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We present a detailed 31P nuclear magnetic resonance (NMR) study of the molecular rotation in the compound [Cu(pz)2(2-HOpy)](PF6)2, where pz = C4H4N2 and 2-HOpy = C5H4NHO. Here, a freezing of the PF6 rotation modes is revealed by several steplike increases of the temperature-dependent second spectral moment, with accompanying broad peaks of the longitudinal and transverse nuclear spin-relaxation rates. An analysis based on the Bloembergen-Purcell-Pound (BPP) theory quantifies the related activation energies as Ea/kB = 250 and 1400 K. Further, the anisotropy of the second spectral moment of the 31P absorption line was calculated for the rigid lattice, as well as in the presence of several sets of PF6 reorientation modes, and is in excellent agreement with the experimental data. Whereas the anisotropy of the frequency shift and enhancement of nuclear spinrelaxation rates is driven by the molecular rotation with respect to the dipole fields stemming from the Cu ions, the second spectral moment is determined by the intramolecular interaction of nuclear 19F and 31P moments in the presence of the distinct rotation modes.

We present a detailed $^{31}$P nuclear magnetic resonance (NMR) study of the molecular rotation in the compound [Cu(pz)$_{2}$(2-HOpy)$_{2}$](PF$_{6}$)$_{2}$, where pz = C$_4$H$_4$N$_2$ and 2-HOpy = C$_5$H$_4$NHO. Here, a freezing of the PF$_6$ rotation modes is revealed by several steplike increases of the temperature-dependent second spectral moment, with accompanying broad peaks of the longitudinal and transverse nuclear spin-relaxation rates. An analysis based on the Bloembergen-Purcell-Pound (BPP) theory quantifies the related activation energies as $E_{a}/k_{B}$ = 250 and 1400 K. Further, the anisotropy of the second spectral moment of the $^{31}$P absorption line was calculated for the rigid lattice, as well as in the presence of several sets of PF$_6$ reorientation modes, and is in excellent agreement with the experimental data. Whereas the anisotropy of the frequency shift and enhancement of nuclear spin-relaxation rates is driven by the molecular rotation with respect to the dipole fields stemming from the Cu ions, the second spectral moment is determined by the intramolecular interaction of nuclear $^{19}$F and $^{31}$P moments in the presence of the distinct rotation modes., 9 pages, 5 figures; additionally 2 pages with 3 figures of supplemental material; typos corrected, references added, supplemental material added

We report on a comprehensive characterization of the newly synthesized Cu2+-based molecular magnet [Cu(pz)2(2−HOpy)2](PF6)2 (CuPOF), where pz=C4H4N2 and 2−HOpy=C5H4NHO. From a comparison of theoretical modeling to results of bulk magnetometry, specific heat, μ+SR, ESR, and NMR spectroscopy, this material is determined as an excellent realization of the two dimensional square-lattice S=12 antiferromagnetic Heisenberg model with a moderate intraplane nearest-neighbor exchange coupling of J/kB=6.80(5) K, and an extremely small interlayer interaction of about 1 mK. At zero field, the bulk magnetometry reveals a temperature-driven crossover of spin correlations from isotropic to XY type, caused by the presence of a weak intrinsic easy-plane anisotropy. A transition to long-range order, driven by the low-temperature XY anisotropy under the influence of the interlayer coupling, occurs at TN=1.38(2) K, as revealed by μ+SR. In applied magnetic fields, our 1H-NMR data reveal a strong increase of the magnetic anisotropy, manifested by a pronounced enhancement of the transition temperature to commensurate long-range order at TN=2.8 K and 7 T.

We report on a comprehensive characterization of the newly synthesized Cu$^{2+}$-based molecular magnet [Cu(pz)$_2$(2-HOpy)$_2$](PF$_6$)$_2$ (CuPOF), where pz = C$_4$H$_4$N$_2$ and 2-HOpy = C$_5$H$_4$NHO. From a comparison of theoretical modeling to results of bulk magnetometry, specific heat, $\mu^+$SR, ESR, and NMR spectroscopy, this material is determined as an excellent realization of the 2D square-lattice $S=1/2$ antiferromagnetic Heisenberg model with a moderate intraplane nearest-neighbor exchange coupling of $J/k_\mathrm{B} = 6.80(5)$ K, and an extremely small interlayer interaction of about 1 mK. At zero field, the bulk magnetometry reveals a temperature-driven crossover of spin correlations from isotropic to $XY$ type, caused by the presence of a weak intrinsic easy-plane anisotropy. A transition to long-range order, driven by the low-temperature $XY$ anisotropy under the influence of the interlayer coupling, occurs at $T_\mathrm{N} = 1.38(2)$ K, as revealed by $\mu^+$SR. In applied magnetic fields, our $^1$H-NMR data reveal a strong increase of the magnetic anisotropy, manifested by a pronounced enhancement of the transition temperature to commensurate long-range order at $T_\mathrm{N} =2.8$ K and 7 T., Comment: 14 pages, 8 figures, as well as 10 pages and 18 figures of supplemental material

