of Co(NCS)

A large single crystal of a compound from the family of coordination polymer [Co(NCS)2(L)2]n chains was synthesized and its magnetic properties are reported. [Co(NCS)2(4-(3-phenylpropyl)pyridine)2]n is ferromagnetic with Tc = 3.39 K. Single-ion ab initio calculations predict an almost Ising-type magnetic anisotropy and the direction of the magnetic easy-axis nearly along the Co–Npy bond of the apical pyridine-based co-ligand. Both predictions are confirmed by single-crystal magnetic measurements. The magnetic relaxation of the single crystal sample significantly differs from the powder sample data, and clearly shows the presence of two separate relaxation processes. The process dominant below 3.2 K demonstrates a single chain magnet (SCM) behaviour, with a crossover between single-wall and two-wall processes, in spite of the fact that the system is ferromagnetically ordered. The faster process that dominates just below Tc is attributed to spin waves. Micromagnetic Monte Carlo simulations of the investigated compound show that the dipolar field cancels for some chains located at the border between 3-dimensional domains. Such chains are responsible for the measured ac signal, and demonstrate the SCM behaviour. The quantitative analysis of the SCM relaxation time is supported by preparing and examining a corresponding diamagnetically diluted compound, [CoxCd1−x(NCS)2(4-(3-phenylpropyl)pyridine)2]n (x = 0.013), which behaves as a field-induced single-ion magnet. The relaxation pathways for single Co(II) spins are determined to be Raman, direct, and quantum tunneling processes, which were included in an improved approach to describe the magnetic relaxation in the Co(II)-based SCM compound.

For piecewise monotone interval maps we look at Birkhoff spectra for regular potential functions. This means considering the Hausdorff dimension of the set of points for which the Birkhoff average of the potential takes a fixed value. In the uniformly hyperbolic case we obtain complete results, in the case with parabolic behaviour we are able to describe the part of the sets where the lower Lyapunov exponent is positive. In addition we give some lower bounds on the full spectrum in this case. This is an extension of work of Hofbauer on the entropy and Lyapunov spectra., 22 pages

Reaction of FeCl2, KSCN, and 4-acetylpyridine in dry ethanol leads to [Fe(NCS)2(4-acetylpyridine)2]n (1-Fe) that, in contrast to the previously reported chain isomer, consists of layers. Specific h...

Let $\{s_n\}_{n\in\N}$ be a decreasing nonsummable sequence of positive reals. In this paper, we investigate the weighted Birkhoff average $\frac{1}{S_n}\sum_{k=0}^{n-1}s_k\phi(T^kx)$ on aperiodic irreducible subshift of finite type $\Sigma_{\bf A}$ where $\phi: \Sigma_{\bf A}\mapsto \R$ is a continuous potential. Firstly, we show the entropy spectrum of the weighed Birkhoff averages remains the same as that of the Birkhoff averages. Then we calculate the packing spectrum of the weighed Birkhoff averages. It turns out that we can have two cases, either the packing dimension of every level set equals to its Hausdorff dimension or for every nonempty level set it is equal to the packing dimension of the whole space.

A homoleptic gadolinium(III) complex with the smallest helicene-type ligand, 1,10-phenanthroline-N,N'-dioxide (phendo) [Gd(phendo)4](NO3)3·xMeOH (phendo = 1,10-phenanthroline-N,N'-dioxide, MeOH = methanol), shows slow relaxation of the magnetization characteristic for Single Ion Magnets (SIM), despite negligible magnetic anisotropy, confirmed by ab initio calculations. Solid state dilution magnetic and EPR studies reveal that the magnetization dynamics of the [Gd(phendo)4]3+ cation is controlled mainly by a Raman process. Pulsed EPR experiments demonstrate long phase memory times (up to 2.7 μs at 5 K), enabling the detection of Rabi oscillations at 20 K, which confirms coherent control of its spin state. ispartof: JOURNAL OF PHYSICAL CHEMISTRY LETTERS vol:11 issue:4 pages:1508-1515 ispartof: location:United States status: published

Working on strongly irreducible planar self-affine sets satisfying the strong open set condition, we calculate the Birkhoff spectrum of continuous potentials and the Lyapunov spectrum., Comment: 32 pages, 1 figure

