Supramolecular Spin Chains via Radical-Radical Contacts Stabilizing Ferromagnetic Interactions between Heisenberg or Ising-like Spins.

A new paramagnetic ligand, 4-(2'-4-(2''-furyl)-pyrimidyl)-1,2,3,5-dithiadiazolyl (furylpymDTDA) and three transition metal coordination complexes, M(hfac)2(furylpymDTDA) M = Mn, Co, Ni; hfac = 1,1,1,5,5,5-hexafluoroacetylacetonato-), are reported. The solid-state structures are influenced by the geometry of the coordination sphere of the M(II) centers: trigonal (Mn) vs. octahedral (Co and Ni). While the hs-Mn(II) complex exhibits pairwise multi-centre 2-electron bonds (i.e., pancake bonds) between the planar π radical DTDA moieties, the hs-Co(II) and Ni(II) complexes crystallize with close contacts between coordinated furylpymDTDA radical ligands that define linear 1D arrays of molecular units. The magnetic data for the hs-Co(II) and Ni(II) complexes indicate ferromagnetic (FM) interactions between molecular units, apparently mediated by radical-radical contacts along the supramolecular chains. Computational analysis suggests proximity between regions of large α- and ß-spin density on neighbouring molecular sites enabling FM exchange, in accordance with the McConnell I mechanism. The magnetic data for the Ni(II) complex are consistent with a Heisenberg spin chain, whereas the hs-Co(II) complex exhibits Ising-like spin chain behaviour and a magnetic phase transition to an FM ordered state at 4.6 K.

Deciphering competing interactions of Kitaev-Heisenberg-\texorpdfstring{$\Gamma$}~~system in clusters: part I - static properties.

Recently, the Kitaev-Heisenberg-$\Gamma$ system has been used to explore various aspects of Kitaev spin liquid physics. Here, we consider a few small clusters of up to twelve sites and study them in detail to unravel many interesting findings due to the competition between all possible signs and various magnitudes of these interactions under the influence of an external magnetic field. When Heisenberg interaction is taken anti-ferromagnetic, one obtains plateaus in correlation functions where, surprisingly, the exact groundstate reduces to the eigenstate of Heisenberg interaction as well. On the other hand, for ferromagnetic Heisenberg interaction, its competition with Kitaev interaction results in non-monotonicity in the correlation functions. We discuss, in detail, the competing effects on low energy spectrum, flux operator, magnetization, susceptibility, and specific heat. Finally, we discuss how our findings could be helpful to explain some of the recent experimental and theoretical findings in materials with Kitaev interactions.

A comparison of pulse and CW EPR T2-relaxation measurements of an inhomogeneously broadened nitroxide spin probe undergoing Heisenberg spin exchange 2. The intercept discrepancy.

Experimental confirmation of a theoretical prediction of a non-linear broadening of the spin packets of nitroxide free radicals due to Heisenberg spin exchange at low concentrations, C, is presented. A recent demonstration that spectra with resolved proton hyperfine structure may be analyzed efficiently and accurately was utilized to confirm the theory. As C→0, a plot of the spin-packet line width (SPW) curves downward due to the presence of proton hyperfine couplings that increase the number of distinguishable quantum spin states. At higher C, the broadening is linear with C and the results for the spin exchange rate constant determined from the slope of the broadening of the average spin-packet line width and electron spin echo measurements are in agreement. It is shown that applying modest digital smoothing does not change the values of the SPW. An example of a practical application of these methods to published work is presented, allowing an enigma to be resolved.

Magnetic Excitations in Ferromagnetically Coupled Spin-1 Nanographenes.