Cu(pz)$_2$(ClO$_4$)$_2$ (with pz denoting pyrazine C$_4$H$_4$N$_2$) is a two-dimensional spin-1/2 square-lattice antiferromagnet with $T_{\mathrm{N}}$ = 4.24 K. Due to a persisting focus on the low-temperature magnetic properties, its room-temperature structural and physical properties caught no attention up to now. Here we report a study of the structural features of Cu(pz)$_2$(ClO$_4$)$_2$ in the paramagnetic phase, up to 330 K. By employing magnetization, specific heat, $^{35}$Cl nuclear magnetic resonance, and neutron diffraction measurements, we provide evidence of a second-order phase transition at $T^{\star}$ = 294 K, not reported before. The absence of a magnetic ordering across $T^{\star}$ in the magnetization data, yet the presence of a sizable anomaly in the specific heat, suggest a structural order-to-disorder type transition. NMR and neutron-diffraction data corroborate our conjecture, by revealing subtle angular distortions of the pyrazine rings and of ClO$^-_4$ counteranion tetrahedra, shown to adopt a configuration of higher symmetry above the transition temperature., 10 pages, 12 figures

The metal-organic compound [Cu(pz)2(2-OHpy)2](PF6)2 (CuPOF) is a molecular-based analog of the two-dimensional quantum 𝑆 = 1/2 Heisenberg antiferromagnet (2D QHAF) with well-isolated Cu(pz) layers and a very low 𝑘𝐵𝑇𝑁/𝐽 = 0.21 ratio (𝐽/𝑘𝐵 = 6.8 K, 𝑇𝑁 = 1.38 K). We present a focus study of the low-temperature phase transition to long-range order performed via 1H and 31P nuclear magnetic resonance (NMR), as well as high-field magnetometry. A low-temperature Minimum of the temperature-dependent local and uniform magnetizations at 𝑇𝑚𝑖𝑛 indicates a presence of the magnetic order. Within the ordered state, a splitting of the 1H NMR spectra reveals commensurate AF order, presumably of checkerboard type. The phase transition, manifested as a sharp maximum of the temperature-dependent 31P nuclear spin-lattice relaxation rate 1/𝑇1, occurs at temperatures slightly lower than 𝑇𝑚𝑖𝑛, indicating an easy-plane anisotropy as well as a crossover between isotropic and XY behavior.

We present results of electron paramagnetic resonance (EPR) and neutron diffraction studies of CuCl2·2NC5H, which is regarded as one of the best known uniform spin-1/2 Heisenberg antiferro-magnet chain systems. We revealed that at TN = 1.12 K CuCl2·2NC5H5 undergoes the transition into the magnetically ordered spiral state with Q = (0.5, 0.4, 0.5) r.l.u.. It was shown that the zig-zag interchain interactions result in a noticeable geometrical frustration, also affecting the ordered moment per Cu2+ and EPR properties, including the angular dependence of the linewidth. The temperature dependencies of the EPR parameters are discussed.

Cu(pz)2(ClO4)2 (with pz denoting pyrazine, C4H4N2) is among the best realizations of a two-dimensional spin-1/2 square-lattice antiferromagnet. Below T_N = 4.21 K, its weak interlayer couplings induce a 3D magnetic order, strongly influenced by external magnetic fields and/or hydrostatic pressure. Previous work, focusing on the [H, T] phase diagram, identified a spin-flop transition, resulting in a field-tunable bicritical point. However, the influence of external pressure has not been investigated yet. Here we explore the extended [p, H, T] phase diagram of Cu(pz)2(ClO4)2 under pressures up to 12 kbar and magnetic fields up to 7.1 T, via magnetometry and 35Cl nuclear magnetic resonance (NMR) measurements. The application of magnetic fields enhances T_XY , the crossover temperature from the Heisenberg to the XY model, thus pointing to an enhancement of the effective anisotropy. The applied pressure has an opposite effect [dT_N/dp = 0.050(8) K/kbar], as it modifies marginally the interlayer couplings, but likely changes more significantly the orbital reorientation and the square-lattice deformation. This results in a remodeling of the effective Hamiltonian, whereby the field and pressure effects compensate each other. Finally, by comparing the experimental data with numerical simulations we estimate T_BKT, the temperature of the Berezinskii-Kosterlitz-Thouless topological transition and argue why it is inaccessible in our case., 7 pages, 9 figures

