Bonner-Fisher Model Research Articles

Stabilization of Short‐ and Long‐Range Magnetic Ordering through the Cooperative Effect of 1D [CuO4]∞ Chains and [CuO2X2] Quadrilateral in Quasi‐1D Spin‐1/2 Systems

AbstractQuasi‐1D chain antiferromagnets with reduced structural dimensionality are a rich playground for investigating novel quantum phenomena. We report the synthesis, crystal structure, and magnetism of two novel quasi‐1D antiferromagnets, β‐PbCu2(TeO3)2Cl2 (I) and PbCu2(TeO3)2Br2 (II). Their magnetic frameworks are constructed via Cu‐based quasi‐1D [Cu(2)O4]∞ zigzag chains with square‐planar [Cu(1)O2X2] (X=Cl or Br) separated among 1D chains. Specific heat measurements show λ peaks at ~9 K and ~19 K for I and II, respectively. Moreover, both broad maximums (χmax=90 K for I and 80 K for II) and small kinks (TN≈9 K for I and 19 K for II) have been observed in magnetic susceptibility measurements of I and II. Bonner–Fisher model fitting, and theoretical analyses were performed to evaluate the magnetic exchange interactions. Our experimental and theoretical results and structure‐properties relationship analysis reveal the coexistence of short‐ and long‐range magnetic ordering from the cooperative effect of 1D [CuO4]∞ chains and [CuO2X2] quadrilateral.

Stabilization of Short- and Long-Range Magnetic Ordering through the Cooperative Effect of 1D [CuO4]∞ Chains and [CuO2X2] Quadrilateral in Quasi-1D Spin-1/2 Systems.

Quasi-1D chain antiferromagnets with reduced structural dimensionality are a rich playground for investigating novel quantum phenomena. We report the synthesis, crystal structure, and magnetism of two novel quasi-1D antiferromagnets, β-PbCu2(TeO3)2Cl2 (I) and PbCu2(TeO3)2Br2 (II). Their magnetic frameworks are constructed via Cu-based quasi-1D [Cu(2)O4]∞ zigzag chains with square-planar [Cu(1)O2X2] (X=Cl or Br) separated among 1D chains. Specific heat measurements show λ peaks at ~9 K and ~19 K for I and II, respectively. Moreover, both broad maximums (χmax=90 K for I and 80 K for II) and small kinks (TN≈9 K for I and 19 K for II) have been observed in magnetic susceptibility measurements of I and II. Bonner-Fisher model fitting, and theoretical analyses were performed to evaluate the magnetic exchange interactions. Our experimental and theoretical results and structure-properties relationship analysis reveal the coexistence of short- and long-range magnetic ordering from the cooperative effect of 1D [CuO4]∞ chains and [CuO2X2] quadrilateral.

Structure and Magnetic Properties of Pseudo-1D Chromium Thiolate Coordination Polymers

The synthesis, structure, and magnetic properties of two novel, pseudo-one-dimensional (1D) chromium thiolate coordination polymers (CPs), CrBTT and Cr2BDT3, are reported. The structures of these materials were determined using X-ray powder diffraction revealing highly symmetric 1D chains embedded within a CP framework. The magnetic coupling of this chain system was measured by SQUID magnetometry, revealing a switch from antiferromagnetic to ferromagnetic behavior dictated by the angular geometrical constraints within the CP scaffold consistent with the Goodenough-Kanamori-Anderson rules. Intrachain magnetic coupling constants JNN of -32.0 and +5.7 K were found for CrBTT and Cr2BDT3, respectively, using the 1D Bonner-Fisher model of magnetism. The band structure of these materials has also been examined by optical spectroscopy and density functional theory calculations revealing semiconducting behavior. Our findings here demonstrate how CP scaffolds can support idealized low-dimensional structural motifs and dictate magnetic interactions through tuning of geometry and inter-spin couplings.

Quantum antiferromagnet bluebellite comprising a maple-leaf lattice made of spin- 1/2Cu2+ ions

Spin-1/2 maple-leaf lattice antiferromagnets are expected to show interesting phenomena originating from frustration effects and quantum fluctuations. We report the hydrothermal synthesis of a powder sample of bluebellite ${\mathrm{Cu}}_{6}\mathrm{I}{\mathrm{O}}_{3}{(\mathrm{OH})}_{10}\mathrm{Cl}$ as a first potential candidate. Magnetization and heat capacity measurements reveal moderate frustration with a Curie-Weiss temperature of $--35\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, and a magnetic transition at ${T}_{N}=17\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. Surprisingly, the magnetic susceptibility and heat capacity above ${T}_{N}$ are well reproduced by the Bonner-Fisher model, which suggests that a one-dimensional spin correlation with a magnetic interaction of 25 K occurs in the apparently two-dimensional lattice. This emergent one-dimensionality cannot be explained by orbital ordering or dimensional reduction due to geometrical frustration. We believe that there is an unknown mechanism to cause one-dimensionality in the spin-1/2 maple-leaf lattice antiferromagnet.

