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Funding: Deutsche Forschungsgemeinschaft (DFG) through the SFB 1143 and the Wurzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter–ct.qmat (EXC 2147, Project No. 390858490), as well as the support of the HLD at HZDR, a member of the European Magnetic Field Laboratory (EMFL). We gratefully acknowledge support from the European Research Council (through the QUESTDO project, 714193), the Leverhulme Trust, and the Royal Society. We thank the Elettra synchrotron for access to the APE-HE beamline under proposal number 20195300. The research leading to this result has been supported by the project CALIPSOplus under Grant Agreement 730872 from the EU Framework Programme for Research and Innovation HORIZON 2020. Part of this work has been performed in the framework of the Nanoscience Foundry and Fine Analysis (NFFA-MUR Italy Progetti Internazionali) project (www.trieste.NFFA.eu).

The interface of Ni-NiO thin films was developed by thermal evaporation of nickel and subsequent annealing in oxygen atmosphere at 400 °C at varying duration of time. The evolution of layer thicknesses with annealing time was studied using rutherford backscattering spectrometry. The structural characterization showed grain growth stagnation for Ni at higher duration of annealing. The Ni phase had more crystallinity compared to the NiO phase. The surface was studied using atomic force microscope. The magnetic domains were also imaged. Magnetic stripe domain patterns were observed for selected films. Variation in saturation magnetisation and coercivity with annealing time was observed. The observation of weak exchange bias shows the importance of antiferromagnetic phase in determining the exchange bias properties. Thermal annealing of Ni films caused a competition among oxidation and grain growth.

Magnetism of the spin-$\frac12$ $\alpha$-KVOPO$_4$ is studied by thermodynamic measurements, $^{31}$P nuclear magnetic resonance (NMR), neutron diffraction, and density-functional band-structure calculations. Ferromagnetic Curie-Weiss temperature of $\theta_{\rm CW}\simeq 15.9$ K and the saturation field of $\mu_0H_s\simeq 11.3$ T suggest the predominant ferromagnetic coupling augmented by a weaker antiferromagnetic exchange that leads to a short-range order below 5 K and the long-range antiferromagnetic order below $T_{\rm N}\simeq 2.7$ K in zero field. Magnetic structure with the propagation vector $\mathbf k=(0,\frac12,0)$ and the ordered magnetic moment of 0.58 $\mu_B$ at 1.5 K exposes a non-trivial spin lattice where strong ferromagnetic dimers are coupled antiferromagnetically. The reduction in the ordered magnetic moment with respect to the classical value (1 $\mu_{\rm B}$) indicates sizable quantum fluctuations in this setting, despite the predominance of ferromagnetic exchange. We interpret this tendency toward ferromagnetism as arising from the effective orbital order in the folded chains of the VO$_6$ octahedra., Comment: 12 pages, 14 figures, 58 references

While the Heisenberg model for magnetic Mott insulators on planar lattice structures is comparatively well understood in the case of transition metal ions, the intrinsic spin-orbit entanglement of $4f$ magnetic ions on such lattices shows fascinating new physics largely due to corresponding strong anisotropies both in their single-ion and their exchange properties. We show here that the Yb delafossites, containing perfect magnetic ${\mathrm{Yb}}^{3+}$ triangular lattice planes with pseudospin $s=\frac{1}{2}$ at low temperatures, are an ideal platform to study these phenomena. Competing frustrated interactions may lead to an absence of magnetic order associated to a gapless spin liquid ground state with a huge linear specific heat exceeding that of many heavy fermions, whereas the application of a magnetic field induces anisotropic magnetic order with successive transitions into different long-range ordered structures. In this comparative study, we discuss our experimental findings in terms of a unified crystal-field and exchange model. We combine electron paramagnetic resonance (EPR) experiments and results from neutron scattering with measurements of the magnetic susceptibility, isothermal magnetization up to full polarization, and specific heat to determine the relevant model parameters. The impact of the crystal field is discussed as well as the symmetry-compatible form of the exchange tensor, and we give explicit expressions for the anisotropic $g$ factor, the temperature dependence of the susceptibility, the exchange-narrowed EPR linewidth, and the saturation field.