Magnetic excitations in the strong-leg quantum spin ladder compound (C$_7$H$_{10}$N)$_2$CuBr$_4$ (known as DIMPY) in the field-induced Tomonaga-Luttinger spin liquid phase are studied by means of high-field electron spin resonance (ESR) spectroscopy. The presence of a gapped ESR mode with unusual non-linear frequency-field dependence is revealed experimentally. Using a combination of analytic and exact diagonalization methods, we compute the dynamical structure factor and identify this mode with longitudinal excitations in the antisymmetric channel. We argue that these excitations constitute a fingerprint of the spin dynamics in a strong-leg spin-1/2 Heisenberg antiferromagnetic ladder and owe its ESR observability to the uniform Dzyaloshinskii-Moriya interaction.

Magnetic excitations in the strong-leg quantum spin ladder compound (C7H10N)2CuBr4 (known as DIMPY) in the field-induced Tomonaga-Luttinger spin-liquid phase are studied by means of high-field electron spin resonance (ESR) spectroscopy. The presence of a gapped ESR mode with unusual nonlinear frequency-field dependence is revealed experimentally. Using a combination of analytic and exact-diagonalization methods, we compute the dynamical structure factor and identify this mode with longitudinal excitations in the antisymmetric channel. We argue that these excitations constitute a fingerprint of the spin dynamics in a strong-leg spin-1/2 Heisenberg antiferromagnetic ladder and owe their ESR observability to the uniform Dzyaloshinskii-Moriya interaction.

Experiments in the antiferromagnetic phase of a quasi 2D $S=1/2$ quasi-square lattice antiferromagnet Cu(pz)2(ClO4)2 reveal a biaxial type of the anisotropy, instead of the easy-plane one, considered before. The weak in-plane anisotropy, found by means of electron spin resonance spectroscopy and magnetization measurements, is about an order of magnitude weaker, than the off-plane anisotropy. The weak in-plane anisotropy results in a spin-flop phase transition for the magnetic field aligned along easy axis, and, thereby, in a bicritical point on the phase diagram. A remarkable feature of the weak in-plane anisotropy is the abrupt change of its sign at the spin-flop point. This anisotropy switching disappears at the tilting of magnetic field to the easy axis by the angle of 10$^\circ$ within the plane. The nature of the abrupt anisotropy reversal remains unclear. The phase diagram is characterized by the increase of the ordering temperature in the magnetic field used, except for a dip near the bicritical point., 14 pages, 22 figures

By means of electron spin resonance investigations we revealed the crucial role of the interchain coupling in the spin dynamics of the spin-1/2 Heisenberg antiferromagnetic (AF) chain material copper-pyrazine-dinitrate, Cu(C$_4$H$_4$N$_2$)(NO$_3$)$_2$. We found that the dominating interchain interaction is of a zig-zag type. This interaction gives rise to geometrical frustration effects and strongly influences the character of AF ordering. Combining our experimental findings with the results of a quasiclassical approach we argue that at low temperatures the system orders in an incommensurate spiral state., 5 pages, 5 figures

We report systematic high-field electron spin resonance (ESR) studies of the quasi-two-dimensional spin- ½ Heisenberg antiferromagnet Cu(pz)2(ClO4)2 (pz denotes pyrazine or C4H4N2). The linewidth and resonance-field temperature dependences of the ESR absorptions in this compound were investigated in the frequency range from 85 to 416 GHz in magnetic fields up to 16 T. A pronounced ESR linewidth anomaly was revealed in the vicinity of TN. This anomaly reflects enhanced critical fluctuations in this compound at the 3D ordering. The experiment revealed a significant change in the linewidth behavior for magnetic fields above 7 T, whose origin will be discussed.

