Magneto-structural Correlations in Ni2+-Halide···Halide-Ni2+ Chains.

We present the magnetic properties of a new family of S = 1 molecule-based magnets, NiF2(3,5-lut)4·2H2O and NiX2(3,5-lut)4, where X = HF2, Cl, Br, or I (lut = lutidine C7H9N). Upon creation of isolated Ni-X···X-Ni and Ni-F-H-F···F-H-F-Ni chains separated by bulky and nonbridging lutidine ligands, the effect that halogen substitution has on the magnetic properties of transition-metal-ion complexes can be investigated directly and in isolation from competing processes such as Jahn-Teller distortions. We find that substitution of the larger halide ions turns on increasingly strong antiferromagnetic interactions between adjacent Ni2+ ions via a novel through-space two-halide exchange. In this process, the X···X bond lengths in the Br and I materials are more than double the van der Waals radius of X yet can still mediate significant magnetic interactions. We also find that a simple model based on elongation/compression of the Ni2+ octahedra cannot explain the observed single-ion anisotropy in mixed-ligand compounds. We offer an alternative that takes into account the difference in the electronegativity of axial and equatorial ligands.

Linear-in temperature resistivity from an isotropic Planckian scattering rate.

A variety of 'strange metals' exhibit resistivity that decreases linearly with temperature as the temperature decreases to zero1-3, in contrast to conventional metals where resistivity decreases quadratically with temperature. This linear-in-temperature resistivity has been attributed to charge carriers scattering at a rate given by h/τ = αkBT, where α is a constant of order unity, h is the Planck constant and kB is the Boltzmann constant. This simple relationship between the scattering rate and temperature is observed across a wide variety of materials, suggesting a fundamental upper limit on scattering-the 'Planckian limit'4,5-but little is known about the underlying origins of this limit. Here we report a measurement of the angle-dependent magnetoresistance of La1.6-xNd0.4SrxCuO4-a hole-doped cuprate that shows linear-in-temperature resistivity down to the lowest measured temperatures6. The angle-dependent magnetoresistance shows a well defined Fermi surface that agrees quantitatively with angle-resolved photoemission spectroscopy measurements7 and reveals a linear-in-temperature scattering rate that saturates at the Planckian limit, namely α = 1.2 ± 0.4. Remarkably, we find that this Planckian scattering rate is isotropic, that is, it is independent of direction, in contrast to expectations from 'hotspot' models8,9. Our findings suggest that linear-in-temperature resistivity in strange metals emerges from a momentum-independent inelastic scattering rate that reaches the Planckian limit.

Controlling Magnetic Anisotropy in a Zero-Dimensional S = 1 Magnet Using Isotropic Cation Substitution.

The [Zn1-xNix(HF2)(pyz)2]SbF6 (x = 0.2; pyz = pyrazine) solid solution exhibits a zero-field splitting (D) that is 22% larger [D = 16.2(2) K (11.3(2) cm-1)] than that observed in the x = 1 material [D = 13.3(1) K (9.2(1) cm-1)]. The substantial change in D is accomplished by an anisotropic lattice expansion in the MN4 (M = Zn or Ni) plane, wherein the increased concentration of isotropic Zn(II) ions induces a nonlinear variation in M-F and M-N bond lengths. In this, we exploit the relative donor atom hardness, where M-F and M-N form strong ionic and weak coordinate covalent bonds, respectively, the latter being more sensitive to substitution of Ni by the slightly larger Zn(II) ion. In this way, we are able to tune the single-ion anisotropy of a magnetic lattice site by Zn-substitution on nearby sites. This effect has possible applications in the field of single-ion magnets and the design of other molecule-based magnetic systems.

SquidLab-A user-friendly program for background subtraction and fitting of magnetization data.

