Dimensionality selection in a molecule-based magnet

Field-Tunable Berezinskii-Kosterlitz-Thouless Correlations in a Heisenberg Magnet

We report the manifestation of field-induced Berezinskii-Kosterlitz-Thouless (BKT) correlations in the weakly coupled spin-1/2 Heisenberg layers of the molecular-based bulk material [Cu(pz)_{2}(2-HOpy)_{2}](PF_{6})_{2}. At zero field, a transition to long-range order occurs at 1.38 K, caused by a weak intrinsic easy-plane anisotropy and an interlayer exchange of J^{'}/k_{B}≈1  mK. Because of the moderate intralayer exchange coupling of J/k_{B}=6.8  K, the application of laboratory magnetic fields induces a substantial XY anisotropy of the spin correlations. Crucially, this provides a significant BKT regime, as the tiny interlayer exchange J^{'} only induces 3D correlations upon close approach to the BKT transition with its exponential growth in the spin-correlation length. We employ nuclear magnetic resonance measurements to probe the spin correlations that determine the critical temperatures of the BKT transition as well as that of the onset of long-range order. Further, we perform stochastic series expansion quantum Monte Carlo simulations based on the experimentally determined model parameters. Finite-size scaling of the in-plane spin stiffness yields excellent agreement of critical temperatures between theory and experiment, providing clear evidence that the nonmonotonic magnetic phase diagram of [Cu(pz)_{2}(2-HOpy)_{2}](PF_{6})_{2} is determined by the field-tuned XY anisotropy and the concomitant BKT physics.

Approaching the isotropic spin-ladder regime: structure and magnetism of all-pyrazine-bridged copper(II)-based antiferromagnetic ladders

The crystal structure and magnetic properties of two all-pyrazine-bridged antiferromagnetic spin ladders are reported. The complexes, catena-(bis(3-X-4-pyridone)(μ-pyrazine)copper(II)(-μ-pyrazine)diperchlorate ([Cu(pz)_1.5(L)₂](ClO₄)₂ where L = 3-X-4-pyridone and X = Br (1) or Cl (2)), contain copper(II)-based ladders in which both the rung and rail bridges are pyrazine molecules bonded through the x²-y² orbital of the copper(II) ions. This structural scaffold is proposed to approach the isotropic spin-ladder regime. 1 and 2 crystallize in the monoclinic space group P2₁/c. Due to the bulk of the 3-X-4-HOpy ligands, the ladders are well isolated in the a-direction (1, 15.6 Å; 2, 15.5 Å). The ladders, which run in the b-direction, are stacked in the c-direction with the separation (1, 7.87 Å; 2, 7.82 Å) between copper(II) ions caused by the bulk of a semi-coordinate perchlorate ion coordinated in the axial position. Computational evaluation of magnetic J_AB couplings between Cu-moieties of 2 supports the experimentally proposed magnetic topology and agrees with an isolated isotropic spin-ladder (J_rail = -4.04 cm^-1 (-5.77 K) and J_rung = -3.89 cm^-1 (-5.56 K)). These complexes introduce a convenient scaffold for synthesizing isotropic spin-ladders with modest superexchange interactions, the strength of which may be tuned by variations in L. The magnetic susceptibility down to 1.8 K, for both compounds, is well described by the strong-rung ladder model giving nearly isotropic exchange with J_rung ≈ J_rail ≈ -5.5 K (1) and -5.9 K (2) using the Hamiltonian. Theoretical simulations of the magnetic response of 2 using the isotropic ladder model are in excellent agreement with experiment. The measured magnetization to 5 T indicates a quantum-dominated magnetic spectrum. Again, calculated lower and saturation (4.3 and 24 T, respectively) critical fields for 2 are consistent with experimental measurements, and magnetization data at very low temperatures indeed suggest the presence of quantum effects. Further, the computational study of short- and long-range spin ordering indicates that a 2D-to-3D crossover might be feasible at lower temperatures. Analysis of the Boltzmann population corroborates the presence of accessible triplet states above the singlet ground state enabling the aforementioned 2D-to-3D crossover.