In the pursuit of high-spin building blocks for the formation of covalently bonded 1D or 2D materials with controlled magnetic interactions, $\pi$-electron magnetism offers an ideal framework to engineer ferromagnetic interactions between nanographenes. As a first step in this direction, we explore the spin properties of ferromagnetically coupled triangulenes -- triangular nanographenes with spin $S = 1$. By combining in-solution synthesis of rationally designed molecular precursors with on-surface synthesis, we successfully achieve covalently bonded $S = 2$ triangulene dimers and $S = 3$ trimers on Au(111). Starting with the triangulene dimer, we meticulously characterize its low-energy magnetic excitations using inelastic electron tunneling spectroscopy (IETS). IETS reveals conductance steps corresponding to a quintet-to-triplet excitation, and a zero-bias peak resulting from higher-order spin-spin scattering of the five-fold degenerate ferromagnetic ground state. The Heisenberg model captures the key parameters of inter-triangulene ferromagnetic exchange, and its successful extension to the larger $S = 3$ system validates the model's accuracy. We anticipate that incorporating ferromagnetically coupled building blocks into the repertoire of magnetic nanographenes will unlock new possibilities for designing carbon nanomaterials with complex magnetic ground states.

Tomonaga-Luttinger liquid and quantum criticality in spin- 1 2 antiferromagnetic Heisenberg chain C 14 H 18 CuN 4 O 10 via Wilson ratio.

The ground state of a one-dimensional spin- 1 2 uniform antiferromagnetic Heisenberg chain (AfHc) is a Tomonaga-Luttinger liquid which is quantum-critical with respect to applied magnetic fields up to a saturation field µ 0 H s beyond which it transforms to a fully polarized state. Wilson ratio has been predicted to be a good indicator for demarcating these phases [Phys. Rev. B 96, 220401 (2017)]. From detailed temperature and magnetic field-dependent magnetization, magnetic susceptibility and specific heat measurements in a metalorganic complex and comparisons with field theory and quantum transfer matrix method calculations, the complex was found to be a very good realization of a spin- 1 2 AfHc. Wilson ratio obtained from experimentally obtained magnetic susceptibility and magnetic contribution of specific heat values was used to map the magnetic phase diagram of the uniform spin- 1 2 AfHc over large regions of phase space demarcating Tomonaga-Luttinger liquid, saturation field quantum critical, and fully polarized states. Luttinger parameter and spinon velocity were found to match very well with the values predicted from conformal field theory.

A reinterpretation of Heisenberg's Umdeutung in prescriptive-dynamical terms.

There has been a lot of discussion about Heisenberg's Umdeutung paper of 1925, which is universally credited as the first formulation of modern quantum mechanics. Much of this discussion has been characterized by puzzlement over the manner in which Heisenberg arrived at his formulation, supposedly through Bohr's atomic theory in conjunction with two philosophical principles, namely the Correspondence Principle and the Observability Principle. I provide textual, contextual, and philosophical evidence that the "prescriptive-dynamical framework" - recently advocated in the literature on independent grounds - is the perfect perspective from which to understand Heisenberg's work and the significance of the two principles he utilized to arrive at it.

The spin-SHeisenberg antiferromagnet on the orthogonal-dimer lattice.

The spin-SHeisenberg antiferromagnet on the orthogonal-dimer lattice is studied. In most of the investigations of the antiferromagnet on this lattice beginning with the study by Shastry and Sutherland, theS=1/2case has intensively been treated. In the present study, the cases ofS = 1 and 3/2 are particularly treated by the numerical-diagonalization method based on the Lanczos algorithm applied to finite-size clusters. We successfully capture the edge of the exact-dimer phase and that of the Néel-ordered phase. A significant finding is the existence of an intermediate phase between both the edges irrespective of spin-S.

Engrams to Remember: A Conversation Between Johannes Gräff and Steve Ramirez.

Johannes Gräff (JG): Steve, in preparation for this conversation, I pulled out the book "In search of memory" by Eric Kandel from my bookshelf. Obviously one big question is, given that this book was written more than 20 years ago: Are we there yet? Have we found memory?

Dynamical analysis and the soliton solutions of (2+1)-dimensional Heisenberg ferro-magnetic spin chains model with beta fractional derivative.

This paper investigates the soliton solutions and dynamical analysis of (2+1)-dimensional Heisenberg ferro-magnetic spin chains model with beta fractional derivative, which is transformed into the ordinary differential equation. By using the second-order complete discriminant system, the soliton solutions are presented. By utilizing the theory of planar dynamical system, the phase portraits of the dynamical system and its disturbance system are drawn. Moreover, three-dimensional, two-dimensional, and contour plots of soliton solutions for (2+1)-dimensional Heisenberg ferro-magnetic spin chains model with beta fractional derivative have also been plotted.