We present an open-source program free to download for academic use with a full user-friendly graphical interface for performing flexible and robust background subtraction and dipole fitting on magnetization data. For magnetic samples with small moment sizes or sample environments with large or asymmetric magnetic backgrounds, it can become necessary to separate background and sample contributions to each measured raw voltage measurement before fitting the dipole signal to extract magnetic moments. Originally designed for use with pressure cells on a Quantum Design MPMS3 SQUID magnetometer, SquidLab is a modular object-oriented platform implemented in Matlab with a range of importers for different widely available magnetometer systems (including MPMS, MPMS-XL, MPMS-IQuantum, MPMS3, and S700X models) and has been tested with a broad variety of background and signal types. The software allows background subtraction of baseline signals, signal preprocessing, and performing fits to dipole data using Levenberg-Marquardt non-linear least squares or a singular value decomposition linear algebra algorithm that excels at picking out noisy or weak dipole signals. A plugin system allows users to easily extend the built-in functionality with their own importers, processes, or fitting algorithms. SquidLab can be downloaded, under Academic License, from the University of Warwick depository (wrap.warwick.ac.uk/129665).

Magnetic order and enhanced exchange in the quasi-one-dimensional molecule-based antiferromagnet Cu(NO3)2(pyz)3.

The quasi-one-dimensional molecule-based Heisenberg antiferromagnet Cu(NO3)2(pyz)3 has an intrachain coupling J = 13.7(1) K () and exhibits a state of long-range magnetic order below TN = 0.105(1) K. The ratio of interchain to intrachain coupling is estimated to be |J'/J| = 3.3 × 10-3, demonstrating a high degree of isolation for the Cu chains.

Field-induced canting of magnetic moments in GdCo5 at finite temperature: first-principles calculations and high-field measurements.

We present calculations and experimental measurements of the temperature-dependent magnetization of a single crystal of GdCo5 in magnetic fields of order 60 T. At zero temperature the calculations, based on density-functional theory in the disordered-local-moment picture, predict a field-induced transition from an antiferromagnetic to a canted alignment of Gd and Co moments at 46.1 T. At higher temperatures the calculations find this critical field to increase along with the zero-field magnetization. The experimental measurements observe this transition to occur between 44-48 T at 1.4 K. Up to temperatures of at least 100 K, the experiments continue to observe the transition; however, at variance with the calculations, no strong temperature dependence of the critical field is apparent. We assign this difference to the inaccurate description of the zero-field magnetization of the calculations at low temperatures, due to the use of classical statistical mechanics. Correcting for this effect, we recover a consistent description of the high-field magnetization of GdCo5 from theory and experiment.

Implications of bond disorder in a S=1 kagome lattice.

Strong hydrogen bonds such as F···H···F offer new strategies to fabricate molecular architectures exhibiting novel structures and properties. Along these lines and, to potentially realize hydrogen-bond mediated superexchange interactions in a frustrated material, we synthesized [H2F]2[Ni3F6(Fpy)12][SbF6]2 (Fpy = 3-fluoropyridine). It was found that positionally-disordered H2F+ ions link neutral NiF2(Fpy)4 moieties into a kagome lattice with perfect 3-fold rotational symmetry. Detailed magnetic investigations combined with density-functional theory (DFT) revealed weak antiferromagnetic interactions (J ~ 0.4 K) and a large positive-D of 8.3 K with ms = 0 lying below ms = ±1. The observed weak magnetic coupling is attributed to bond-disorder of the H2F+ ions which leads to disrupted Ni-F···H-F-H···F-Ni exchange pathways. Despite this result, we argue that networks such as this may be a way forward in designing tunable materials with varying degrees of frustration.

Bimetallic MOFs (H3O)x[Cu(MF6)(pyrazine)2]·(4 - x)H2O (M = V4+, x = 0; M = Ga3+, x = 1): co-existence of ordered and disordered quantum spins in the V4+ system.

The title compounds are bimetallic MOFs containing [Cu(pyz)2]2+ square lattices linked by MF6n- octahedra. In each, only the Cu2+ spins exhibit long-range magnetic order below 3.5 K (M = V4+) and 2.6 K (M = Ga3+). The V4+ spins remain disordered down to 0.5 K.