We report gapless quantum spin liquid behavior in the layered triangular ${\mathrm{Sr}}_{3}{\mathrm{CuSb}}_{2}{\mathrm{O}}_{9}$ system. X-ray diffraction shows superlattice reflections associated with atomic site ordering into triangular Cu planes well separated by Sb planes. Muon spin relaxation measurements show that the $S=\frac{1}{2}$ moments at the magnetically active Cu sites remain dynamic down to 65 mK in spite of a large antiferromagnetic exchange scale evidenced by a large Curie-Weiss temperature ${\ensuremath{\theta}}_{\mathrm{CW}}\ensuremath{\simeq}\ensuremath{-}143\text{ }\text{ }\mathrm{K}$ as extracted from the bulk susceptibility. Specific heat measurements also show no sign of long-range order down to 0.35 K. The magnetic specific heat (${C}_{m}$) below 5 K reveals a ${C}_{m}=\ensuremath{\gamma}T+\ensuremath{\alpha}{T}^{2}$ behavior. The significant ${T}^{2}$ contribution to the magnetic specific heat invites a phenomenology in terms of the so-called Dirac spinon excitations with a linear dispersion. From the low-$T$ specific heat data, we estimate the dominant exchange scale to be $\ensuremath{\sim}36\text{ }\text{ }\mathrm{K}$ using a Dirac spin liquid ansatz which is not far from the values inferred from microscopic density functional theory calculations ($\ensuremath{\sim}45\text{ }\text{ }\mathrm{K}$) as well as high-temperature susceptibility analysis ($\ensuremath{\sim}70\text{ }\text{ }\mathrm{K}$). The linear specific heat coefficient is about $18\text{ }\text{ }\mathrm{mJ}/\mathrm{mol}\text{ }{\mathrm{K}}^{2}$ which is somewhat larger than for typical Fermi liquids.

${\mathrm{TaSnS}}_{2}$ single crystal and polycrystalline samples are investigated in detail by magnetization, electrical resistivity, and specific heat as well as Raman spectroscopy and nuclear magnetic resonance (NMR). Studies are focused on the temperature and magnetic field dependence of the superconducting state. We determine the critical fields for both directions $B\ensuremath{\parallel}c$ and $B\ensuremath{\perp}\phantom{\rule{0.16em}{0ex}}c$. Additionally, we investigate the dependence of the resistivity, the critical temperature, and the structure through Raman spectroscopy under high pressure up to 10 GPa. At a pressure of $\ensuremath{\approx}3\phantom{\rule{0.28em}{0ex}}\mathrm{GPa}$ the superconductivity is suppressed below our minimum temperature. The Sn NMR powder spectrum shows a single line which is expected for the ${\mathrm{TaSnS}}_{2}$ phase and confirms the high sample quality. Pronounced de Haas-van Alphen oscillations in the ac susceptibility of polycrystalline sample reveal two pairs of frequencies indicating coexisting small and large Fermi surfaces. The effective mass of the smaller Fermi surface is $\ensuremath{\approx}0.5{m}_{\mathrm{e}}$. We compare these results with the band structures from DFT calculations. Our findings on ${\mathrm{TaSnS}}_{2}$ are discussed in terms of a quasi-two-dimensional BCS superconductivity.

We report gapless quantum spin liquid behavior in the layered triangular Sr_{3}CuSb_{2}O_{9} system. X-ray diffraction shows superlattice reflections associated with atomic site ordering into triangular Cu planes well separated by Sb planes. Muon spin relaxation measurements show that the S=1/2 moments at the magnetically active Cu sites remain dynamic down to 65 mK in spite of a large antiferromagnetic exchange scale evidenced by a large Curie-Weiss temperature θ_{CW}≃-143 K as extracted from the bulk susceptibility. Specific heat measurements also show no sign of long-range order down to 0.35 K. The magnetic specific heat (C_{m}) below 5 K reveals a C_{m}=γT+αT^{2} behavior. The significant T^{2} contribution to the magnetic specific heat invites a phenomenology in terms of the so-called Dirac spinon excitations with a linear dispersion. From the low-T specific heat data, we estimate the dominant exchange scale to be ∼36 K using a Dirac spin liquid ansatz which is not far from the values inferred from microscopic density functional theory calculations (∼45 K) as well as high-temperature susceptibility analysis (∼70 K). The linear specific heat coefficient is about 18 mJ/mol K^{2} which is somewhat larger than for typical Fermi liquids.