Study on imidazolate-bridged divalent copper ion complexes capped with tris(1-pyrazolyl)methane

Four kinds of non-substituted imidazolate(im)-bridged copper(II) complexes using tris(1-pyrazolyl)methane (pz3CH) as a capping ligand, namely, [Cu(μ-im)(pz3CH)]nXn (X=BF4 (1), ClO4 (2), CF3SO3 (3), (SO4)0.5 (4)) were prepared. Their crystal structures have been determined, and despite the different space groups (orthorhombic Pna21 for 1–3 and monoclinic P21/n for 4) and the variety of counter anions, they consist of equally-spacing polymeric chains. The Cu ion in 1–3 has a quasi-six-coordination environment, while the Cu ion in 4 has a nearly five-coordination one. The Bonner-Fisher model gave the exchange coupling parameters 2J/kB=−98.2(16), −106.6(10), −102.0(6), and −104.2(8) K for 1–4, respectively. The strong exchange couplings originate in the equatorial coordination of the Nim atoms. We revealed that the magnitude of J values is influenced by the counter anion. The usability of the neutral pz3CH capping ligand as well as anionic pz3BH− has been shown.

Low temperature, high magnetic field investigations of the nature of magnetism in the molecular semiconductor β- cobalt phthalocyanine (C32H16CoN8)

Results from detailed investigations of the magnetic properties of a powder sample of β-CoPc for the temperatures T=0.4K to 300K and in magnetic fields H up to 90kOe are reported. X-ray diffraction confirmed the β-phase and scanning electron microscopy showed plate-like morphology of the sample. For T>3K, the data of magnetic susceptibility χ vs. T fit the Curie–Weiss (CW) law yielding θ=−2.5K, µ=2.16µB per Co2+ and g=2.49 for spin S=1/2 of the low spin-state of Co2+. However for T<3K, the χ vs. T data deviates from the CW law yielding a peak in χ at Tmax=1.9K. It is shown that the χ vs. T data from 0.4K to 300K fits well with the predictions of the Bonner–Fisher (BF) model for S=1/2 Heisenberg linear chain antiferromagnet with the Co2+–Co2+ exchange J/kB = −1.5K (Ĥ=−2J Σ Si•Si+1). The data of magnetization M vs. H at T=1K agrees with the predictions of the BF model with J/kB=−1.5K, yielding saturation magnetization MS=12.16emu/g above 60kOe corresponding to complete alignment of the spins.

Magnetic Determination of the Electronic State of Cu and Exchange Interactions in the $\alpha $ - and $\beta $ -Phases of Molecular Semiconductor Copper Phthalocyanine (C32H16N8Cu)

Using the analysis of the magnetization data in the $\alpha $ - and $\beta $ -phases of copper phthalocyanine (CuPc) samples, the electronic state of Cu and exchange interactions are reported. After verifying the crystal structure of the powder samples using X-ray diffraction, the temperature dependence (2–250 K) of the magnetization $M$ of both samples was measured in magnetic field $H=1$ kOe and isothermally at 2 and 5 K in $H$ up to 90 kOe. The data were analyzed first using the modified Curie-Weiss law, $\chi = \chi _{o}+ C/(T+\theta )$ , showing good fit for $T >4$ K and yielding $\theta =2.3$ K (0.2 K) for $\alpha $ -CuPc ( $\beta $ -CuPc) and spin $S=1/2$ characteristic of Cu2+. The data were next fitted to the Bonner-Fisher model for $S=1/2$ antiferromagnetic Heisenberg chain showing an excellent fit to all the $M$ versus $T$ data and yielding the Cu2+–Cu2+ exchange constant $J/k_{B}=3.4$ K (0.4 K) for the $\alpha $ -CuPc ( $\beta $ -CuPc). The isothermal data of $M$ versus $H$ are analyzed taking exchange coupling into account. The large difference in the magnitudes of $J/k_{B}$ for the two phases is discussed in terms of the differences in their crystal structures.