Octanuclear Heterobimetallic {Ni4Ln4} Assemblies Possessing Ln4 Square Grid [2 × 2] Motifs: Synthesis, Structure, and Magnetism.

Octanuclear heterobimetallic complexes, [Ln4Ni4(H3L)4(µ3-OH)4(µ2-OH)4]4Cl·xH2O·yCHCl3 (Dy(3+), x = 30.6, y = 2 (1); Tb(3+), x = 28, y = 0 (2) ; Gd(3+), x = 25.3, y = 0 (3); Ho(3+), x = 30.6, y = 3 (4)) (H5L = N1,N3-bis(6-formyl-2-(hydroxymethyl)-4-methylphenol)diethylenetriamine) are reported. These are assembled by the cumulative coordination action of four doubly deprotonated compartmental ligands, [H3L](2-), along with eight exogenous -OH ligands. Within the core of these complexes, four Ln(3+)'s are distributed to the four corners of a perfect square grid while four Ni(2+)'s are projected away from the plane of the Ln4 unit. Each of the four Ni(2+)'s possesses distorted octahedral geometry while all of the Ln(3+)'s are crystallographically equivalent and are present in an elongated square antiprism geometry. The magnetic properties of compound 3 are dominated by an easy-plane single-ion anisotropy of the Ni(2+) ions [DNi = 6.7(7) K] and dipolar interactions between Gd(3+) centers. Detailed ac magnetometry reveals the presence of distinct temperature-dependent out-of-phase signals for compounds 1 and 2, indicative of slow magnetic relaxation. Magnetochemical analysis of complex 1 implies the 3d and the 4f metal ions are engaged in ferromagnetic interactions with SMM behavior, while dc magnetometry of compound 2 is suggestive of an antiferromagnetic Ni-Tb spin-exchange with slow magnetic relaxation due to a field-induced level crossing. Compound 4 exhibits an easy-plane single-ion anisotropy for the Ho(3+) ions and weak interactions between spin centers.

Heterometallic trinuclear {CoLn(III)} (Ln = Gd, Tb, Ho and Er) complexes in a bent geometry. Field-induced single-ion magnetic behavior of the Er(III) and Tb(III) analogues.

Through the use of a multi-site compartmental ligand, 2-methoxy-6-[{2-(2-hydroxyethylamino)ethylimino}methyl]phenol (LH3), the family of heterometallic, trinuclear complexes of the formula [CoLn(L)2(µ-O2CCH3)2(H2O)3]·NO3·xMeOH·yH2O has been expanded beyond Ln = Dy(III) to include Gd(III) (), Tb(III) (), Ho(III) () and Er(III) () for , and (x = 1; y = 1) and for (x = 0; y = 2). The metallic core of these complexes consists of a (Co(III)-Ln(III)-Co(III)) motif bridged in a bent geometry resulting in six-coordinated distorted Co(III) octahedra and nine-coordinated Ln(III) monocapped square-antiprisms. The magnetic characterization of these compounds reveals the erbium and terbium analogues to display a field induced single-ion magnetic behavior similar to the dysprosium analogue but at lower temperatures. The energy barrier for the reversal of the magnetization of the CoTb(III) analogue is Ueff ≥ 15.6(4) K, while for the CoEr(III) analogue Ueff ≥ 9.9(8) K. The magnetic properties are discussed in terms of distortions of the 4f electron cloud.

Antiferromagnetism in a Family of S = 1 Square Lattice Coordination Polymers NiX2(pyz)2 (X = Cl, Br, I, NCS; pyz = Pyrazine).