Here, we report the synthesis and magnetic properties of a Yb-based triangular-lattice compound LiYbS$_2$. At low temperatures, it features an effective spin-$\frac{1}{2}$ state due to the combined effect of crystal electric field and spin orbit coupling. Magnetic susceptibility measurements and $^7$Li nuclear magnetic resonance experiments reveal the absence of magnetic long range ordering down to 2~K, which suggests a possible quantum spin liquid ground state. A dominant antiferromagnetic nearest neighbour exchange interaction $J/k_{\rm B}\simeq$ 5.3~K could be extracted form the magnetic susceptibility. The NMR linewidth analysis yields the coupling constant between the Li nuclei and Yb$^{3+}$ ions which was found to be purely dipolar in nature., Comment: (accepted)

Here, we report the synthesis and magnetic properties of a novel, centrosymmetric, quasi-1D spin chain system La3VWS3O6, with hexagonal crystal structure (P63/m, a = 9.460 76(3), c = 5.518 09(2) Å). Pure powders were obtained by solid-state reactions from La2O3, WO3 and metal powders of V and W. X-ray powder diffraction, specific heat, magnetization, 139La-nuclear magnetic resonance (NMR), and electric resistivity measurements indicate that the compound is a low dimensional magnet with an S = 1 spin chain that exhibits no sign of magnetic ordering above 2 K. A single ion anisotropy (D/k B ~ 10 K), caused by magneto-crystalline effects, is probably responsible for a thermodynamic entropy release at lower temperatures, which concurs with 139La-NMR data. By detailed comparison with non-centrosymmetric Ba3V2S4O3, having a very similar magnetic lattice, it is obvious that the presence of crystallographic inversion symmetry has an effect on the behaviour of the magnetic chains.

High-quality single crystals of NaYbSe$_2$, which resembles a perfect triangular-lattice antiferromagnet without the intrinsic disorder, are investigated by magnetization and specific heat, as well as the local probe techniques nuclear magnetic resonance (NMR) and electron spin resonance (ESR). The low-field measurements confirm the absence of any spin freezing or long-range magnetic order down to 50~mK, which suggests a quantum spin liquid ground (QSL) state with gapless excitations. The instability of the QSL state is observed upon applying magnetic fields. For the $H\bot c$ direction, a field-induced magnetic phase transition is observed above 2~T from the $C_{\rm p}(T)$ data, agreeing with a clear $\frac{M_s}{3}$ plateau of $M(H)$, which is associated with an up-up-down (uud) spin arrangement. For the $H\|c$ direction, a field-induced transition could be evidenced at a much higher field range (9 - 21~T). The $^{23}$Na NMR measurements provide microscopic evidence for field-induced ordering for both directions. A reentrant behavior of $T_{\rm N}$, originating from the thermal and quantum spin fluctuations, is observed for both directions. The anisotropic exchange interactions $J_{\perp}\simeq$ 4.7~K and $J_z\simeq$2.33~K are extracted from the modified bond-dependent XXZ model for the spin-$\frac{1}{2}$ triangular-lattice antiferromagnet. The absence of magnetic long-range order at zero fields is assigned to the effect of strong bond-frustration, arising from the complex spin-orbit entangled $4f$ ground state. Finally, we derive the highly anisotropic magnetic phase diagram, which is discussed in comparison with the existing theoretical models for spin-$\frac{1}{2}$ triangular-lattice antiferromagnets., 6 Figures

Structural and magnetic properties of a quasi-one-dimensional spin-$\frac{1}{2}$ compound ${\mathrm{NaVOPO}}_{4}$ are explored by x-ray diffraction, magnetic susceptibility, high-field magnetization, specific heat, electron spin resonance, and $^{31}\mathrm{P}$ nuclear magnetic resonance measurements, as well as complementary ab initio calculations. Whereas magnetic susceptibility of ${\mathrm{NaVOPO}}_{4}$ may be compatible with the gapless uniform spin chain model, detailed examination of the crystal structure reveals a weak alternation of the exchange couplings with the alternation ratio $\ensuremath{\alpha}\ensuremath{\simeq}0.98$ and the ensuing zero-field spin gap ${\mathrm{\ensuremath{\Delta}}}_{0}/{k}_{\mathrm{B}}\ensuremath{\simeq}2.4\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ directly probed by field-dependent magnetization measurements. No long-range order is observed down to 50 mK in zero field. However, applied fields above the critical field ${H}_{c1}\ensuremath{\simeq}1.6\phantom{\rule{0.28em}{0ex}}\mathrm{T}$ give rise to a magnetic ordering transition with the phase boundary ${T}_{N}\ensuremath{\propto}{(H\ensuremath{-}{H}_{c1})}^{\frac{1}{\ensuremath{\phi}}}$, where $\ensuremath{\phi}\ensuremath{\simeq}1.8$ is close to the value expected for Bose-Einstein condensation of triplons. With its weak alternation of the exchange couplings and small spin gap, ${\mathrm{NaVOPO}}_{4}$ lies close to the quantum critical point.