Magnetic Orderings in Li2Cu(WO4)2 with Tungstate-Bridged Quasi-1D Spin-1/2 Chains.

By both experimental measurements and theoretical calculations, we investigated the magnetic and electronic properties of Li2Cu(WO4)2 as a tungstate-bridged quasi-one-dimensional (1D) copper spin-(1/2) chain system. Interestingly, magnetic susceptibility χ(T) and specific heat measurements show that the system undergoes a three-dimensional antiferromagnetic (AF)-like ordering at TN ≈ 3.7 K, below a broad χ(T) maximum at ∼8.9 K indicating a low-dimensional short-range AF spin correlation. Bonner-Fisher model fitting of χ(T) leads to an AF intrachain exchange constant of J/kB = 15.8 ± 0.1 K, and mean-field theory estimation gives an interchain coupling constant of J⊥/kB = 1.6 K, which supports the quasi-1D nature of this spin system. Theoretical evaluation of exchange coupling constants within the generalized gradient approximation (GGA) plus on-site Coulomb interaction (U) shows that the dominant AF exchange interaction is of ∼13.9 K along the a-axis with weak interchain coupling, in agreement with the experimental result of a quasi-1D spin-(1/2) chain system. The GGA+U calculations also predict that Li2Cu(WO4)2 is a charge transfer-type AF semiconductor with a direct band gap of 1.5 eV.

Structures and magnetic properties of three compounds from imidazolate-bridged copper(II) pyrazolylborate complexes

Three kinds of imidazolate-bridged copper(II) complexes using pz3BH anion as a capping ligand, namely, [Cu4(μ-im)4(pz3BH)4][Cu(pz3BH)2]2 (1), polymorphic [Cu4(μ-im)4(pz3BH)4] (1t), and [Cu(μ-im)(pz3BH)]n (1p) were afforded (Him=imidazole; pz3BH=hydrotris(1-pyrazolyl)borate). Their crystal structures were determined to reveal that 1 and 1t involve a tetranuclear macrocycle while 1p consists of a polymeric chain. The im nitrogen atoms occupied the copper equatorial positions. The magnetic susceptibility measurements showed that the im bridges played the role of an antiferromagnetic coupler. The Bonner–Fisher model with the Heisenberg spin Hamiltonian as H=−Σ 2JSi·Si+1 gave 2J/kB=−115.5(6)K for 1p. The magnitude of the present interaction belongs to the largest class, when compared with those of the known im-bridged copper(II) complexes.

Molecular motion in pyridazinium/crown ether supramolecular cation salts of a nickel dithiolene complex

Supramolecular cations formed by monoprotonated pyridazinium cations and cis-anti-cis-dicyclohexano[18]-crown-6 (DCH[18]-crown-6) or dibenzo[18]-crown-6 (DB[18]-crown-6) were introduced into [Ni(dmit)2]− salts (where dmit2− = 2-thione-1,3-dithiole-4,5-dithiolate). X-ray crystal structure analysis of (pyridazinium+)(DCH[18]-crown-6)[Ni(dmit)2]− (1) revealed a chair-type conformation of the DCH[18]-crown-6 moiety. A V-shaped conformation of the DB[18]-crown-6 moiety was observed in (pyridazinium+)(DB[18]-crown-6)2[Ni(dmit)2]−(H2O)2 (2). Nitrogen atoms in the pyridazinium cations interacted with the oxygen atoms of the DCH[18]-crown-6 and DB[18]-crown-6 through N–H+O hydrogen bonds, forming 1:1 and 1:2 supramolecular structures, respectively. Sufficient space for molecular motions of the pyridazinium cations, namely flip-flop and in-plane rotations, exists in salt 1. Disorder in nitrogen atoms was observed by X-ray analysis, indicating dynamic motion of the pyridazinium cation, namely flip-flop motion and in-plane motion. A potential energy calculation further supported the possibility of dynamic motion of cations in the crystal. By contrast, the flip-flop motion of the pyridazinium group in salt 2 is restricted by the two nearest-neighbouring DB[18]-crown-6 molecules. Weak antiferromagnetic intermolecular interactions between the [Ni(dmit)2]− anions in the two-dimensional layers of salt 1 were observed, resulting in alternating antiferromagnetic Heisenberg chain-type magnetic susceptibility. Quasi-one-dimensional intermolecular interactions between the [Ni(dmit)2]− anions were observed in salt 2, whose magnetic behaviour followed the Bonner–Fisher model.

