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The magnetic properties of the two isostructural molecule-based magnets, Ni(NCS)$_{2}$(thiourea)$_{2}$, $S$ = 1, [thiourea = SC(NH$_2$)$_2$] and Co(NCS)$_{2}$(thiourea)$_{2}$, $S$ = 3/2, are characterised using several techniques in order to rationalise their relationship with structural parameters and ascertain magnetic changes caused by substitution of the spin. Zero-field heat capacity and muon-spin relaxation measurements reveal low-temperature long-range ordering in both compounds, in addition to Ising-like ($D < 0$) single-ion anisotropy ($D_{\rm{Co}} \sim$ -100 K, $D_{\rm{Ni}} \sim$ -10 K). Crystal and electronic structure, combined with DC-field magnetometry, affirm highly quasi-one-dimensional behaviour, with ferromagnetic intrachain exchange interactions $J_{\rm{Co}}\approx+4$ K and $J_{\rm{Ni}}\sim+100$ K and weak antiferromagnetic interchain exchange, on the order of $J'$ $\sim-0.1$ K. Electron charge and spin-density mapping reveals through-space exchange as a mechanism to explain the large discrepancy in $J$-values despite, from a structural perspective, the highly similar exchange pathways in both materials. Both species can be compared to the similar compounds $M$Cl$_2$(thiourea)$_4$, $M$ = Ni(II) (DTN) and Co(II) (DTC), where DTN is know to harbour two magnetic field-induced quantum critical points. Direct comparison of DTN and DTC with the compounds studied here shows that substituting the halide Cl$^-$ ion, for the NCS$^-$ ion, results in a dramatic change in both the structural and magnetic properties., Comment: Main text: 13 pages - 11 figures, 2 tables. Supplemental information: 6 pages - 2 figures, 6 tables

[Ni(HF$_2$)(3-Clpyridine)$_4$]BF$_4$ (NBCT) is a one-dimensional, $S = 1$ spin chain material that shows no magnetic neutron Bragg peaks down temperatures of 0.1 K. Previous work identified NBCT to be in the Haldane phase and near a quantum phase transition as a function of $D/J$ to the large-$D$ quantum paramagnet phase (QPM), where $D$ is the axial single-ion anisotropy and $J$ is the intrachain superexchange. Herein, inelastic neutron scattering results are presented on partially deuterated, $^{11}$B enriched NBCT polycrystalline samples in zero magnetic field and down to temperatures of 0.3 K. Comparison to density matrix renormalization group calculations yields $D/J = 1.51$ and a significant rhombic single-ion anisotropy $E$ ($E/D \approx 0.03$, $E/J \approx 0.05$). These $D$, $J$, and $E$ values place NBCT in the large-$D$ QPM phase but precipitously near a quantum phase transition to a long-range ordered phase.

The molecular coordination complex NiI$_2$(3,5-lut)$_4$ [where (3,5-lut) $=$ (3,5-lutidine) $=$ (C$_7$H$_9$N)] has been synthesized and characterized by several techniques including synchrotron X-ray diffraction, ESR, SQUID magnetometry, pulsed-field magnetization, inelastic neutron scattering and muon spin relaxation. Templated by the configuration of 3,5-lut ligands the molecules pack in-registry with the Ni--I$\cdots$I--Ni chains aligned along the $c$--axis. This arrangement leads to through-space I$\cdots$I magnetic coupling which is directly measured for the first time in this work. The net result is a near-ideal realization of the $S = 1$ Haldane chain with $J = 17.5~\rm{K}$ and energy gaps of $\Delta^{\parallel} = 5.3~{\rm K}$ $\Delta^{\perp} =7.7~{\rm K}$, split by the easy-axis single-ion anisotropy $D=-1.2~{\rm K}$. The ratio $D/J = -0.07$ affords one of the most isotropic Haldane systems yet discovered, while the ratio $\Delta_0/J = 0.40(1)$ (where $\Delta_0$ is the average gap size) is close to its ideal theoretical value, suggesting a very high degree of magnetic isolation of the spin chains in this material. The Haldane gap is closed by orientation-dependent critical fields $\mu_0H_{\rm c}^{\parallel} = 5.3~\rm{T}$ and $\mu_0H_{\rm c}^{\perp} = 4.3~\rm{T}$, which are readily accessible experimentally and permit investigations across the entirety of the Haldane phase, with the fully polarized state occurring at $\mu_0 H_{\rm s}^{\parallel}=46.0~\rm{T}$ and $\mu_0 H_{\rm s}^{\perp}=50.7~\rm{T}$. The results are explicable within the so-called fermion model, in contrast to other reported easy-axis Haldane systems. Zero-field magnetic order is absent down to $20~{\rm mK}$ and emergent end-chain effects are observed in the gapped state, as evidenced by detailed low-temperature measurements., Comment: 13 pages, 8 figures plus supporting information