We present an experimental study of the two-dimensional S=1/2 square-lattice antiferromagnet Cu(pz)$_2$(ClO$_4$)$_2$ (pz denotes pyrazine - $C_4H_4N_2$) using specific heat measurements, neutron diffraction and cold-neutron spectroscopy. The magnetic field dependence of the magnetic ordering temperature was determined from specific heat measurements for fields perpendicular and parallel to the square-lattice planes, showing identical field-temperature phase diagrams. This suggest that spin anisotropies in Cu(pz)$_2$(ClO$_4$)$_2$ are small. The ordered antiferromagnetic structure is a collinear arrangement with the magnetic moments along either the crystallographic b- or c-axis. The estimated ordered magnetic moment at zero field is m_0=0.47(5)mu_B and thus much smaller than the available single-ion magnetic moment. This is evidence for strong quantum fluctuations in the ordered magnetic phase of Cu(pz)$_2$(ClO$_4$)$_2$. Magnetic fields applied perpendicular to the square-lattice planes lead to an increase of the antiferromagnetically ordered moment to m_0=0.93(5)mu_B at mu_0H=13.5T - evidence that magnetic fields quench quantum fluctuations. Neutron spectroscopy reveals the presence of a gapped spin excitations at the antiferromagnetic zone center, and it can be explained with a slightly anisotropic nearest neighbor exchange coupling described by J_1^{xy}=1.563(13)meV and J_1^z=0.9979(2)J_1^{xy}.

The magnetic properties of a new family of molecular-based quasi-two dimension $S=1/2$ Heisenberg antiferromagnets are reported. Three compounds, ($Cu(pz)_2(ClO_4)_2$, $Cu(pz)_2(BF_4)_2$, and $[Cu(pz)_2(NO_3)](PF_6)$) contain similar planes of Cu$^{2+}$ ions linked into magnetically square lattices by bridging pyrazine molecules (pz = $C_4H_4N_2$). The anions provide charge balance as well as isolation between the layers. Single crystal measurements of susceptibility and magnetization, as well as muon spin relaxation studies, reveal low ratios of N\'{e}el temperatures to exchange strengths ($4.25 / 17.5 = 0.243$, $3.80/15.3=0.248$, and $3.05/10.8=0.282$, respectively) while the ratio of the anisotropy fields $H_A$ (kOe) to the saturation field $H_\mathrm{SAT}$ (kOe) are small ($2.6/490 = 5.3\times10^{-3}$, $2.4/430=5.5\times10^{-3}$, and $0.07/300=2.3\times10^{-4}$, respectively), demonstrating close approximations to a 2D Heisenberg model. The susceptibilities of ClO$_4$ and BF$_4$ show evidence of an exchange anisotropy crossover (Heisenberg to $XY$) at low temperatures; their ordering transitions are primarily driven by the $XY$ behavior with the ultimate 3D transition appearing parasitically. The PF$_6$ compound remains Heisenberg-like at all temperatures, with its transition to the N\'{e}el state due to the interlayer interactions. Effects of field-induced anisotropy have been observed., Comment: Accepted for publication in Physical Review B

Experimental studies of the spin-1 Haldane-chain material [Ni(C2H8N2)2NO2](BF4) (NENB) doped with diamagnetic Zn(II) ions in a range up to nominally 5% by means of the magnetic-susceptibility and the electron-spin resonance (ESR) techniques are reported. The presence of fractional S = 1/2 chain-end states, revealed by ESR and susceptibility measurements is found to be responsible for spin-glass freezing effects. It is suggested that a higher doping with Zn ions suppresses the spin-glass behaviour by creating shorter and isolated chain fragments.

Results of high-field ESR and magnetization studies of the new spin-1 Haldane-chain material [Ni(C2H8N2)2NO2](BF4) (NENB) are reported. A definite signature of the Haldane state in NENB was obtained. From the analysis of the frequency-field dependence of magnetic excitations in NENB, the spin-Hamiltonian parameters were calculated, yielding \Delta/k_{B} = 17.4~K, g_{\parallel}=2.14, D/k_{B}=7.5~K, and |E/k_{B}|=0.7~K for the Haldane gap, g factor and the crystal-field anisotropy constants, respectively. The presence of fractional S=1/2 chain-end states, revealed by ESR and magnetization measurements, is found to be responsible for spin-glass freezing effects. In addition, extra states in the excitation spectrum of NENB have been observed in the vicinity of the Haldane gap, which origin is discussed.

Results of high-field ESR and magnetization studies of the new spin-1 Haldane-chain material [Ni(C2H8N2)2NO2](BF4) (NENB) are reported. A definite signature of the Haldane state in NENB was obtained. From the analysis of the frequency-field dependence of magnetic excitations in NENB, the spin-Hamiltonian parameters were calculated, yielding Δ/kB = 17.4 K, gk = 2.14, D/kB = 7.5 K, and |E/kB| = 0.7 K for the Haldane gap, g factor and the crystal-field anisotropy constants, respectively. The presence of fractional S = 1/2 chain-end states, revealed by ESR and magnetization measurements, is found to be responsible for spin-glass freezing effects. In addition, extra states in the excitation spectrum of NENB have been observed in the vicinity of the Haldane gap, which origin is discussed.