Structural diversity and magnetic properties of five copper–organic frameworks containing one-, two-, and three-types of organic ligands

Five novel compounds {[Cu(CMA)]·0.8H(2)O}(n) (1), {[Cu(CMA)(bpy)(0.5)]·0.5DMF}(n) (2), {[Cu(CMA)(bpy)(H(2)O)]·0.5H(2)O}(n) (3), {[Cu(2)(CMA)(DPA)(bpy)(2)(H(2)O)]ClO(4)}(n) (4) and {[Cu(3)(CMA)(DPA)(bpy)(4)(OH)](ClO(4))(2)·3H(2)O)}(n) (5) (H(2)CMA = 3-(carboxymethoxy)-5-methylbenzoic acid, HDPA = 2-(3,5-dimethylphenoxy)acetic acid, bpy = 4,4'-bipyridine) were synthesized and characterized by single crystal X-ray diffraction. Interestingly, the kinds of ligands included in these compounds are different: 1 contains single-ligand CMA(2-); 2 and 3 comprise two kinds of ligands (CMA(2-) and bpy); 4 and 5 cover three kinds of ligands (CMA(2-), DPA(-) and bpy). Structural analyses reveal that 1-3, and 5 are three-dimensional (3D) frameworks, while 4 is a 2D layer. Noteworthily, 1 possesses two types of channels: six-star and hexagonal ones. 3 displays a three-fold interpenetrating 3D framework. The structural diversity of the compounds may have originated from different anions, solvents and temperatures. Variable-temperature magnetic susceptibility measurements were carried out on compounds 1, 2 and 4, and the magnetic properties are dramatically different due to the structural diversities. The magnetic data of 1 shows an antiferromagnetic interaction with J = -54.84 cm(-1) estimated from the Bonner-Fisher model. The magnetic data of 2 was least-square fitted to the Blenaey-Bowers equation with J = -131.01 cm(-1), indicating the existence of a strong antiferromagnetic interaction between two adjacent Cu(2+). The magnetic data of linear tetranuclear structure 4 was best fitted to the expression derived from the Hamiltonian H = -2(2J(1)S(1)S(2) + J(2)S(1)S(1*)). The best fitting parameters are J(1) = -17.48 cm(-1) and J(2) = -65.26 cm(-1), which also indicate an antiferromagnetic interaction. Simultaneously, the magneto-structural relationship was discussed.

Quantification of entanglement from magnetic susceptibility for a Heisenberg spin 1/2 system

We report temperature and magnetic field dependent magnetization and quantification of entanglement from the experimental data for dichloro (thiazole) copper (II), a Heisenberg spin chain system. The plot of magnetic susceptibility vs. temperature indicates an infinite spin chain. Isothermal magnetization measurements (as functions of magnetic field) were performed at various temperatures below the antiferromagnetic (AFM) ordering, where the AFM correlations persist significantly. These magnetization curves are fitted to the Bonner–Fisher model. Magnetic susceptibility is used as an entanglement witness to quantify the amount of entanglement in the system.

Synthesis, Structure and Solid State Properties of Cyclohexanemethylamine Substituted Phenalenyl Based Molecular Conductor

We report the preparation, crystallization and solid state characterization of a cyclohexanemethylamine substituted spirobiphenalenyl radical; in the solid state the compound is iso-structural with its dehydro-analog (benzylamine-substitued compound), and the molecules packed in a one-dimensional fashion that we refer to as a π-step stack. Neighboring molecules in the stack interact via the overlap of one pair of active (spin bearing) carbon atoms per phenalenyl unit. The magnetic susceptibility measurement indicates that in the solid state the radical remains paramagnetic and the fraction of Curie spins is 0.75 per molecule. We use the analytical form of the Bonner-Fisher model for the S = 1/2 antiferromagnetic Heisenberg chain of isotropically interacting spins with intrachain spin coupling constant J = 6.3 cm−1, to fit the experimentally observed paramagnetism [χp (T)] in the temperature range 4–330 K. The measured room temperature conductivity (σRT = 2.4 × 10–3 S/cm) is comparable with that of the iso-structural benzyl radical, even though the calculated band dispersions are smaller than that of the unsaturated analog.

Supramolecular approach to the formation of magneto-active physical gels

Magnetic fibers were obtained through self-assembly of a nitroxide radical gelator derived from an L-isoleucine-based scaffold. Spins in the fibers are aligned one-dimensionally due to the parallel β-sheet conformation of the intermolecular hydrogen bonds. The spin nanowires exhibit magnetic behavior reproducible by the Bonner–Fisher model.