The crystal structures of NiX2(pyz)2 (X = Cl (1), Br (2), I (3), and NCS (4)) were determined by synchrotron X-ray powder diffraction. All four compounds consist of two-dimensional (2D) square arrays self-assembled from octahedral NiN4X2 units that are bridged by pyz ligands. The 2D layered motifs displayed by 1-4 are relevant to bifluoride-bridged [Ni(HF2)(pyz)2]EF6 (E = P, Sb), which also possess the same 2D layers. In contrast, terminal X ligands occupy axial positions in 1-4 and cause a staggered packing of adjacent layers. Long-range antiferromagnetic (AFM) order occurs below 1.5 (Cl), 1.9 (Br and NCS), and 2.5 K (I) as determined by heat capacity and muon-spin relaxation. The single-ion anisotropy and g factor of 2, 3, and 4 were measured by electron-spin resonance with no evidence for zero-field splitting (ZFS) being observed. The magnetism of 1-4 spans the spectrum from quasi-two-dimensional (2D) to three-dimensional (3D) antiferromagnetism. Nearly identical results and thermodynamic features were obtained for 2 and 4 as shown by pulsed-field magnetization, magnetic susceptibility, as well as their Néel temperatures. Magnetization curves for 2 and 4 calculated by quantum Monte Carlo simulation also show excellent agreement with the pulsed-field data. Compound 3 is characterized as a 3D AFM with the interlayer interaction (J⊥) being slightly stronger than the intralayer interaction along Ni-pyz-Ni segments (J(pyz)) within the two-dimensional [Ni(pyz)2](2+) square planes. Regardless of X, J(pyz) is similar for the four compounds and is roughly 1 K.

Experimental and Theoretical Electron Density Analysis of Copper Pyrazine Nitrate Quasi-Low-Dimensional Quantum Magnets.

The accurate electron density distribution and magnetic properties of two metal-organic polymeric magnets, the quasi-one-dimensional (1D) Cu(pyz)(NO3)2 and the quasi-two-dimensional (2D) [Cu(pyz)2(NO3)]NO3·H2O, have been investigated by high-resolution single-crystal X-ray diffraction and density functional theory calculations on the whole periodic systems and on selected fragments. Topological analyses, based on quantum theory of atoms in molecules, enabled the characterization of possible magnetic exchange pathways and the establishment of relationships between the electron (charge and spin) densities and the exchange-coupling constants. In both compounds, the experimentally observed antiferromagnetic coupling can be quantitatively explained by the Cu-Cu superexchange pathway mediated by the pyrazine bridging ligands, via a σ-type interaction. From topological analyses of experimental charge-density data, we show for the first time that the pyrazine tilt angle does not play a role in determining the strength of the magnetic interaction. Taken in combination with molecular orbital analysis and spin density calculations, we find a synergistic relationship between spin delocalization and spin polarization mechanisms and that both determine the bulk magnetic behavior of these Cu(II)-pyz coordination polymers.

[Ni(HF2)(3-Clpy)4]BF4 (py = pyridine): evidence for spin exchange along strongly distorted F···H···F- bridges in a one-dimensional polymeric chain.

[Ni(HF(2))(3-Clpy)(4)]BF(4) (py = pyridine) is a simple one-dimensional (1D) coordination polymer composed of compressed NiN(4)F(2) octahedra that form chains with bridging HF(2)(-) ligands. In spite of significant distortion of the HF(2)(-) bridge, a quasi-1D antiferromagnetic (AFM) behavior was observed with J(FHF) = 4.86 K.

Influence of HF2- geometry on magnetic interactions elucidated from polymorphs of the metal-organic framework [Ni(HF2)(pyz)2]PF6 (pyz = pyrazine).

A tetragonal polymorph of [Ni(HF(2))(pyz)(2)]PF(6) (designated ß) is isomorphic to its SbF(6)-congener at 295 K and features linear Ni-FHF-Ni pillars. Enhancements in the spin exchange (J(FHF) = 7.7 K), Néel temperature (T(N) = 7 K), and critical field (B(c) = 24 T) were found relative to monoclinic α-PF(6). DFT reveals that the HF(2)(-) bridges are significantly better mediators of magnetic exchange than pyz (J(pyz)), where J(FHF) ≈ 3J(pyz), thus leading to quasi-1D behavior. Spin density resides on all atoms of the HF(2)(-) bridge whereas N-donor atoms of the pyz ring bear most of the density.