Although low-dimensional $S = 1$ antiferromagnets remain of great interest, difficulty in obtaining high-quality single crystals of the newest materials hinders experimental research in this area. Polycrystalline samples are more readily produced, but there are inherent problems in extracting the magnetic properties of anisotropic systems from powder data. Following a discussion of the effect of powder-averaging on various measurement techniques, we present a methodology to overcome this issue using thermodynamic measurements. In particular we focus on whether it is possible to characterise the magnetic properties of polycrystalline, anisotropic samples using readily available laboratory equipment. We test the efficacy of our method using the magnets [Ni(H$_{2}$O)$_{2}$(3,5-lutidine)$_{4}$](BF$_{4}$)$_{2}$ and Ni(H$_{2}$O)$_{2}$(acetate)$_{2}$(4-picoline)$_{2}$, which have negligible exchange interactions, as well as the antiferromagnet [Ni(H$_{2}$O)$_{2}$(pyrazine)$_{2}$](BF$_{4}$)$_{2}$, and show that we are able to extract the anisotropy parameters in each case. The results obtained from the thermodynamic measurements are checked against electron-spin resonance and neutron diffraction. We also present a density functional method, which incorporates spin-orbit coupling to estimate the size of the anisotropy in [Ni(H$_{2}$O)$_{2}$(pyrazine)$_{2}$](BF$_{4}$)$_{2}$.

The magnetic ground state of the quasi-one-dimensional spin-1 antiferromagnetic chain is sensitive to the relative sizes of the single-ion anisotropy ($D$) and the intrachain ($J$) and interchain ($J'$) exchange interactions. The ratios $D/J$ and $J'/J$ dictate the material's placement in one or other of three competing phases: a Haldane gapped phase, a quantum paramagnet and an XY-ordered state, with a quantum critical point at their junction. We have identified [Ni(HF)$_2$(pyz)$_2]$SbF$_6$, where pyz = pyrazine, as a candidate in which this behavior can be explored in detail. Combining neutron scattering (elastic and inelastic) in applied magnetic fields of up to 10~tesla and magnetization measurements in fields of up to 60~tesla with numerical modeling of experimental observables, we are able to obtain accurate values of all of the parameters of the Hamiltonian [$D = 13.3(1)$~K, $J = 10.4(3)$~K and $J' = 1.4(2)$~K], despite the polycrystalline nature of the sample. Density-functional theory calculations result in similar couplings ($J = 9.2$~K, $J' = 1.8$~K) and predict that the majority of the total spin population of resides on the Ni(II) ion, while the remaining spin density is delocalized over both ligand types. The general procedures outlined in this paper permit phase boundaries and quantum-critical points to be explored in anisotropic systems for which single crystals are as yet unavailable.

Using a mixed-ligand synthetic scheme, we create a family of quasi-two-dimensional antiferromagnets, namely, [Cu(HF$_2$)(pyz)$_2$]ClO$_4$ [pyz = pyrazine], [Cu$L_2$(pyz)$_2$](ClO$_4$)$_2$ [$L$ = pyO = pyridine-N-oxide and 4-phpyO = 4-phenylpyridine-N-oxide. These materials are shown to possess equivalent two-dimensional [Cu(pyz)$_2$]$^{2+}$ nearly square layers, but exhibit interlayer spacings that vary from 6.5713~\AA ~to 16.777~\AA, as dictated by the axial ligands. We present the structural and magnetic properties of this family as determined via x-ray diffraction, electron-spin resonance, pulsed- and quasistatic-field magnetometry and muon-spin rotation, and compare them to those of the prototypical two-dimensional magnetic polymer Cu(pyz)$_2$(ClO$_4$)$_2$. We find that, within the limits of the experimental error, the two-dimensional, {\it intralayer} exchange coupling in our family of materials remains largely unaffected by the axial ligand substitution, while the observed magnetic ordering temperature decreases slowly with increasing layer separation. Despite the structural motifs common to this family and Cu(pyz)$_2$(ClO$_4$)$_2$, the latter has significantly stronger two-dimensional exchange interactions and hence a higher ordering temperature. We discuss these results, as well as the mechanisms that might drive the long-range order in these materials, in terms of departures from the ideal $S=1/2$ two-dimensional square-lattice Heisenberg antiferromagnet. In particular, we find that both spin exchange anisotropy in the intralayer interaction and interlayer couplings (exchange, dipolar, or both) are needed to account for the observed ordering temperatures, with the intralayer anisotropy becoming more important as the layers are pulled further apart., Comment: 17 pages, 5 figures