Silver(ii) triflate with one-dimensional [Ag(ii)(SO3CF3)4/2]∞ chains hosting antiferromagnetism

Silver(II) triflate, previously reported by Leung et al. in 1979 (Can. J. Chem., 1979, 57, 326–329), crystallizes in a triclinic P cell with a = 4.9117(11) A, b = 5.1136(10) A, c = 11.033(3) A, α = 79.955(14)°, β = 75.771(16)°, γ = 61.571(17)° and V = 235.68(10) A3 and is isomorphous to Cu(SO3CF3)2. The compound has a layered structure with an interlayer separation of 10.67 A; the van der Waals gaps open between the CF3 groups from neighbouring sheets. Ag(II) is coordinated by six O atoms in the form of an elongated octahedron; the adjacent Ag2+ cations are linked via –OSO– bridges; direct –O– bridges are absent. The [Ag(II)(SO3CF3)2]∞ layers consist of one-dimensional chains which interact weakly with each other via longer Ag⋯OSO–Ag contacts. This results in a 1D rather than 2D antiferromagnetic ordering, which can be described via the Bonner–Fisher model with a superexchange constant, Jintra-chain, of 104 K (9.0 meV) per pair of interacting Ag2+ cations. The magnetic ordering persists even at room temperature leading to a broad ESR signal with g = 2.199. DFT calculations confirm the 1D character of electronic structure and antiferromagnetism residing within the [Ag(II)(SO3CF3)4/2]∞ chains with a |Jinter-chain|/|Jintra-chain| ratio of ∼10−3 to 10−2. The calculated indirect bandgap at the Fermi level of ∼1 eV opens between rather flat valence and conduction bands, which are predominated by contributions from Ag and O atoms. Ag(SO3CF3)2 is extremely sensitive to moisture and decomposes instantly when exposed to atmosphere. When dry, it rapidly decomposes thermally above 120 °C, but its slow exothermic decay to AgSO3CF3 takes place even at room temperature. Silver(II) triflate is also photosensitive and irradiating it with a 632.8 nm laser radiation at a power greater than 0.17 mW leads to its decomposition to Ag(I) triflate and Ag(I)2S2O7.

Analysis on the exchange interactions in three metal-organic coordination network systems possessing one-dimensional magnetism

The nature of the exchange interactions in three metal-organic coordination networks families is examined. These families have a general form ML2(bpy). Since (bpy) molecules are very long, our networks are reduced to effectively one-dimensional chain systems with very weak interchain interaction. The Bonner–Fisher and Fisher classical spin models are applied to fit the magnetic susceptibility data, and results of the fits are discussed. Metal ions inside MCl2(bpy) and M(N3)2(bpy) interact with ferromagnetic interactions and can be described with Fisher classical spin model, while metal ions in M(ox)(bpy) interact with antiferromagnetic interaction and it can be described with the Bonner–Fisher model. Fitting parameter J produced from our models has higher value in M(N3)2(bpy) than in MCl2(bpy) for the same M. It was found that the total spin value is dominant factor to the strength of the magnetic interaction.

Structures and magnetic properties of imidazolate-bridged tetranuclear and polymeric copper(II) complexes

Eight kinds of imidazolate-bridged copper(II) complexes were found to be classified into two categories from the magnetic properties. The crystal structures of [Cu(L)(μ-im)] n (Him = imidazole; L = nonane-4,6-dionate, 2,6-dimethylheptane-3,5-dionate) and [Cu(L)(μ-im)] 4 (L = nonane-4,6-dionate, 1-phenylbutane-1,3-dionate) were determined, to reveal that they consist of polymeric chains and tetranuclear cycles, respectively. Note that the nonane-4,6-dionate derivative gave the two phases. The Bonner–Fisher model (a one-dimensional antiferromagnetic chain model) was plausibly applied to [Cu(L)(μ-im)] n for the best fit, while a square model was to [Cu(L)(μ-im)] 4. The complexes with unknown crystal structures were also subjected to magnetic measurements, and the tetra- and polymeric structures could be clearly distinguished from each other by fitting the magnetic data to appropriate models. The exchange parameters were comparable for both series (2 J/ k B = −78 to −97 K) because the structurally common bridges Cu–N(eq)–N(eq)–Cu afford comparable magnitudes of couplings.