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.

The magnetic properties of well-separated Ni²⁺ chains are highly dependent on the bridging halide ligands. By increasing the size of the halide ions, we can decrease the single-ion anisotropy such that the system moves from easy plane to easy axis. Through-space magnetic interactions between adjacent Ni²⁺ ions are also turned on as the larger halides are substituted into the exchange pathway.

Tight-Binding Approach to Pyrazine-Mediated Superexchange in Copper-Pyrazine Antiferromagnets

We investigate the cause of spatial superexchange anisotropy in a family of copper-based, quasi-two-dimensional materials with very similar geometries. The compounds in this family differ mainly in their inter-layer separation but they have very different magnetic interactions, even within the basal plane. We use density functional theory and Wannier functions to parameterize two complimentary tight-binding models and show that the superexchange between the Cu²⁺ ions is dominated by a σ-mediated interaction between hybrid Cu-pyrazine orbitals centered on the copper atoms. We find no correlations between the strength of this exchange interaction and homologous geometric features across the compounds, such as Cu and pyrazine bond lengths and orientations of nearby counterions. We find that the pyrazine tilt angles do not affect the Cu-pyrazine-Cu exchange because the lowest unoccupied molecular orbital on pyrazine is at a very high energy (relative to the frontier orbitals, which are Cu-based). We conclude that careful control of the entire crystal structure, including non-homologous geometric features such as the inter-layer organic ligands, is vital for engineering magnetic properties.

Quasi-one dimensional magnetic interactions in the three-dimensional hyper-honeycomb framework [(C2H5)3NH]2Cu2(C2O4)3

The Cu(ii) ions in [(C2H5)3NH]2Cu2(C2O4)3 form a hyperhoneycomb lattice and show no indication of long-range magnetic order down to 60 mK. It has therefore been suggested that [(C2H5)3NH]2Cu2(C2O4)3 is a three dimensional quantum spin liquid. We construct a tight-binding model of [(C2H5)3NH]2Cu2(C2O4)3 from Wannier orbital overlaps. Including interactions within the Jahn-Teller distorted Cu-centered eg Wannier orbitals leads to a highly anisotropic effective Heisenberg model. We show that this anisotropy arrises from interference between different superexchange pathways. This demonstrates that when two (or more) orbitals contribute to the localised spin superexchange can be significantly richer than in the textbook single orbital case. The hyper-honeycomb lattice contains two symmetry distinct sublattices of Cu atoms arranged in coupled chains. We show that one sublattice is strongly dimerized, the other forms isotropic antiferromagnetic chains. Integrating out the strongest (intradimer) exchange interactions leaves extremely weakly coupled Heisenberg chains.

Pyrazine-bridged Cu(ii) chains: diaquabis(n-methyl-2-pyridone)copper(ii) perchlorate complexes

A family of pyrazine-bridged, linear chain complexes of Cu(ii) of the formula [CuL₂(H₂O)₂(pz)](ClO₄)₂ [pz = pyrazine; L = n-methyl-2(1H)-pyridone, n = 3 (1), 5 (2), and 6 (3)] has been prepared. Single-crystal X-ray diffraction shows six-coordinate, pyrazine-bridged chains with trans-pairs of ancillary ligands. The substituted pyridine molecules exist in their pyridone tautomers and are coordinated through the carbonyl oxygen atom. The structure is stabilized by intramolecular hydrogen bonds between the pyridone and water molecule, and via hydrogen bonds between the water molecules and perchlorate ions. 2 undergoes a crystallographic phase transition between C2/c (high temperature phase) and P1[combining macron] (low temperature phase). Powder EPR spectra reveal that all complexes are rhombic, although differences between g_x and g_y can only be seen clearly at Q-band. Variable temperature magnetic susceptibility data show antiferromagnetic interactions and the data were fit to the uniform chain model yielding J/k_B = -9.8, -9.2 and -11 K for 1-3 respectively. Attempts to model an interchain interaction strength indicate that the chains are very well isolated.