Experimental studies of magnetic susceptibility and electron-spin resonance (ESR) properties of the spin-1 Haldane-chain material [Ni(C2H8N2)2NO2](BF4) (NENB) doped with non-magnetic Zn-ions in a range up to 5% are reported. The presence of fractional S = 1/2 chain-end states, revealed by ESR and susceptibility measurements in nominally pure single crystals of NENB, is found to be responsible for spin-glass freezing effects. Higher doping ratio of Zn-ions suppresses the spin-glass behaviour by creating shorter and isolated chain fragments. The effect of non-magnetic doping on the lineshape of ESR spectra of fractional S = 1/2 chain-end states is discussed.

Results of magnetization and high-field ESR studies of the new spin-1 Haldane-chain material [Ni(C2H8N2)2NO2](BF4) (NENB) are reported. A definite signature of the Haldane state in NENB was obtained. From the analysis of the frequency-field dependence of magnetic excitations in NENB, the spin-Hamiltonian parameters were calculated, yielding Delta = 17.4 K, g_parallel = 2.14, D = 7.5 K, and |E| = 0.7 K for the Haldane gap, g factor and the crystal-field anisotropy constants, respectively. The presence of fractional S = 1/2 chain-end states, revealed by ESR and magnetization measurements, is found to be responsible for spin-glass freezing effects. In addition, extra states in the excitation spectrum of NENB have been observed in the vicinity of the Haldane gap, which origin is discussed., 5 pages, 6 figures

We present an investigation of magnetic ordering in the two-dimensional S=1/2 quantum magnet Cu(Pz)2(ClO)4)2 using specific heat and zero-field muon-spin relaxation (µ+SR). The magnetic contribution to the specific heat is consistent with an exchange strength of 17.7(3) K. We find unambiguous evidence for a transition to a state of three-dimensional long-range order below a critical temperature TN=4.21(1) K using µ+SR even though there is no feature in the specific heat at that temperature. The absence of a specific heat anomaly at TN is consistent with recent theoretical predictions. The ratio of TN/J=0.24 corresponds to a ratio of intralayer to interlayer exchange constants of |J´ /J| =6.8x10−4, indicative of excellent two-dimensional isolation. The scaled magnetic specific heat of [Cu(Pz)2(HF2)]BF4, a compound with an analogous structure, is very similar to that of Cu(Pz)2(ClO)4)2 although both differ slightly from the predicted value for an ideal 2D S=1/2 Heisenberg antiferromagnet.

We have synthesized and characterized a new spin-1/2 Heisenberg antiferromagnetic ladder: bis 5-iodo-2-aminopyridinium tetrabromocuprate(II) dihydrate. X-ray diffraction studies show the structure of the compound to consist of well isolated stacked ladders and the interaction between the Cu(2+) atoms to be due to direct Br...Br contacts. Magnetic susceptibility and magnetization studies show the compound to be in the strong-coupling limit, with the interaction along the rungs (J' ~ 13 K) much greater than the interaction along the rails (J ~ 1 K). Magnetic critical fields are observed near 8.3 T and 10.4 T, respectively, establishing the existence of the energy gap., 10 pages, 4 figures, submitted to Phys. Rev. B Figure 4 did not print. *.eps files replaced with figures.ps file

High field mangetization, field-dependent specific heat measurements, and zero field inelastic magnetic neutron scattering have been used to explore the magnetic properties of copper pyrazine dinitrate (Cu(C4H4N2)(NO3)2). The material is an ideal one-dimensional spin-1/2 Heisenberg antiferromagnet with nearest neighbor exchange constant J=0.90(1) meV and chains extending along the orthorhombic a-direction. As opposed to previosly studied molecular-based spin-1/2 magnetic systems, coppyer pyrazine dinitrate remains gapless and paramagnetic for g mu_B H/J at least up to 1.4 and for k_B T/J at least down to 0.03 this makes the material an excellent model system for exploring the T=0 critical line which is expected in the H - T phase diagram on the one-dimensional spin-1/2 Heisenberg antiferromagnet. As a first example of such a study we present accurate measurements of the Sommerfeld constant of the spinon gas versus g mu_B H/J < 1.4 which reveal a decrease of the averages spinon velocity by 32% in that field range. The results are in excellent agreement with numerical calculations based on the Bethe ansatz with no adjustable parameters., Comment: 9 pages with figures included, 9 figures, Submitted to Phys. Rev. B (8/31/98), email comments to dhr@pha.jhu.edu