Alcoholysis/hydrolysis of 1,1′-carbonyldiimidazole as a means of preparing unprecedented, imidazole-containing one-dimensional coordination polymers of copper(II)

The use of 1,1'-carbonyldiimidazole, (im)(2)CO, for the synthesis of imidazolate (im(-)) and/or imidazole (Him)-containing copper(II) coordination polymers is described. The [Cu(2)(O(2)CMe)(4)(H(2)O)(2)]/(im)(2)CO reaction system in EtOH yields the new polymeric species [Cu(O(2)CMe)(im)(Him)(EtOH)](n) () and the known compound [Cu(im)(2)](n) (), depending on the reaction conditions. A mechanism for the alcoholysis/hydrolysis of (im)(2)CO is proposed. Complex comprises neutral, zigzag chains with the eta(1):eta(1):mu im(-) ligand bridging two neighbouring Cu(II) atoms. Each square pyramidal metal centre is coordinated to two imidazolate nitrogen atoms, the pyridine-type nitrogen atom of the terminal imidazole ligand, one acetate oxygen atom and the ethanol oxygen atom. The dc magnetic susceptibility data for have been analysed according to the Bonner-Fisher model for an equally spaced S = 1/2 chain, revealing moderate antiferromagnetic Cu(II)Cu(II) exchange interactions (J = -33.5 cm(-1) using the H = -2J summation operatorS(i)S(i+1) spin Hamiltonian). The reaction system Cu(NO(3))(2).3H(2)O/(im)(2)CO in EtOH leading to the preparation of known trans-[Cu(NO(3))(2)(Him)(4)] () is also described. With terephthalate(-2) (tp(2-)), instead of MeCO(2)(-), in MeOH/H(2)O the product is the new, 1D linear coordination polymer [Cu(tp)(Him)(2)(H(2)O)](n).2nH(2)O (.2nH(2)O). Adjacent square pyramidal Cu(II) atoms are singly bridged by the bis-monodentate tp(2-) ligand, while two monodentate Him groups and one H(2)O molecule complete five-coordination at each metal centre. The chains of and .2nH(2)O form interesting, hydrogen-bonded 3D networks. The combined work demonstrates the usefulness of (im)(2)CO in the preparation of interesting Cu(II) coordination polymers which can not be obtained by the use of Him.

The competing roles of topology and spin density in the magnetic behavior of spin-delocalized radicals: Donor–acceptor annelated nitronyl nitroxides

The effects of acceptor–donor interactions in thienyl substituted benzimidazole-nitronyl nitroxides (TBNN) on the absorption spectroscopy, spin density distribution, magnetic behavior, and crystallographic packing were explored through spectroscopy, computation, and characterization of structure and magnetic properties in the crystalline phase. The electronic spectra of the radicals exhibit a strong broad absorption in the NIR ( λ max ∼ 1000 nm) that exhibits solvatochromism consistent with charge transfer between the thienyl (donor) and benzonitronyl nitroxide (acceptor) dyads. Computational analysis allowed assignment of the transition as a HOMO–SOMO transition (TD-DFT UB3LYP/6-31G∗∗). The TBNN radicals form highly disordered slipped π-stacks in the solid state that give rise to antiferromagnetic interactions consistent with 1D chain interactions. The magnetic behavior was well-fit to a Bonner–Fisher model to give exchange parameters of J = −2 to −10 cm −1 depending on substitution. The weak exchange parameters are attributed to the degree of solid-state disorder, and the observed properties can be rationalized by the effects of substitution on the electronic structure and topology of the radicals.

Structure-dependent exchange in the organic magnets Cu(II)Pc and Mn(II)Pc

We study exchange couplings in the organic magnets copper(II) phthalocyanine [Cu(II)Pc] and manganese(II) phthalocyanine [Mn(II)Pc] by a combination of Green's function perturbation theory and ab initio density-functional theory (DFT). Based on the indirect exchange model, our perturbation-theory calculation of Cu(II)Pc qualitatively agrees with the experimental observations. DFT calculations performed on Cu(II)Pc dimer show a very good quantitative agreement with exchange couplings that our theoretical group extracts by using a global fitting for the magnetization measurements to a spin-$\frac{1}{2}$ Bonner-Fisher model. These two methods give us remarkably consistent trends for the exchange couplings in Cu(II)Pc when changing the stacking angles. The situation is more complex for Mn(II)Pc owing to the competition between superexchange and indirect exchange.