Reaction of Co(NCS)2 and Ni(NCS)2 with 4-tert-butylpyridine in ethyl acetate leads to the formation of mixed crystals of a layered compound with the composition [CoxNi1-x(NCS)2(4-tert-butylpyridine]n. The mixed crystal formation was investigated by a combination of atomic absorption spectroscopy, X-ray powder diffraction and IR spectroscopy. Magnetic and specific heat measurements prove dominating ferromagnetic exchange interactions within the layers and a ferromagnetic transition. Depending on the synthetic method, inhomogeneous samples were obtained, for which predominantly the large difference in the solubility of the homometallic compounds might be responsible. Very long reaction time leads to much better samples for which a distinct critical temperature is observed that increases smoothly with increasing Ni content.

We provide examples of transitive partially hyperbolic dynamics (specific but paradigmatic examples of homoclinic classes) which blend different types of hyperbolicity in the one-dimensional center direction. These homoclinic classes have two disjoint parts: an "exposed" piece which is poorly homoclinically related with the rest and a "core" with rich homoclinic relations. There is an associated natural division of the space of ergodic measures which are either supported on the exposed piece or on the core. We describe the topology of these two parts and show that they glue along nonhyperbolic measures. Measures of maximal entropy are discussed in more detail. We present examples where the measure of maximal entropy is nonhyperbolic. We also present examples where the measure of maximal entropy is unique and nonhyperbolic, however in this case the dynamics is nontransitive.

This paper considers self-conformal iterated function systems (IFSs) on the real line whose first level cylinders overlap. In the space of self-conformal IFSs, we show that generically (in topological sense) if the attractor of such a system has Hausdorff dimension less than $1$ then it has zero appropriate dimensional Hausdorff measure and its Assouad dimension is equal to $1$. Our main contribution is in showing that if the cylinders intersect then the IFS generically does not satisfy the weak separation property and hence, we may apply a recent result of Angelevska, K\"aenm\"aki and Troscheit [BLMS, 2020]. This phenomenon holds for transversal families (in particular for the translation family) typically, in the self-similar case, in both topological and in measure theoretical sense, and in the more general self-conformal case in the topological sense., Comment: 27 pages including Appendix; v2: minor updates, accepted version in RSE Proc A

A large single crystal of a compound from the family of coordination polymer [Co(NCS)2(L)2]n chains was synthesized and its magnetic properties are reported. [Co(NCS)2(4-(3-phenylpropyl)pyridine)2]n is ferromagnetic with Tc = 3.39 K. Single-ion ab initio calculations predict an almost Ising-type magnetic anisotropy and the direction of the magnetic easy-axis nearly along the Co-Npy bond of the apical pyridine-based co-ligand. Both predictions are confirmed by single-crystal magnetic measurements. The magnetic relaxation of the single crystal sample significantly differs from the powder sample data, and clearly shows the presence of two separate relaxation processes. The process dominant below 3.2 K demonstrates a single chain magnet (SCM) behaviour, with a crossover between single-wall and two-wall processes, in spite of the fact that the system is ferromagnetically ordered. The faster process that dominates just below Tc is attributed to spin waves. Micromagnetic Monte Carlo simulations of the investigated compound show that the dipolar field cancels for some chains located at the border between 3-dimensional domains. Such chains are responsible for the measured ac signal, and demonstrate the SCM behaviour. The quantitative analysis of the SCM relaxation time is supported by preparing and examining a corresponding diamagnetically diluted compound, [CoxCd1-x(NCS)2(4-(3-phenylpropyl)pyridine)2]n (x = 0.013), which behaves as a field-induced single-ion magnet. The relaxation pathways for single Co(ii) spins are determined to be Raman, direct, and quantum tunneling processes, which were included in an improved approach to describe the magnetic relaxation in the Co(ii)-based SCM compound.

Michael Barnsley introduced a family of fractals sets which are repellers of piecewise affine systems. The study of these fractals was motivated by certain problems that arose in fractal image compression, but the results we obtained can be applied for the computation of the Hausdorff dimension of the graph of some functions, like generalized Takagi functions and fractal interpolation functions. In this paper, we introduce this class of fractals and present the tools in the one-dimensional dynamics and nonconformal fractal theory that are needed to investigate them. This is the first part in a series of two papers. In the continuation, there will be more proofs and we apply the tools introduced here to study some fractal function graphs.