We present the synthesis and a detailed investigation of structural and magnetic properties of polycrystalline ${\mathrm{NaVOAsO}}_{4}$ by means of x-ray diffraction, magnetization, electron spin resonance (ESR), and $^{75}\mathrm{As}$ nuclear magnetic resonance (NMR) measurements as well as density-functional band structure calculations. Temperature-dependent magnetic susceptibility, ESR intensity, and NMR line shift could be described well using an alternating spin-$1/2$ chain model with the exchange coupling $J/{k}_{\mathrm{B}}\ensuremath{\simeq}52$ K and an alternation parameter $\ensuremath{\alpha}\ensuremath{\simeq}0.65$. From the high-field magnetization measured at $T=1.5$ K, the critical field of the gap closing is found to be ${H}_{\mathrm{c}}\ensuremath{\simeq}16$ T, which corresponds to the zero-field spin gap of ${\mathrm{\ensuremath{\Delta}}}_{0}/{k}_{\mathrm{B}}\ensuremath{\simeq}21.4$ K. Both NMR shift and spin-lattice relaxation rate show an activated behavior at low temperatures, further confirming the singlet ground state. The spin chains do not coincide with the structural chains, whereas the couplings between the spin chains are frustrated. Because of a relatively small spin gap, ${\mathrm{NaVOAsO}}_{4}$ is a promising compound for further experimental studies under high magnetic fields.

Platelike high-quality ${\mathrm{NaYbS}}_{2}$ rhombohedral single crystals with lateral dimensions of a few mm have been grown and investigated in great detail by bulk methods such as magnetization and specific heat, but also by local probes such as nuclear magnetic resonance (NMR), electron-spin resonance (ESR), muon-spin relaxation ($\ensuremath{\mu}\mathrm{SR}$), and inelastic neutron scattering over a wide field and temperature range. Our single-crystal studies clearly evidence a strongly anisotropic quasi-two-dimensional magnetism and an emerging spin-orbit entangled ${J}_{\mathrm{eff}}=\frac{1}{2}$ state of Yb towards low temperatures together with an absence of long-range magnetic order down to 260 mK. In particular, the clear and narrow Yb ESR lines together with narrow $^{23}\mathrm{Na}$ NMR lines evidence an absence of inherent structural distortions in the system, which is in strong contrast to the related spin-liquid candidate ${\mathrm{YbMgGaO}}_{4}$ falling within the same space group $R\overline{3}m$. This identifies ${\mathrm{NaYbS}}_{2}$ as a rather pure spin-$\frac{1}{2}$ triangular-lattice magnet and a putative quantum spin liquid.

The structural and magnetic properties of the square-cupola antiferromagnet Sr(TiO)Cu$_{4}$(PO$_{4}$)$_{4}$ are investigated via x-ray diffraction, magnetization, heat capacity, and $^{31}$P nuclear magnetic resonance experiments on polycrystalline samples, as well as density-functional band-structure calculations. The temperature-dependent unit cell volume could be described well using the Debye approximation with the Debye temperature of $\theta_{\rm D} \simeq $ 550~K. Magnetic response reveals a pronounced two-dimensionality with a magnetic long-range-order below $T_{\rm N} \simeq 6.2$~K. High-field magnetization exhibits a kink at $1/3$ of the saturation magnetization. Asymmetric $^{31}$P NMR spectra clearly suggest strong in-plane anisotropy in the magnetic susceptibility, as anticipated from the crystal structure. From the $^{31}$P NMR shift vs bulk susceptibility plot, the isotropic and axial parts of the hyperfine coupling between $^{31}$P nuclei and the Cu$^{2+}$ spins are calculated to be $A_{\rm hf}^{\rm iso} \simeq 6539$ and $A_{\rm hf}^{\rm ax} \simeq 952$~Oe/$\mu_{\rm B}$, respectively. The low-temperature and low-field $^{31}$P NMR spectra indicate a commensurate antiferromagnetic ordering. Frustrated nature of the compound is inferred from the temperature-dependent $^{31}$P NMR spin-lattice relaxation rate and confirmed by our microscopic analysis that reveals strong frustration of the square cupola by next-nearest-neighbor exchange couplings.