An $S=1$ antiferromagnetic polymeric chain, [Ni(HF$_2$)(3-Clpy)$_4$]BF$_4$ (py = pyridine), has previously been identified to have intrachain, nearest-neighbor antiferromagnetic interaction strength $J/k_{\mathrm{B}} = 4.86$ K and single-ion anisotropy (zero-field splitting) $D/k_{\mathrm{B}} = 4.3$ K, so the ratio $D/J = 0.88$ places this system close to the $D/J \approx 1$ gapless critical point between the topologically distinct Haldane and Large-$D$ phases. The magnetization was studied over a range of temperatures, 50 mK $\leq T \leq 1$ K, and magnetic fields, $B \leq 10$ T, in an attempt to identify a critical field, $B_{\mathrm{c}}$, associated with the closing of the Haldane gap, and the present work places an upper bound of $B_{\mathrm{c}} \leq (35 \pm 10)$ mT. At higher fields, the observed magnetic response is qualitatively similar to the "excess" signal observed by other workers at 0.5 K and below 3 T. The high-field (up to 14.5 T), multi-frequency (nomially 200 GHz to 425 GHz) ESR spectra at 3 K reveal several broad features considered to be associated with the linear-chain sample., Comment: 5 pages, 4 figures

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-neighbour coupling strength., Comment: 8 pages, 6 figures

We present the results of a muon-spin relaxation (muSR) investigation into magnetic ordering in several families of layered quasi-two-dimensional molecular antiferromagnets based on transition metal ions such as S=1/2 Cu2+ bridged with organic ligands such as pyrazine. In many of these materials magnetic ordering is difficult to detect with conventional magnetic probes. In contrast, muSR allows us to identify ordering temperatures and study the critical behavior close to T_N . Combining this with measurements of in-plane magnetic exchange J and predictions from quantum Monte Carlo simulations we may assess the degree of isolation of the 2D layers through estimates of the effective inter-layer exchange coupling and in-layer correlation lengths at T_N . We also identify the likely metal-ion moment sizes and muon stopping sites in these materials, based on probabilistic analysis of the magnetic structures and of muon-fluorine dipole-dipole coupling in fluorinated materials., Comment: Text and figures as published in Physical Review B

High field specific heat, Cp, and magnetic susceptibility, \c{hi}, measurements were performed on the quasi-two dimensional Heisenberg antiferromagnet [Cu(pyz)2(pyO)2](PF6)2. While no Cp anomaly is observed down to 0.5 K in zero magnetic field, the application of field parallel to the crystallographic ab-plane induces a lambda-like anomaly in Cp, consistent with Ising-type magnetic order. On the other hand, when the field is parallel to the c-axis, Cp and \c{hi} show evidence of XY-type antiferromagnetism. We argue that it is a small but finite easy-plane anisotropy in quasi-two dimensional [Cu(pyz)2(pyO)2](PF6)2 that allows the unusual observation of field induced XY and Ising-type magnetic states., Comment: 4 figures

Manganese tricyanomethanide, Mn[C(CN)3]2, consists of two interpenetrating three-dimensional rutile-like networks. In each network, the tridentate C(CN)3- anion gives rise to superexchange interactions between the Mn2+ ions (S=5/2) that can be mapped onto the "row model" for partially frustrated triangular magnets. We present heat capacity measurements that reveal a phase transition at T_N = 1.18K, indicative of magnetic ordering. The zero-field magnetically ordered structure was solved from neutron powder diffraction data taken between 0.04 and 1.2 K. It consists of an incommensurate spiral with a temperature independent propagation vector Q=(2Q 0 0)=(+/-0.622 0 0), where different signs relate to the two different networks. This corresponds to (+/-0.311 +/-0.311 0) in a quasi-hexagonal representation. The ordered moment mu=3.3mu_B is about 2/3 of the full Mn2+ moment. From the values of T_N and Q, the exchange parameters J/k = 0.15 K and J'/J = 0.749 are estimated. The magnetic-field dependence of the intensity of the <2Q 0 0> Bragg reflection, measured for external fields H||Q, indicates the presence of three different magnetic phases. We associate them with the incommensurate spiral (H < 13.5 kOe), an intermediate phase (13.5 kOe < H < 16 kOe), and the "2-1" spin-flop like magnetic structure (H > 16 kOe) proposed for related compounds. For increasing fields, Q continuously approaches the value 1/3, corresponding to the commensurate magnetic structure of the fully frustrated triangular lattice. This value is reached at H_c = 19 kOe. At this point, the field-dependence reverses and Q adopts a value of 0.327 at 26 kOe, the highest field applied in the experiment. Except for H_c, the magnetic ordering is incommensurate in all three magnetic phases of Mn[C(CN)3]2., Comment: accepted for publication in J. Phys.: Condens. Matter