We are interested in the set of normal sequences in the space $\{0,1\}^{\mathbb N}$ with a given frequency of the pattern $11$ in the positions $k$, $2k$. The topological entropy of such sets is determined.

This is the second part in a series of two papers. Here, we give an overview on the dimension theory of some dynamically defined function graphs, like Takagi and Weierstrass function, and we study the dimension of Markovian fractal interpolation functions and generalized Takagi functions generated by non-Markovian dynamics.

Reaction of Co(NCS)2 with 4-bromopyridine leads to the formation of discrete complexes with the composition Co(NCS)2(4-bromopyridine)4·(CH3CN)0.67 (1), Co(NCS)2(4-bromopyridine)2(H2O)2 (2), Co(NCS)2(4-bromopyridine)2(CH3OH)2 (3) and Co(NCS)2(4-bromopyridine)2(CH3CN)2 (4). Upon heating compounds 2 and 4 transform into a crystalline product with the composition Co(NCS)2(4-bromopyridine)2 (5-I) that also can easily be obtained from solution. In this compound, the Co cations are linked by single μ-1,3-bridging thiocyanate anions into layers. Thermal decomposition of 3 leads to a second isomer (5-II), which is thermodynamically metastable and can also be synthesized from solution under kinetic control. In contrast to 5-I, the Co cations are linked by pairs of anionic ligands into linear chains. The magnetic exchange is very weak in 5-I, but much stronger and ferromagnetic along the linear chains in 5-II. AF ordering in 5-II is reached at 3.05 K, and magnetic relaxation is observed at the metamagnetic transition with an Arrhenius barrier of 17.1(3) cm-1. Ab initio computational studies reveal a different type of magnetic anisotropy to be present in the two crystallographically - independent Co centers in 5-II.

Two different isomers of [Co(NCS)

Reaction of mixtures of Co(NCS)2 and Ni(NCS)2 with ethylisonicotinate in EtOH in a ratio of 1:2 leads to the formation of solid solutions (mixed crystals) of the layered compound [CoxNi1–x(NCS)2(ethylisonicotinate)2]n that are always contaminated with an additional crystalline phase. Pure samples of the desired layer compound are accessible by using an excess of the metal salts, but in this case the Co content in the solid solutions, as determined by atomic absorption spectroscopy and energy dispersive X-ray spectroscopy, is always lower than that used in the synthesis. Therefore, solid solutions of CoxNi1–x(NCS)2(ethylisonicotinate)4 were synthesized that upon heating transform into solid solutions of the desired layered compound, and in this case the Co/Ni ratio exactly corresponds to that used in the synthesis. The formation of solid solutions of all compounds is already indicated by comparison of the experimental powder X-ray diffraction pattern of the solid solutions with that of physical mixtures wi...

We describe the shrinking target set for the Bedford-McMullen carpets, with targets being either cylinders or geometric balls.

Reaction of Ni(NCS)2 with 4-(Boc-amino)pyridine in acetonitrile leads to the formation of a new coordination polymer with the composition Ni(NCS)2(4-(Boc-amino)pyridine)2·MeCN (1-MeCN). In the crystal structure the Ni(II) cations are linked by the anionic ligands into chains that are further connected into layers by intermolecular N–H···O hydrogen bonding. These layers are stacked and channels are formed, in which acetonitrile molecules are located. Solvent removal leads to the ansolvate 1, which shows microporosity as proven by sorption measurements. Single crystal X-ray investigations reveal that the solvent removal leads to a change in symmetry from primitive to C-centered, which is reversible and which proceeds via a topotactic reaction leaving the network intact. The magnetic properties of 1-MeCN and 1 are governed by the ferromagnetic exchange between spins of Ni(II) forming chains. The susceptibility and specific heat for such a quantum Heisenberg chain of S = 1 spins with zero-field splitting are ...