Magnetic Network on Demand: Pressure Tunes Square Lattice Coordination Polymers Based on {[Cu(pyrazine)2]2+}n

We report the pressure-induced structural and magnetic changes in [CuCl(pyz)₂](BF₄) (pyz = pyrazine) and [CuBr(pyz)₂](BF₄), two members of a family of three-dimensional coordination polymers based on square mesh {[Cu(pyz)₂]²⁺}_n layers. High-pressure X-ray diffraction and density functional theory calculations have been used to investigate the structure-magnetic property relationship. Although structurally robust and almost undeformed within a large pressure range, the {[Cu(pyz)₂]²⁺}_n network can be electronically modified by adjusting the interaction of the apical linkers interconnecting the layers, which has strong implications for the magnetic properties. It is then demonstrated that the degree of covalent character of the apical interaction explains the difference in magnetic exchange between the two species. We have also investigated the mechanical deformation of the network induced by nonhydrostatic compression that affects the structure depending on the crystal orientation. The obtained results suggest the existence of "Jahn-Teller frustration" triggered at the highest hydrostatic pressure limit.

Mechanomagnetics in Elastic Crystals: Insights from [Cu(acac)2 ]

We predict that the magnetic properties of [Cu(acac)₂ ], an elastically flexible crystal, change drastically when the crystal is bent. It is found that unbent [Cu(acac)₂ ] is an almost perfect Tomonaga-Luttinger liquid. Broken-symmetry density-functional calculations reveal that the magnetic exchange interactions along the chains are an order of magnitude larger than the interchain exchange. The geometrically frustrated interchain interactions cannot magnetically order the material at any experimentally accessible temperature. The ordering temperature (T_N ), calculated from the chain-random-phase approximation, increases by 24 orders of magnitude when the material is bent. We demonstrate that geometric frustration both suppresses T_N and enhances the sensitivity of T_N to bending. In [Cu(acac)₂ ], T_N is extremely sensitive to bending but remains too low for practical applications, even when bent. Partially frustrated materials could achieve the balance of high T_N and good sensitivity to bending required for practical applications of mechanomagnetic elastic crystals.

Halide-bi-bridged polymers of amide substituted pyridines and -pyrazines: polymorphism, structures, thermal stability and magnetism

The structural trends, polymorphic behaviour, magnetic properties and thermal stability of a family of halide-bi-bridged polymers of CuX₂ and amide-substituted pyridines and -pyrazines are reported, and compared with related compounds in the literature.

Giant Pressure Dependence and Dimensionality Switching in a Metal-Organic Quantum Antiferromagnet

We report an extraordinary pressure dependence of the magnetic interactions in the metal-organic system [CuF_{2}(H_{2}O)_{2}]_{2}pyrazine. At zero pressure, this material realizes a quasi-two-dimensional spin-1/2 square-lattice Heisenberg antiferromagnet. By high-pressure, high-field susceptibility measurements we show that the dominant exchange parameter is reduced continuously by a factor of 2 on compression. Above 18 kbar, a phase transition occurs, inducing an orbital re-ordering that switches the dimensionality, transforming the quasi-two-dimensional lattice into weakly coupled chains. We explain the microscopic mechanisms for both phenomena by combining detailed x-ray and neutron diffraction studies with quantitative modeling using spin-polarized density functional theory.

Strong Coupling of Microwave Photons to Antiferromagnetic Fluctuations in an Organic Magnet

Coupling between a crystal of di(phenyl)-(2,4,6-trinitrophenyl)iminoazanium radicals and a superconducting microwave resonator is investigated in a circuit quantum electrodynamics (circuit QED) architecture. The crystal exhibits paramagnetic behavior above 4 K, with antiferromagnetic correlations appearing below this temperature, and we demonstrate strong coupling at base temperature. The magnetic resonance acquires a field angle dependence as the crystal is cooled down, indicating anisotropy of the exchange interactions. These results show that multispin modes in organic crystals are suitable for circuit QED, offering a platform for their coherent manipulation. They also utilize the circuit QED architecture as a way to probe spin correlations at low temperature.