Dimensionality selection in a molecule-based magnet.

Gaining control of the building blocks of magnetic materials and thereby achieving particular characteristics will make possible the design and growth of bespoke magnetic devices. While progress in the synthesis of molecular materials, and especially coordination polymers, represents a significant step towards this goal, the ability to tune the magnetic interactions within a particular framework remains in its infancy. Here we demonstrate a chemical method which achieves dimensionality selection via preferential inhibition of the magnetic exchange in an S=1/2 antiferromagnet along one crystal direction, switching the system from being quasi-two- to quasi-one-dimensional while effectively maintaining the nearest-neighbor coupling strength.

Ag(nic)2 (nic = nicotinate): a spin-canted quasi-2D antiferromagnet composed of square-planar S = 1/2 Ag(II) ions.

Square-planar S = 1/2 Ag(II) ions in polymeric Ag(nic)(2) are linked by bridging nic monoanions to yield 2D corrugated sheets. Long-range magnetic order occurs below T(N) = 11.8(2) K due to interlayer couplings that are estimated to be about 30 times weaker than the intralayer exchange interaction.

Structural, electronic, and magnetic properties of quasi-1D quantum magnets [Ni(HF2)(pyz)2]X (pyz = pyrazine; X = PF6(-), SbF6(-)) exhibiting Ni-FHF-Ni and Ni-pyz-Ni spin interactions.

[Ni(HF(2))(pyz)(2)]X {pyz = pyrazine; X = PF(6)(-) (1), SbF(6)(-) (2)} were structurally characterized by synchrotron X-ray powder diffraction and found to possess axially compressed NiN(4)F(2) octahedra. At 298 K, 1 is monoclinic (C2/c) with unit cell parameters, a = 9.9481(3), b = 9.9421(3), c = 12.5953(4) Å, and ß = 81.610(3)° while 2 is tetragonal (P4/nmm) with a = b = 9.9359(3) and c = 6.4471(2) Å and is isomorphic with the Cu-analogue. Infinite one-dimensional (1D) Ni-FHF-Ni chains propagate along the c-axis which are linked via µ-pyz bridges in the ab-plane to afford three-dimensional polymeric frameworks with PF(6)(-) and SbF(6)(-) counterions occupying the interior sites. A major difference between 1 and 2 is that the Ni-F-H bonds are bent (∼157°) in 1 but are linear in 2. Ligand field calculations (LFT) based on an angular overlap model (AOM), with comparison to the electronic absorption spectra, indicate greater π-donation of the HF(2)(-) ligand in 1 owing to the bent Ni-F-H bonds. Magnetic susceptibility data for 1 and 2 exhibit broad maxima at 7.4 and 15 K, respectively, and λ-like peaks in dχT/dT at 6.2 and 12.2 K that are ascribed to transitions to long-range antiferromagnetic order (T(N)). Muon-spin relaxation and specific heat studies confirm these T(N)'s. A comparative analysis of χ vs T to various 1D Heisenberg/Ising models suggests moderate antiferromagnetic interactions, with the primary interaction strength determined to be 3.05/3.42 K (1) and 5.65/6.37 K (2). However, high critical fields of 19 and 37.4 T obtained from low temperature pulsed-field magnetization data indicate that a single exchange constant (J(1D)) alone is insufficient to explain the data and that residual terms in the spin Hamiltonian, which could include interchain magnetic couplings (J(⊥)), as mediated by Ni-pyz-Ni, and single-ion anisotropy (D), must be considered. While it is difficult to draw absolute conclusions regarding the magnitude (and sign) of J(⊥) and D based solely on powder data, further support offered by related Ni(II)-pyz compounds and our LFT and density-functional theory (DFT) results lead us to a consistent quasi-1D magnetic description for 1 and 2.

A chiral ferromagnetic molecular metal.