Reaction of Co(NCS)2 with 2,6-dimethylpyrazine (2,6-DMPy) leads to the formation of a compound with the composition Co(NCS)2(2,6-DMPy)4 (Co-0D) that consists of discrete complexes, in which the Co cations are octahedrally coordinated. Upon heating, half of the 2,6-DMPy ligands are removed leading to the two-dimensional coordination polymer [Co(NCS)2(2,6-DMPy)2]n (Co-2D), shown by thermogravimetry and X-ray powder diffraction. On further heating, the intermediate Co-2D loses the next 2,6-DMPy ligand and transforms into [Co(NCS)2(2,6-DMPy)]n (Co-3D). The crystal structures of Co-2D and Co-3D were solved and refined using powder X-ray diffraction data. The crystal structure of Co-2D consists of octahedrally coordinated Co cations that are linked by pairs of anionic ligands into dimers, which are further connected by single thiocyanate anions into layers. In Co-3D, octahedrally and tetrahedrally coordinated Co cations are present, that are linked by μ-1,3-bridging single thiocyanate anions into a novel three-...

Reaction of Co(NCS)2 with different coligands leads to the formation of three compounds with the general composition [Co(NCS)2(L)2]n (L = aniline (1), morpholine (2), and ethylenethiourea (3)). In ...

Reaction of Co(NCS)2 with 4-bromopyridine leads to the formation of discrete complexes with the composition Co(NCS)2(4-bromopyridine)4·(CH3CN)0.67 (1), Co(NCS)2(4-bromopyridine)2(H2O)2 (2), Co(NCS)2(4-bromopyridine)2(CH3OH)2 (3) and Co(NCS)2(4-bromopyridine)2(CH3CN)2 (4). Upon heating compounds 2 and 4 transform into a crystalline product with the composition Co(NCS)2(4-bromopyridine)2 (5-I) that also can easily be obtained from solution. In this compound, the Co cations are linked by single μ-1,3-bridging thiocyanate anions into layers. Thermal decomposition of 3 leads to a second isomer (5-II), which is thermodynamically metastable and can also be synthesized from solution under kinetic control. In contrast to 5-I, the Co cations are linked by pairs of anionic ligands into linear chains. The magnetic exchange is very weak in 5-I, but much stronger and ferromagnetic along the linear chains in 5-II. AF ordering in 5-II is reached at 3.05 K, and magnetic relaxation is observed at the metamagnetic transition with an Arrhenius barrier of 17.1(3) cm-1. Ab initio computational studies reveal a different type of magnetic anisotropy to be present in the two crystallographically - independent Co centers in 5-II.

The reaction of Ni(NCS)2 with 3-ethylpyridine in water leads to the formation of two known modifications of Ni(NCS)2(3-ethylpyridine)4 (1-I and 1-II) as well as of Ni(NCS)2(3-ethylpyridine)2(H2O)2 (2) that consist of discrete complexes. If the synthesis is performed in ethyl acetate, the new compound [Ni(NCS)2(3-ethylpyridine)2]n (3-lc) formed that comprises linear and corrugated Ni(NCS)2 chains in one crystal. By changing the solvent to dichloromethane, a solvate of compound 3 is obtained that consists exclusively of corrugated chains (3c-CH2Cl2). 3c-CH2Cl2 is unstable and transforms immediately into 3-lc. Upon heating the precursor complexes 1-I, 1-II and 2, the 3-ethylpyridine ligands are removed in two steps leading to a mixture of 3-lc and an additional isomer of 3 (3-l) in the first step that decomposes upon further heating into a compound with the composition [Ni(NCS)2(3-ethylpyridine)]n (4). Ex and in situ XRPD measurements reveal that a mixture of two modifications (4-I and 4-II) is always formed, preventing their structure determination by XRPD. Time dependent investigations in solution prove that 3-l is formed under kinetic control and transforms into 3-lc within several hours that is thermodynamically stable at room-temperature. Structure analysis of 3-l shows that in contrast to 3-lc and 3c-CH2Cl2 this isomer consists exclusively of linear Ni(NCS)2 chains. Magnetic measurements of the new chain compounds 3-l and 3-lc shows χT values that are typical for Ni(II) cations with S = 1. For 3-l the exchange constant was determined by fitting of the magnetic data leading to a value that is similar to that of [Ni(NSC)2(2,2′-bipyridine)2]n.