Nonlocality of mixtures of the ground and first excited states withinJ1-J2Heisenberg model.

We investigate both bipartite and multipartite nonlocality in theJ1-J2Heisenberg model. Bipartite nonlocality is measured by the Clauser-Horne-Shimony-Holt inequality, while multipartite nonlocality is explored through Bell-type inequalities. Our findings reveal that neither ground-state nor full thermal-state nonlocality reliably characterizes quantum phase transitions (QPTs). However, we uncover that the mixed-state nonlocality of the ground and first excited states exhibits distinctive characteristics applicable to both bipartite and multipartite scenarios. We also demonstrate how mixed-state quantum correlation behaviors depend on varying temperature regimes. In the bipartite case, we observe a phenomenon known as 'correlation reversal' with increasing temperature, a previously unreported occurrence in other models. For the multipartite case, the ability to signify phase transitions is significantly enhanced as the temperature rises. Furthermore, we discover a linear scaling effect that provides valuable insights for extrapolating QPTs in the thermodynamic limit asN→∞. Additionally, we identify the critical temperature at which mixed-state nonlocality becomes a reliable indicator of phase transitions.

Critical behaviors of van der Waals itinerant ferromagnet Fe3.8GaTe2.

The critical behavior of the van der Waals ferromagnet Fe3.8GaTe2was systematically studied through measurements of isothermal magnetization, with the magnetic field applied along thec-axis. Fe3.8GaTe2undergoes a non-continuous paramagnetic to ferromagnetic phase transition at the Curie temperatureTc∼ 355 K. A comprehensive analysis of isotherms aroundTcutilizing the modified Arrott diagram, the Kouvel-Fisher method, the Widom scaling law, and the critical isotherm analysis yielded the critical exponent ofß= 0.411,γ= 1.246, andδ= 3.99. These critical exponents are found to be self-consistent and align well with the scaling equation at high magnetic fields, underscoring the reliability and intrinsic nature of these parameters. However, the low-field data deviates from the scaling relation, exhibiting a vertical trend whenT

Monte Carlo Based Techniques for Quantum Magnets with Long-Range Interactions.

Long-range interactions are relevant for a large variety of quantum systems in quantum optics and condensed matter physics. In particular, the control of quantum-optical platforms promises to gain deep insights into quantum-critical properties induced by the long-range nature of interactions. From a theoretical perspective, long-range interactions are notoriously complicated to treat. Here, we give an overview of recent advancements to investigate quantum magnets with long-range interactions focusing on two techniques based on Monte Carlo integration. First, the method of perturbative continuous unitary transformations where classical Monte Carlo integration is applied within the embedding scheme of white graphs. This linked-cluster expansion allows extracting high-order series expansions of energies and observables in the thermodynamic limit. Second, stochastic series expansion quantum Monte Carlo integration enables calculations on large finite systems. Finite-size scaling can then be used to determine the physical properties of the infinite system. In recent years, both techniques have been applied successfully to one- and two-dimensional quantum magnets involving long-range Ising, XY, and Heisenberg interactions on various bipartite and non-bipartite lattices. Here, we summarise the obtained quantum-critical properties including critical exponents for all these systems in a coherent way. Further, we review how long-range interactions are used to study quantum phase transitions above the upper critical dimension and the scaling techniques to extract these quantum critical properties from the numerical calculations.

Magnetic exchange interactions and non-Debye relaxation in spin-3/2 frustrated Kagomé magnet Co3V2O8.