A series of lanthanide(III) based coordination polymers have been synthesized using chelidamic acid (CA) as a ligand, $$[\hbox {Ln}(\hbox {C}_{7}\hbox {H}_{2}\hbox {NO}_{5})(\hbox {H}_{2}\hbox {O})_{3}].\hbox {H}_{2}\hbox {O}$$ (Ln = Eu, Gd, Tb, and Dy). All the compounds were prepared by solvothermal technique using $$\hbox {H}_{2}\hbox {O-DMF}$$ as solvents (4:1, volume ratio). Compounds were characterized through various instrumental techniques such as single-crystal X-ray diffraction, powder X-ray diffraction, thermogravimetric analysis, IR spectroscopy, etc. In all the cases lanthanide ion adopts distorted dodecahedron geometry. And these dodecahedrons are connected through chelidamic acid ligand to form the two-dimensional structure. These layers are H-bonded to form the three-dimensional supramolecular structure. The optical band gap energy measurements exhibit that the variation of the band gap energy is independent of the f-electrons. This is due to the weak bonding connectivity between the metal ion and ligands, which could not perturb the density of states significantly. The variable-temperature magnetic measurements exhibit the paramagnetic behavior of all the compounds though the effective magnetic moments rise with increasing number of f-electrons. The present study illustrates the usefulness of the lanthanides for the structure building as well as the role of f-electrons for opto-electronic behaviors. SYNOPSIS A series of two-dimensional isostructural Lanthanum coordination polymers have been synthesized and comparisons of various properties have been made. Figure shows the reaction scheme for the observed coordination polymer.

Temperature- and field-dependent 1H-, 19F-, and 79,81Br-NMR measurements together with zero - field 79,81Br-NQR measurements on polycrystalline samples of barlowite, Cu4(OH)6FBr are conducted to study the magnetism and possible structural distortions on a microscopic level. The temperature dependence of the 79,81Br-NMR spin-lattice relaxation rates 1/T1 indicate a phase transition at TN \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\simeq $$\end{document}≃ 15 K which is of magnetic origin, but with an unusually weak slowing down of fluctuations below TN. Moreover, 1/T1T scales linear with the bulk susceptibility which indicates persisting spin fluctuations down to 2 K. Quadupolare resonance (NQR) studies reveal a pair of zero-field NQR- lines associated with the two isotopes of Br with the nuclear spins of I = 3/2. Quadrupole coupling constants of vQ ≃ 28.5 MHz and 24.7 MHz for 79Br- and 81Br-nuclei are determined from Br-NMR and the asymmetry parameter of the electric field gradient was estimated to η ≃ 0.2. The Br-NQR lines are consistent with our findings from Br-NMR and they are relatively broad, even above TN. This broadening and the relative large η value suggests a symmetry reduction at the Br- site reflecting the presence of a local distortion in the lattice. Our density-functional calculations show that the displacements of Cu2 atoms located between the kagome planes do not account for this relatively large η. On the other hand, full structural relaxation, including the deformation of kagome planes, leads to a better agreement with the experiment.

We have correlated the structure-property relationship of three manganese-based inorganic-organic hybrid structures. Compound 1, [Mn2(OH-BDC)2(DMF)3] (where BDC = 1,4-benzene dicarboxylic acid and DMF = N,N'-dimethylformamide), contains Mn2O11 dimers as secondary building units (SBUs), which are connected by carboxylate anions forming Mn-O-C-O-Mn chains. Compound 2, [Mn2(BDC)2(DMF)2], contains Mn4O20 clusters as SBUs, which also form Mn-O-C-O-Mn chains. In compound 3, [Mn3(BDC)3(DEF)2] (where DEF = N,N'-diethylformamide), the distorted MnO6 octahedra are linked to form a one-dimensional chain with Mn-O-Mn connectivity. The magnetic properties were investigated by means of magnetization and heat capacity measurements. The temperature dependent magnetic susceptibility of all the three compounds could be nicely fitted using a one-dimensional S = 5/2 Heisenberg antiferromagnetic chain model and the value of intra-chain exchange coupling (J/k(B)) between Mn(2+) ions was estimated to be ∼1.1 K, ∼0.7 K, and ∼0.46 K for compounds 1, 2, and 3, respectively. Compound 1 does not undergo any magnetic long-range-order down to 2 K while compounds 2 and 3 undergo long-range magnetic order at T(N) ≈ 4.2 K and ≈4.3 K, respectively, which are of spin-glass type. From the values of J/k(B) and T(N) the inter-chain coupling (J(⊥)/k(B)) was calculated to be about 0.1J/k(B) for both compounds 2 and 3, respectively.