The cobalt(II) in [Co(NCS)2(4‐methoxypyridine)2]n are linked by pairs of thiocyanate anions into linear chains. In contrast to a previous structure determination, two crystallographically independent cobalt(II) centers have been found to be present. In the antiferromagnetic state, below the critical temperature (T c=3.94 K) and critical field (H c=290 Oe), slow relaxations of the ferromagnetic chains are observed. They originate mainly from defects in the magnetic structure, which has been elucidated by micromagnetic Monte Carlo simulations and ac measurements using pristine and defect samples. The energy barriers of the relaxations are Δτ1=44.9(5) K and Δτ2=26.0(7) K for long and short spin chains, respectively. The spin excitation energy, measured by using frequency‐domain EPR spectroscopy, is 19.1 cm−1 and shifts 0.1 cm−1 due to the magnetic ordering. Ab initio calculations revealed easy‐axis anisotropy for both CoII centers, and also an exchange anisotropy Jxx/Jzz of 0.21. The XXZ anisotropic Heisenberg model (solved by using the density renormalization matrix group technique) was used to reconcile the specific heat, susceptibility, and EPR data., Slowly relax… The magnetic properties of the linear chain compound [Co(NCS)2(4‐methoxypyridine)2]n have been investigated both experimentally and theoretically. Slow relaxations of the ferromagnetic chains were observed in the antiferromagnetic state and the specific heat, susceptibility, and EPR data obtained have been reconciled by using the XXZ anisotropic Heisenberg model (see figure).

Two different isomers of [Co(NCS)2(4-chloropyridine)2]n (3C and 3L) were synthesized from solution and by thermal decomposition of Co(NCS)2(4-chloropyridine)2(H2O)2 (2), which show a different meta...

Both preserved gapless states and gapping of Dirac states due to broken time reversal symmetry in bismuth chalcogenide topological insulators with surface and bulk magnetic impurities have been observed and reported in the literature. In order to shed more light on the mechanism of such effects we have performed comprehensive element selective study of the impact of Fe impurity position in the Bi2Se3 lattice on its magnetism. The iron atoms were imbedded in the structure (volume dopants) or deposited on the surface (adatoms) and they revealed striking phenomena. Volume doping preserves non-trivial topology of Bi1.98Fe0.02Se3. Fe atoms not only substitute Bi, but also locate in van der Waals gap. The former are magnetically isotropic, while the latter reveal large magnetic moment (4.5 μ B) with perpendicular anisotropy if located near the surface. Majority of Fe adatoms on the surface of Bi2Se3 exhibit weaker moment (3.5 μ B) with in-plane anisotropy, as expected for non-interacting species. Negligible interaction between surface electronic states and magnetic adatoms is confirmed by identical vibration spectra of Fe deposited on TI surface of Bi2Se3 and non-TI surface of Bi2S3. The data gathered show how indispensable is the knowledge of the magnetic impurity distribution for applications of bismuth chalcogenide systems.

The reaction of Mn(NCS)2 with 4-cyanopyridine (CNpy) leads to the formation of discrete complexes with the composition [Mn(NCS)2(CNpy)4] (1), [Mn(NCS)2(H2O)2(CNpy)2] (2-I and 2-II), and [Mn(NCS)2(H...

A strategy to continuously tune the exchange constant J and the critical temperature Tc in the 1D coordination polymers [Co(NCS)x(NCSe)2−x(pyridine)2]n is reported. For such mixed crystals, prepared by annealing and from solution, an increase of J and Tc with increasing selenocyanate content is observed.

Two new transition metal thiocyanate coordination polymers with the composition [Co(NCS)2(4-vinylpyridine)2]n (1) and [Co(NCS)2(4-benzoylpyridine)2]n (2) were synthesized and their crystal structures were determined. In both compounds the Co cations are octahedrally coordinated by two trans-coordinating 4-vinyl- or 4-benzoylpyridine co-ligands and four μ-1,3-bridging thiocyanato anions and linked into chains by the anionic ligands. While in 1 the N and the S atoms of the thiocyanate anions are also in trans-configuration, in 2 they are in cis-configuration. A detailed magnetic study showed that the intra-chain ferromagnetic coupling is slightly stronger for 2 than for 1, and that the chains in both compounds are weekly antiferromagnetically coupled. Both compounds show a long range magnetic ordering transition at Tc = 3.9 K for 1 and Tc = 3.7 K for 2, which is confirmed by specific heat measurements. They also show a metamagnetic transition at a critical field of 450 Oe (1) and 350 Oe (2), respectively. Below Tc1 and 2 exhibit magnetic relaxations resembling relaxations of single chains. The exchange constants obtained from magnetic and specific heat data are in good accordance with those obtained from constrained DFT calculations carried out on isolated model systems. The ab initio calculations allowed us to find the principal directions of anisotropy.