We report the experimental determination of the magnetic exchange parameter (J/kB= 2.88 ± 0.02 K) for the Spin-3/2 ferromagnetic (FM) Kagomé lattice system: Co3V2O8using the temperature dependence of dc-magnetic susceptibilityχ(T) data by employing the fundamental Heisenberg linear chain model. Our results are quite consistent with the theoretically reported nearest neighbor dominant FM exchange coupling strengthJex-NN∼2.45 K. Five different magnetic phase transitions (6.2-11.2 K) and spin-flip transitions (9.6-7.7 kOe) have been probed using the∂(χT)/∂Tvs.T, heat capacity (CP-T) and differential isothermal magnetization curves. Among such sequence of transitions, the prominent ones being incommensurate antiferromagnetic (AFM) state at 11.2 K, commensurate AFM state at 8.8 K, and commensurate FM state across 6.2 K. All the successive magnetic phase transitions have been mapped onto a single H-T plane through which one can easily distinguish the above-mentioned different phases. The magnetic contribution of theCP-TnearTN(11.2 K) has been analyzed using the power-law expressionCM=A|T-TN|-αresulting in the critical exponentα= 0.18 ± 0.01 (0.15 ± 0.003) forTTN), respectively for the Co3V2O8. It is interesting to note that non-Debye type dipole relaxation is quite prominent in Co3V2O8and was evident from the Kohlrausch-Williams-Watts analysis of complex modulus and impedance spectra (0⩽ß⩽1). Mott's variable-range hopping of charge carriers process is evident through the resistivity analysis (ρac-T-1/4) in the temperature range 275 ∘C-350 ∘C. Moreover, the frequency-dependent analysis ofσac(ω) follows Jonscher's power law yielding two distinct activation energies (Ea∼0.37 and 2.29 eV) between the temperature range 39 ∘C-99 ∘C and 240 ∘C-321 ∘C.

Effect of zero-point motion on properties of quantum particles adsorbed on a substrate.

We qualitatively investigate the effect of zero-point motion (ZPM) on the structure and properties of a film composed of quantum particles adsorbed on a graphite substrate. The amplitude of ZPM is controlled by a change of the particle mass while keeping the interactions fixed. In that sense it is assumed that the interactions can be controlled by future doping methods. The worm-algorithm path integral Monte Carlo (WAPIMC) method is applied to simulate this system in the grand-canonical ensemble, where particles can be exchanged with the external particle reservoir. Another method, namely the multiconfigurational time-dependent Hartree method for bosons is additionally applied to verify some of the WAPIMC results and to provide further information on the entropy and the condensate fraction. Several important findings are reported. It is found that ZPM plays an important role in defining order and disorder in the crystalline structure of the adsorbed film. The total energy of the film drops with a reduction in the amplitude of ZPM, that is, it becomes more negative which is an indication to stronger adsorption. For a few particle numbers, a significant condensate fraction is detected that however drops sharply at critical values of the ZPM amplitude. Most importantly, a connection is established between chaos, in coordinate as well as momentum space, and the Heisenberg uncertainty principle. The importance of the present study lies in the fact that adsorbed two-dimensional films serve as an excellent experimental testbed for demonstrating low-dimensional quantum phenomena in the ground state. The present examination contributes also to a further understanding of the properties of heavy quantum particles adsorbed on substrates.

On the magnetization of the 120° order of the spin-1/2 triangular lattice Heisenberg model: a DMRG revisited.

We revisit the issue about the magnetization of the 120° order in the spin-1/2 triangular lattice Heisenberg model with density matrix renormalization group (DMRG). The accurate determination of the magnetization of this model is challenging for numerical methods and its value exhibits substantial disparities across various methods. We perform a large-scale DMRG calculation of this model by employing bond dimension as large asD=24000and by studying the system with width as large asLy=12. With careful extrapolation with truncation error and suitable finite size scaling, we give a conservative estimation of the magnetization asM0=0.208(8). The ground state energy per site we obtain isEg=-0.5503(8). Our results provide valuable benchmark values for the development of new methods in the future.

(Nano)Granules-Involving Aggregation at a Passage to the Nanoscale as Viewed in Terms of a Diffusive Heisenberg Relation.