The first molecular material with the coexistence of ferromagnetism, metal-like conductivity, and chirality has been prepared using an organic/inorganic approach. In this case, a two-dimensional packing of chiral organic radical cations (responsible for both the electrical conductivity and optical activity) was assembled with a layered bimetallic oxalate-based anionic network (responsible for the magnetic properties). Shubnikov-de Haas oscillations confirmed the presence of a Fermi surface even when the transport properties suggested "insulating"-type behavior at very low temperatures.

Characterization of the antiferromagnetism in Ag(pyz)2(S2O8) (pyz = pyrazine) with a two-dimensional square lattice of Ag2+ ions.

X-ray powder diffraction and magnetic susceptibility measurements show that Ag(pyz)(2)(S(2)O(8)) consists of 2D square nets of Ag(2+) ions resulting from the corner-sharing of axially elongated AgN(4)O(2) octahedra and exhibits characteristic 2D antiferromagnetism. Nevertheless, mu(+)SR measurements indicate that Ag(pyz)(2)(S(2)O(8)) undergoes 3D magnetic ordering below 7.8(3) K.

Strong H...F hydrogen bonds as synthons in polymeric quantum magnets: structural, magnetic, and theoretical characterization of [Cu(HF2)(pyrazine)2]SbF6, [Cu2F(HF)(HF2)(pyrazine)4](SbF6)2, and [CuAg(H3F4)(pyrazine)5](SbF6)2.

Three Cu(2+)-containing coordination polymers were synthesized and characterized by experimental (X-ray diffraction, magnetic susceptibility, pulsed-field magnetization, heat capacity, and muon-spin relaxation) and electronic structure studies (quantum Monte Carlo simulations and density functional theory calculations). [Cu(HF(2))(pyz)(2)]SbF(6) (pyz = pyrazine) (1a), [Cu(2)F(HF)(HF(2))(pyz)(4)](SbF(6))(2) (1b), and [CuAg(H(3)F(4))(pyz)(5)](SbF(6))(2) (2) crystallize in either tetragonal or orthorhombic space groups; their structures consist of 2D square layers of [M(pyz)(2)](n+) that are linked in the third dimension by either HF(2)(-) (1a and 1b) or H(3)F(4)(-) (2). The resulting 3D frameworks contain charge-balancing SbF(6)(-) anions in every void. Compound 1b is a defective polymorph of 1a, with the difference being that 50% of the HF(2)(-) links are broken in the former, which leads to a cooperative Jahn-Teller distortion and d(x(2))(-y(2)) orbital ordering. Magnetic data for 1a and 1b reveal broad maxima in chi at 12.5 and 2.6 K and long-range magnetic order below 4.3 and 1.7 K, respectively, while 2 displays negligible spin interactions owing to long and disrupted superexchange pathways. The isothermal magnetization, M(B), for 1a and 1b measured at 0.5 K reveals contrasting behaviors: 1a exhibits a concave shape as B increases to a saturation field, B(c), of 37.6 T, whereas 1b presents an unusual two-step saturation in which M(B) is convex until it reaches a step near 10.8 T and then becomes concave until saturation is reached at 15.8 T. The step occurs at two-thirds of M(sat), suggesting the presence of a ferrimagnetic structure. Compound 2 shows unusual hysteresis in M(B) at low temperature, although chi vs T does not reveal the presence of a magnetic phase transition. Quantum Monte Carlo simulations based on an anisotropic cubic lattice were applied to the magnetic data of 1a to afford g = 2.14, J = -13.4 K (Cu-pyz-Cu), and J(perpendicular) = -0.20 K (Cu-F...H...F-Cu), while chi vs T for 1b could be well reproduced by a spin-1/2 Heisenberg uniform chain model for g = 2.127(1), J(1) = -3.81(1), and zJ(2) = -0.48(1) K, where J(1) and J(2) are the intra- and interchain exchange couplings, respectively, which considers the number of magnetic nearest-neighbors (z). The M(B) data for 1b could not be satisfactorily explained by the chain model, suggesting a more complex magnetic structure in the ordered state and the need for additional terms in the spin Hamiltonian. The observed variation in magnetic behaviors is driven by differences in the H...F hydrogen-bonding motifs.