[Co(NCS)2(py)2]n (py = pyridine) is composed of ferromagnetic chains of Co(ii) cations connected by double NCS bridges. The chains are irregular because of two crystallographically inequivalent Co(ii) cations. The coordination polyhedron of the Co(ii) cations is a distorted octahedron built from two N and two S atoms of four equatorial NCS anions and two apical N atoms of the pyridine ligands. Magnetic and specific heat studies show that the compound undergoes a phase transition at 3.7 K to a ferromagnetic state. The determined magnetic interactions, intrachain (J/kB = 28 K) and interchain (zJ'/kB = 0.5 K), confirm the quasi 1D Ising magnetic character of [Co(NCS)2(py)2]n. Using AC magnetic susceptibility measurements the energy barriers for magnetization reversal of different relaxation processes were determined including those of the individual chains. By means of high field-high frequency ESR study the magnetic excitations were observed and explained in the frame of the Ising model in agreement with the results of the magnetic study. Ab initio calculations confirm the high magnetic anisotropy of the system and allow determination of the direction of the easy-axis. The broken symmetry DFT calculations support the ferromagnetic intrachain interactions. The energetic relations relevant for relaxations are discussed. It is concluded that the magnetic model of [Co(NCS)2(py)2]n is not a pure Ising but the transversal exchange plays a role.

Structure and solvatomagnetic properties of two 1D CN-bridged assemblies based on the [Mn(cyclam)]3+ complex (cyclam = 1,4,8,11-tetraazacyclotetradecane) have been characterised. The isostructural {[Mn(cyclam)][Cr(CN)6]·6H2O}n (1·6H2O) and {[Mn(cyclam)][Fe(CN)6]·6H2O}n (2·6H2O) chains crystallise in the space group C2/m. Dried in air at a slightly elevated temperature the hexahydrates undergo irreversible partial dehydration to stable dihydrates 1·2H2O and 2·2H2O, respectively. The structure model of 1·2H2O proposed from the PXRD data shows lower symmetry of the network described by the space group P21 and markedly different relative arrangement of the chains. The Mn-Cr chains are characterised by antiferromagnetic exchange through the CN-bridges (J = −2.8 K for 1·6H2O and −6.0 K for 1·2H2O), which was modelled using quantum Monte Carlo simulations. Together with weaker AF Mn-Cr interactions between the chains it leads to ferrimagnetic ordering. Ferromagnetic intra-chain interactions (J = 4.5 K for 2·6H2O and 7.1 K for 2·2H2O) and antiferromagnetic 3D ordering is observed for the Mn-Fe chains. The dehydration process in both compounds causes an increase in the strength of magnetic exchange, reflecting changes in the CN-bridge geometry.

The self-assembly of Dy(III) -3-hydroxypyridine (3-OHpy) complexes with hexacyanidocobaltate(III) anions in water produces cyanido-bridged {[Dy(III) (3-OHpy)2 (H2 O)4 ] [Co(III) (CN)6 ]}⋅H2 O (1) chains. They reveal a single-molecule magnet (SMM) behavior with a large zero direct current (dc) field energy barrier, ΔE=266(12) cm(-1) (≈385 K), originating from the single-ion property of eight-coordinated Dy(III) of an elongated dodecahedral geometry, which are embedded with diamagnetic [Co(III) (CN)6 ](3-) ions into zig-zag coordination chains. The SMM character is enhanced by the external dc magnetic field, which results in the ΔE of 320(23) cm(-1) (≈460 K) at Hdc =1 kOe, and the opening of a butterfly hysteresis loop below 6 K. Complex 1 exhibits white Dy(III) -based emission realized by energy transfer from Co(III) and 3-OHpy to Dy(III) . Low temperature emission spectra were correlated with SMM property giving the estimation of the zero field ΔE. 1 is a unique example of bifunctional magneto-luminescent material combining white emission and slow magnetic relaxation with a large energy barrier, both controlled by rich structural and electronic interplay between Dy(III) , 3-OHpy, and [Co(III) (CN)6 ](3-) .