We are looking at an aggregation of matter into granules. Diffusion plays a pivotal role here. When going down to the nanometer scale (the so-called nanoscale quantum-size effect limit), quantum mechanics, and the Heisenberg uncertainty relation, may take over the role of classical diffusion, as viewed typically in the mesoscopic/stochastic limit. A d-dimensional entropy-production aggregation of the granules-involving matter in the granule-size space is considered in terms of a (sub)diffusive realization. It turns out that when taking a full d-dimensional pathway of the aggregation toward the nanoscale, one is capable of disclosing a Heisenberg-type (diffusional) relation, setting up an upper uncertainty bound for the (sub)diffusive, very slow granules-including environment that, within the granule-size analogy invoked, matches the quantum limit of h/2πµ (µ-average mass of a granule; h-the Planck's constant) for the diffusion coefficient of the aggregation, first proposed by Fürth in 1933 and qualitatively foreseen by Schrödinger some years before, with both in the context of a diffusing particle. The classical quantum passage uncovered here, also termed insightfully as the quantum-size effect (as borrowed from the quantum dots' parlance), works properly for the three-dimensional (d = 3) case, making use of a substantial physical fact that the (nano)granules interact readily via their surfaces with the also-granular surroundings in which they are immersed. This natural observation is embodied in the basic averaging construction of the diffusion coefficient of the entropy-productive (nano)aggregation of interest.

Electronic Structure of Above-Room-Temperature van der Waals Ferromagnet Fe3GaTe2.

Fe3GaTe2, a recently discovered van der Waals ferromagnet, demonstrates intrinsic ferromagnetism above room temperature, necessitating a comprehensive investigation of the microscopic origins of its high Curie temperature (TC). In this study, we reveal the electronic structure of Fe3GaTe2 in its ferromagnetic ground state using angle-resolved photoemission spectroscopy and density functional theory calculations. Our results establish a consistent correspondence between the measured band structure and theoretical calculations, underscoring the significant contributions of the Heisenberg exchange interaction (Jex) and magnetic anisotropy energy to the development of the high-TC ferromagnetic ordering in Fe3GaTe2. Intriguingly, we observe substantial modifications to these crucial driving factors through doping, which we attribute to alterations in multiple spin-splitting bands near the Fermi level. These findings provide valuable insights into the underlying electronic structure and its correlation with the emergence of high-TC ferromagnetic ordering in Fe3GaTe2.

Spreading of Information on a Network: A Quantum View.

This paper concerns the modeling of the spread of information through a complex, multi-layered network, where the information is transferred from an initial transmitter to a final receiver. The mathematical model is deduced within the framework of operatorial methods, according to the formal mathematical apparatus typical of quantum mechanics. Two different approaches are considered: one based on the (H,ρ)-induced dynamics and one on the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. For each method, numerical results are presented.

Frustrated magnetism of the spin-1 kagome antiferromagnetß-BaNi3(VO4)2(OH)2.

We propose the newly synthesizedß-BaNi3(VO4)2(OH)2(space group:R3‾m) as a candidate for the spin-1 kagome Heisenberg antiferromagnet (KHA). The compound features a uniform kagome lattice of Ni2+(S= 1) ions with a large interlayer distance. High-field measurements at low temperatures reveal a susceptibility local minimum at ∼9 T, resembling a 1/3 magnetization plateau as predicted by the pureS= 1 KHA model. Below ∼6 K, approximately 1% of the spins exhibit spin-glass order, which may be attributed to the nanocrystalline grain size of ∼50 nm. Despite the antiferromagnetic exchange coupling strength of ∼7 K, the majority of spins remain disordered down to ∼0.1 K as indicated by the observed power-law behaviors in magnetic specific heatCm∝T1.4. Our results demonstrate that the low-energy magnetic excitations inß-BaNi3(VO4)2(OH)2are gapless, which contradicts the current theoretical expectations of the ideal model.

Phase Diagram and Quantum Entanglement Properties of a Pentamer S = 1/2 Heisenberg Spin Cluster.

Cluster molecular magnets prove their potential for applications in quantum technologies, encouraging studies of quantum entanglement in spin systems. In the paper we discuss quantum entanglement properties of pentamer cluster composed of spins S=1/2 forming a tetrahedron with additional spin in its center, with geometry reproducing the smallest nonplanar graph. We model the system with isotropic Heisenberg Hamiltonian including external magnetic field and use exact diagonalization approach to explore the ground-state phase diagram and thermodynamic properties within canonical ensemble formalism. We focus the interest on two-spin entanglement quantified by Wootters concurrence. For ground state, we find two states with total cluster spin equal to 3/2 exhibiting entanglement, occurring preferably for antiferromagnetic interactions. For finite temperatures, we predict the presence of magnetic-field-induced entanglement as well as temperature-induced entanglement.