$^{75}$As NMR measurements were performed on a polycrystalline sample of spin-1/2 alternating-spin-chain Heisenberg antiferromagnet AgVOAsO$_4$. Temperature-dependent NMR shift $K(T)$, which is a direct measure of the intrinsic spin susceptibility, agrees very well with the spin-1/2 alternating-chain model, justifying the assignment of the spin lattice. From the analysis of $K(T)$, magnetic exchange parameters were estimated as follows: the leading exchange $J/k_{\rm B} \simeq 38.4$ K, alternation ratio $\alpha = J'/J \simeq 0.68$, and spin gap $\Delta/k_{\rm B} \simeq 15$ K. The transferred hyperfine coupling between the $^{75}$As nucleus and V$^{4+}$ spins obtained by comparing the NMR shift with bulk susceptibility amounts to $A_{\rm hf} \simeq 3.3$ T/$\mu_{\rm B}$. Our temperature-dependent spin-lattice relaxation rate $1/T_1(T)$ also shows an activated behaviour at low temperatures, thus confirming the presence of a spin gap in AgVOAsO$_4$.

Here, we report the synthesis and magnetic properties of a new triangular lattice antiferromagnet Ba$_3$CoTa$_2$O$_9$. The effective spin of Co$^{2+}$ is found to be $J=1/2$ at low temperatures due to the combined effect of crystal field and spin-orbit coupling. Ba$_3$CoTa$_2$O$_9$ undergoes two successive magnetic phase transitions at $T_{N1}\simeq0.70$~K and $T_{N2}\simeq0.57$~K in zero applied field, which is typical for triangular antiferromagnets with the easy-axis magnetic anisotropy. With increasing field, the transition anomalies are found to shift toward low temperatures, confirming the antiferromagnetic nature of the transitions. At higher fields, the transition peaks in the heat capacity data disappear and give way to a broad maximum, which can be ascribed to a Schottky anomaly due to the Zeeman splitting of spin levels. The $H-T$ phase diagram of the compound shows three distinct phases. The possible nature of these phases is discussed., Comment: 6 pages, 7 figures

We report the magnetic properties of iso-structural compounds BiNiPO5 and BiCoPO5 which undergo antiferromagnetic ordering at 17 K and 11 K, respectively. Positive values of θCW suggest the dominant antiferromagnetic (AFM) interactions in both the compounds. Similarly, the (TN/θCW) ratio suggests that BiCoPO5 is a frustrated one dimensional antiferromagnet while BiNiPO5 is more likely a three dimensional antiferromagnet. Magnetic specific heat Cmag was found to be extended towards high temperatures in BiCoPO5 compared to BiNiPO5 supporting the low dimensional character of BiCoPO5. The magnetic isotherm (M vs. H) at 2 K shows the feature of a field induced spin-flop transition in BiCoPO5 as is expected for a strongly anisotropic AFM. We construct the field-temperature (H−T) phase diagram for BiCoPO5 from the specific heat measurements and find that the phase boundary of the PM-AFM transition can be described in terms of a mean-field power law.

We report the thermodynamic properties, magnetic ground state, and microscopic magnetic model of the spin-1 frustrated antiferromagnet ${\mathrm{Li}}_{2}{\mathrm{NiW}}_{2}{\mathrm{O}}_{8}$, showing successive transitions at ${T}_{\mathrm{N}1}\ensuremath{\simeq}18$ K and ${T}_{\mathrm{N}2}\ensuremath{\simeq}12.5$ K in zero field. Nuclear magnetic resonance and neutron diffraction reveal collinear and commensurate magnetic order with the propagation vector $\mathbf{k}=(\frac{1}{2},0,\frac{1}{2})$ below ${T}_{\mathrm{N}2}$. The ordered moment of $1.8{\ensuremath{\mu}}_{B}$ at 1.5 K is directed along $[0.89(9),\ensuremath{-}0.10(5),\ensuremath{-}0.49(6)]$ and matches the magnetic easy axis of spin-$1\phantom{\rule{4pt}{0ex}}{\mathrm{Ni}}^{2+}$ ions, which is determined by the scissor-like distortion of the ${\mathrm{NiO}}_{6}$ octahedra. Incommensurate magnetic order, presumably of spin-density-wave type, is observed in the region between ${T}_{\mathrm{N}2}$ and ${T}_{\mathrm{N}1}$. Density-functional band-structure calculations put forward a three-dimensional spin lattice with spin-1 chains running along the $[01\overline{1}]$ direction and stacked on a spatially anisotropic triangular lattice in the $ab$ plane. We show that the collinear magnetic order in ${\mathrm{Li}}_{2}{\mathrm{NiW}}_{2}{\mathrm{O}}_{8}$ is incompatible with the triangular lattice geometry and thus driven by a pronounced easy-axis single-ion anisotropy of ${\mathrm{Ni}}^{2+}$.