The quasi-one-dimensional [Co(NCS)2(pyridine)2]n coordination polymer built of ferromagnetic chains of Co(II) ions linked by (NCS)2 anions is known as an Ising ferromagnet that magnetically orders at TC = 3.9 K. We performed a neutron diffraction study and show that the magnetic structure is collinear ferromagnetic, static, and without any glassy component. The magnitude of the ordered magnetic moment of Co(II) is 3.65(15) μB, which points to a relatively large contribution of the orbital moment. The direction of the moment is close to the direction of the Co–N(pyridine) bond, which confirms literature ab initio calculations. We show that dipolar interactions are mainly responsible for the magnetic interchain coupling.

Let $\alpha$ be an irrational real number. We show that the set of $\epsilon$-badly approximable numbers \[ \mathrm{Bad}^\varepsilon (\alpha) := \{x\in [0,1]\, : \, \liminf_{|q| \to \infty} |q| \cdot \| q\alpha -x \| \geq \varepsilon \} \] has full Hausdorff dimension for some positive $\epsilon$ if and only if $\alpha$ is singular on average. The condition is equivalent to the average $\frac{1}{k} \sum_{i=1, \cdots, k} \log a_i$ of the logarithms of the partial quotients $a_i$ of $\alpha$ going to infinity with $k$. We also consider one-sided approximation, obtain a stronger result when $a_i$ tends to infinity, and establish a partial result in higher dimensions., Comment: 16 pages

In this paper, we study the dimension theory of a class of piecewise affine systems in euclidean spaces suggested by Michael Barnsley, with some applications to the fractal image compression. It is a more general version of the class considered in the work of Keane, Simon and Solomyak [The dimension of graph directed attractors with overlaps on the line, with an application to a problem in fractal image recognition. {\it Fund. Math.}, {\bf 180}(3):279-292, 2003] and can be considered as the continuation of the works [On the dimension of self-affine sets and measures with overlaps. {\it Proc. Amer. Math. Soc.}, {\bf 144}(10):4427-4440, 2016], [On the dimension of triangular self-affine sets. {\it Erg. Th. \& Dynam. Sys.}, to appear.] by the authors. We also present some applications of our results for the generalized Takagi functions and fractal interpolation functions.

Reaction of Ni(NCS)

Reaction of cobalt thiocyanate with 4-acetylpyridine leads to the formation of [Co(NCS)2(4-acetylpyridine)2]n (3/I). In its crystal structure the Co cations are connected by pairs of μ-1,3-bridging thiocyanato ligands into dimers that are further connected into layers by single anionic ligands. DTA-TG measurements of Co(NCS)2(4-acetyl-pyridine)4 (1) led to the formation of 3/I. In contrast, when the hydrate Co(NCS)2(4-acetyl-pyridine)2(H2O)2 (2) is decomposed, a mixture of 3/I and a thermodynamically metastable form 3/II is obtained. Further investigations reveal that thermal annealing of 2 leads to the formation of 3/II, that contains only traces of the stable form 3/I. DSC and temperature dependent X-ray powder diffraction (XRPD) measurements prove that 3/II transforms into 3/I on heating. The crystal structure of 3/II was determined ab initio from XRPD data. In its crystal structure the Co cations are linked by pairs of bridging thiocyanato anions into a 1D coordination polymer, and thus, 3/II is an isomer of 3/I. Magnetic measurements disclose that the stable form 3/I only shows paramagnetism without any magnetic anomaly down to 2 K. In contrast, the metastable form 3/II shows ferromagnetic behavior. The phase transition into ordered state at Tc = 3.8 K was confirmed by specific heat measurements. Alternating current susceptibility measurements show frequency dependent maxima in χ' and χ″, which is indicative for a slow relaxation of the magnetization.

Reaction of Co(NCS)2 and Ni(NCS)2 with 4-acetylpyridine under different conditions leads to the formation of mixed crystals of the layered compound with the composition [CoxNi1–x(NCS)2(4-acetylpyridine)2]n (x = 0.15 0.3, 0.5, and 0.7). Mixed crystal formation was investigated by a combination of X-ray powder diffraction (XRPD), atomic absorption spectroscopy (AAS), simultaneous scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDX), differential scanning calorimetry (DSC), and magnetic and heat capacity measurements. Dependent on the synthetic method, homo- or heterogeneous mixed crystals were obtained as already indicated by XRPD, where significant differences to the pattern of physical mixtures of the homometallic counterparts [M(NCS)2(4-acetylpyridine)2]n with M = Co or Ni) with the same Co/Ni ratio are observed. Mixed crystals can also be obtained from physical mixtures under thermodynamic control, indicating that they are more stable than the homometallic compounds. This is...