Crossover from one- to three-dimensional behavior in the S = 1/2 Heisenberg antiferromagnet Cu(N2H5)2(SO4)2

From experimental and theoretical analyses of magnetic and specific-heat properties, we present the complete magnetic phase diagram of the quasi-1D antiferromagnet Cu(N₂H₅)₂(SO₄)₂. On cooling and at zero magnetic field this compound enters a 1D regime with short-range magnetic correlations, marked by a broad maximum in the specific heat and magnetic susceptibility at [Formula: see text] K, followed by a tridimensional antiferromagnetically ordered phase below [Formula: see text] K induced by small interchain couplings. The intermediate-temperature 1D regime can be modeled using exact quantum-transfer-matrix calculations, which offer a compatible description of the nonmonotonic behavior of [Formula: see text] as a function of the magnetic field, giving [Formula: see text] K for the intrachain exchange parameter. The analysis of magnetic specific-heat and susceptibility data at low temperature indicates that the interchain exchange couplings are an order of magnitude smaller than the coupling inside the chains.

Spin-orbit coupled molecular quantum magnetism realized in inorganic solid

Molecular quantum magnetism involving an isolated spin state is of particular interest due to the characteristic quantum phenomena underlying spin qubits or molecular spintronics for quantum information devices, as demonstrated in magnetic metal-organic molecular systems, the so-called molecular magnets. Here we report the molecular quantum magnetism realized in an inorganic solid Ba3Yb2Zn5O11 with spin-orbit coupled pseudospin-½ Yb(3+) ions. The magnetization represents the magnetic quantum values of an isolated Yb4 tetrahedron with a total (pseudo)spin 0, 1 and 2. Inelastic neutron scattering results reveal that a large Dzyaloshinsky-Moriya interaction originating from strong spin-orbit coupling of Yb 4f is a key ingredient to explain magnetic excitations of the molecular magnet states. The Dzyaloshinsky-Moriya interaction allows a non-adiabatic quantum transition between avoided crossing energy levels, and also results in unexpected magnetic behaviours in conventional molecular magnets.

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.

Magnetic Structure and Exchange Interactions in Quasi-One-Dimensional MnCl2(urea)2

MnCl2(urea)2 is a new linear chain coordination polymer that exhibits slightly counter-rotated Mn2Cl2 rhomboids along the chain-axis. The material crystallizes in the noncentrosymmetric orthorhombic space group Iba2, with each Mn(II) ion equatorially surrounded by four Cl(-) that lead to bibridged ribbons. Urea ligands coordinate via O atoms in the axial positions. Hydrogen bonds of the Cl···H-N and O···H-N type link the chains into a quasi-3D network. Magnetic susceptibility data reveal a broad maximum at 9 K that is consistent with short-range magnetic order. Pulsed-field magnetization measurements conducted at 0.6 K show that a fully polarized magnetic state is achieved at Bsat = 19.6 T with another field-induced phase transition occurring at 2.8 T. Zero-field neutron diffraction studies made on a powdered sample of MnCl2(urea)2 reveal that long-range magnetic order occurs below TN = 3.2(1) K. Additional Bragg peaks due to antiferromagnetic (AFM) ordering can be indexed according to the Ib'a2' magnetic space group and propagation vector τ = [0, 0, 0]. Rietveld profile analysis of these data revealed a Néel-type collinear ordering of Mn(II) ions with an ordered magnetic moment of 4.06(6) μB (5 μB is expected for isotropic S = (5)/2) oriented along the b-axis, i.e., perpendicular to the chain-axis that runs along the c-direction. Owing to the potential for spatial exchange anisotropy and the pitfalls in modeling bulk magnetic data, we analyzed inelastic neutron scattering data to retrieve the exchange constants: Jc = 2.22 K (intrachain), Ja = -0.10 K (interchain), and D = -0.14 K with J > 0 assigned to AFM coupling. This J configuration is most unusual and contrasts the more commonly observed AFM interchain coupling of 1D chains.