Magnetic frustration in three dimensions (3D) manifests itself in the spin-$\frac12$ insulator Li$_2$CuW$_2$O$_8$. Density-functional band-structure calculations reveal a peculiar spin lattice built of triangular planes with frustrated interplane couplings. The saturation field of 29 T contrasts with the susceptibility maximum at 8.5 K and a relatively low Neel temperature $T_N\simeq 3.9$ K. Magnetic order below $T_N$ is collinear with the propagation vector $(0,\frac12,0)$ and an ordered moment of 0.65(4) $\mu_B$ according to neutron diffraction data. This reduced ordered moment together with the low maximum of the magnetic specific heat ($C^{\max}/R\simeq 0.35$) pinpoint strong magnetic frustration in 3D. Collinear magnetic order suggests that quantum fluctuations play crucial role in this system, where a non-collinear spiral state would be stabilized classically.

We report a $^{7}\mathrm{Li}$ nuclear magnetic resonance (NMR) study of a frustrated three-dimensional spin-$\frac{1}{2}$ antiferromagnet ${\text{Li}}_{2}{\text{CuW}}_{2}{\text{O}}_{8}$ and also explore the effect of nonmagnetic dilution. The magnetic long-range ordering in the parent compound at ${T}_{\mathrm{N}}\ensuremath{\simeq}3.9\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ was detected from the drastic line broadening and a peak in the spin-lattice relaxation rate ($1/{T}_{1}$). The NMR spectrum above ${T}_{\mathrm{N}}$ broadens systematically, and its full width at half maximum (FWHM) tracks the static spin susceptibility. From the analysis of FWHM vs static susceptibility, the coupling between the Li nuclei and ${\text{Cu}}^{2+}$ ions was found to be purely dipolar in nature. The magnitude of the maximum exchange coupling constant is ${J}_{\mathrm{max}}/{k}_{\mathrm{B}}\ensuremath{\simeq}13\phantom{\rule{0.28em}{0ex}}\mathrm{K}$. NMR spectra below ${T}_{\mathrm{N}}$ broaden abruptly and transform into a double-horn pattern reflecting the commensurate nature of the spin structure in the ordered state. Below ${T}_{\mathrm{N}}$, $1/{T}_{1}$ follows a ${T}^{5}$ behavior. The frustrated nature of the compound is confirmed by persistent magnetic correlations at high temperatures well above ${T}_{\mathrm{N}}$. The dilution of the spin lattice with nonmagnetic Zn atoms has dramatic influence on ${T}_{N}$ that decreases exponentially similar to quasi-one-dimensional antiferromagnets, even though ${\text{Li}}_{2}{\text{CuW}}_{2}{\text{O}}_{8}$ has only a weak one-dimensional anisotropy. Heat capacity of doped samples follows power law (${C}_{\mathrm{p}}\ensuremath{\propto}{T}^{\ensuremath{\alpha}}$) below ${T}_{\mathrm{N}}$, and the exponent ($\ensuremath{\alpha}$) decreases from 3 in the parent compound to 1 in the 25% doped sample.