Reaction of Ni(NCS)2 with 4-aminopyridine in different solvents leads to the formation of compounds with the compositions Ni(NCS)2(4-aminopyridine)4 (1), Ni(NCS)2(4-aminopyridine)2(H2O)2 (2), [Ni(N...

The complexes of paramagnetic lanthanide(3+) ions (Gd3+,Tb3+) with 3-pyridone molecules combined in an aqueous solution with paramagnetic hexacyanidochromate(III) metalloligands led to the formation of two novel crystalline {[LnIII(3-pyridone)2(H2O)4][CrIII(CN)6]}·H2O (Ln = Gd, 1; Ln = Tb, 2) materials. They are composed of bimetallic Ln–Cr cyanido-bridged zig-zag chains which are further tightly connected by the rich system of hydrogen bonds involving terminal cyanides, water molecules and 3-pyridone ligands. Both 1 and 2 have a very weak yellowish colour as their strong absorption, related to the d–d transitions of the cyanide Cr(III) complex and 3-pyridone ligands, is moved to the UV range. 1 and 2 exhibit Ln–Cr antiferromagnetic exchange mediated within the coordination chains by molecular cyanide bridges. The magnetic susceptibility for the GdIII–CrIII 7/2–3/2 spin alternating chains of 1 was successfully analysed using quantum Monte Carlo simulations, giving a magnetic coupling constant, J, of −0.82 K. The additional interchain magnetic interactions ensured by the hydrogen bonding network result in the low temperature phase transition to the magnetically ordered state. Magnetic heat capacity measurements showed that 1, which has isotropic Gd(III) spin centers, becomes a molecule-based magnet below 1.06 K, while 2, bearing the highly anisotropic Tb(III), shows a higher critical temperature of 1.61 K. Thus, we show and discuss the crucial role of the non-covalent interactions in the induction of magnetic ordering for low dimensional cyanido-bridged coordination systems, and the positive impact of magnetic anisotropy on the strengthening of magnetic interactions.

The mass transference principle, proved by Beresnevich and Velani in 2006, is a strong result that gives lower bounds for the Hausdorff dimension of limsup sets of balls. We present a version for limsup sets of open sets of arbitrary shape., Comment: 13 pages

An alternating bimetallic {(H3O)[Ni(III)(cyclam)][Fe(II)(CN)6]·5H2O}n chain undergoes reversible dehydration at 40 °C accompanied by electron transfer which leads to Ni(II)-Fe(III) in about 50% of metal centres. The hydrated dark blue form is a paramagnet while the dehydrated yellowish-green form shows ferromagnetic coupling between neighbouring Ni(II) and Fe(III).

A series of carbonato-bridged heteronuclear NiII2LnIII2 complexes 2[(μ4-CO3)2{NiLn(L)(MeOH)(CH3COO)}2]·9H2O·8MeOH (Ln = Tb (1), Dy (2), Ho (3), Er, (4)), [(μ4-CO3)2{NiLn(L)(MeOH)(CH3COO)}2]·2H2O·4MeOH (Ln = Tm (5)) and [(μ4-CO3)2{NiLn(L)(MeOH)(CH3COO)}2]·4MeOH (Ln = Yb (6), Lu(7)) with N,N′-bis(5-bromo-3-methoxysalicylidene)propylene-1,3-diamine (L) are reported. The complexes were obtained by a one-pot reaction with spontaneous fixation of atmospheric CO2 into the coordination species during crystallization process. In each complex the NiII2LnIII2 metal core has a similar topology. The hexadentate Schiff base ligands chelate the Ni(II) and Ln(III) ions forming two binuclear units, that are linked by two CO32− ions giving a carbonato bridged (μ4-CO3)2{NiIILnIII}2 structures. Ferromagnetic interactions between 3d–4f metal centers have been observed for compounds 1 and 2. In complexes 3–6 both the isotropic exchange as well as of thermal depopulation of mJ sublevels and magnetic anisotropy are observed. In compound 7, due to the nonmagnetic nature of the ground state of Lu(III) ions, only a weak antiferromagnetic interaction between Ni(II) ions occurs.