The crystallographic, magnetic, and thermal properties of polycrystalline $\mathrm{Bi}{\mathrm{Mn}}_{2}{\mathrm{PO}}_{6}$ and its nonmagnetic analog $\mathrm{Bi}{\mathrm{Zn}}_{2}{\mathrm{PO}}_{6}$ are investigated by x-ray diffraction, magnetization $M$, magnetic susceptibility $\ensuremath{\chi}$, heat capacity ${C}_{p}$, and $^{31}\mathrm{P}$ nuclear magnetic resonance (NMR) measurements versus applied magnetic field $H$ and temperature $T$ as well as by density-functional band theory and molecular-field calculations. Both compounds show a strong monotonic lattice softening on cooling, where the Debye temperature decreases by a factor of two from ${\ensuremath{\Theta}}_{\mathrm{D}}\ensuremath{\sim}650$ K at $T=300$ K to ${\ensuremath{\Theta}}_{\mathrm{D}}\ensuremath{\sim}300$ K at $T=2$ K. The $\ensuremath{\chi}(T)$ data for $\mathrm{Bi}{\mathrm{Mn}}_{2}{\mathrm{PO}}_{6}$ above 150 K follow a Curie-Weiss law with a Curie constant consistent with a Mn${}^{+2}$ spin $S=5/2$ with $g$ factor $g=2$ and an antiferromagnetic (AFM) Weiss temperature ${\ensuremath{\theta}}_{\mathrm{CW}}\ensuremath{\simeq}\ensuremath{-}78$ K. The $\ensuremath{\chi}$ data indicate long-range AFM ordering below ${T}_{\mathrm{N}}\ensuremath{\simeq}30$ K, confirmed by a sharp $\ensuremath{\lambda}$-shaped peak in ${C}_{\mathrm{p}}(T)$ at 28.8 K. The magnetic entropy at 100 K extracted from the ${C}_{\mathrm{p}}(T)$ data is consistent with spin $S=5/2$ for the Mn${}^{+2}$ cations. The band-theory calculations indicate that $\mathrm{Bi}{\mathrm{Mn}}_{2}{\mathrm{PO}}_{6}$ is an AFM compound with dominant interactions ${J}_{1}/{k}_{\mathrm{B}}\ensuremath{\simeq}6.7$ K and ${J}_{3}/{k}_{\mathrm{B}}\ensuremath{\simeq}5.6$ K along the legs and rungs of a Mn two-leg spin-ladder, respectively. However, sizable and partially frustrating interladder couplings lead to an anisotropic three-dimensional magnetic behavior with long-range AFM ordering at ${T}_{\mathrm{N}}\ensuremath{\simeq}30$ K observed in the $\ensuremath{\chi}$, ${C}_{\mathrm{p}}$, and NMR measurements. A second magnetic transition at $\ensuremath{\approx}$10 K is observed from the $\ensuremath{\chi}$ and NMR measurements but is not evident in the ${C}_{\mathrm{p}}$ data. The ${C}_{\mathrm{p}}$ data at low $T$ suggest a significant contribution from AFM spin waves moving in three dimensions and the absence of a spin-wave gap. A detailed analysis of the NMR spectra indicates commensurate magnetic order between 10 and 30 K, while below 10 K additional features appear that may arise from an incommensurate modulation and/or spin canting. The commensurate order is consistent with microscopic density functional calculations that yield a collinear N\'eel-type AFM spin arrangement both within and between the ladders, despite the presence of multiple weak interactions frustrating this magnetic structure of the Mn spins. Frustration for AFM ordering and the one-dimensional spatial anisotropy of the three-dimensional spin interactions are manifested in the frustration ratio $f=|{\ensuremath{\theta}}_{\mathrm{CW}}|/{T}_{\mathrm{N}}\ensuremath{\simeq}2.6$, indicating a suppression of ${T}_{\mathrm{N}}$ from 68 K in the absence of these effects to the observed value of about 30 K in $\mathrm{Bi}{\mathrm{Mn}}_{2}{\mathrm{PO}}_{6}$.

We present a combined experimental and theoretical study of the spin-$\frac{1}{2}$ compound CuP${}_{2}$O${}_{6}$ that features a network of two-dimensional (2D) antiferromagnetic (AFM) square planes, interconnected via one-dimensional (1D) AFM spin chains. Magnetic susceptibility, high-field magnetization, and electron spin resonance (ESR) data, as well as microscopic density-functional band-structure calculations and subsequent quantum Monte Carlo simulations, show that the coupling ${J}_{2\mathrm{D}}\ensuremath{\simeq}40$ K in the layers is an order of magnitude larger than ${J}_{1\mathrm{D}}\ensuremath{\simeq}3$ K in the chains. Below ${T}_{N}\ensuremath{\simeq}8$ K, CuP${}_{2}$O${}_{6}$ develops long-range order, as evidenced by a weak net moment on the 2D planes induced by anisotropic magnetic interactions of Dzyaloshinsky-Moriya type. A striking feature of this 3D ordering transition is that the 1D moments grow significantly slower than the ones on the 2D units, which is evidenced by the persistent paramagnetic ESR signal below ${T}_{N}$. Compared to typical quasi-2D magnets, the ordering temperature of CuP${}_{2}$O${}_{6}$ ${T}_{N}/{J}_{2\mathrm{D}}\ensuremath{\simeq}0.2$ is unusually low, showing that weakly coupled spins sandwiched between 2D magnetic units effectively decouple these units and impede the long-range ordering.