Antiferromagnetic Heisenberg Model Research Articles

Well isolated copper(II) pyrazine-bridged chains: synthesis and magneto-structural analysis of 2-halo-4-pyridone perchlorate complexes

Two new coordination polymers, [Cu(pz)(L)2(H2O)2](ClO4)2 (L = 2-Cl- (1) or 2-Br-4-pyridone (2); pz = pyrazine), have been synthesized and characterized by X-ray diffraction, EPR and variable temperature magnetic measurements. Both compounds crystallize as well isolated pyrazine-bridged chains with the heterocyclic ligands in the pyridone tautomer and coordinated via the oxygen atom. The Cu ions possess Jahn-Teller elongated octahedral geometries with the Jahn-Teller axis along the Cu-O axis. The water molecules in 2 are inequivalent with one molecule semi-coordinate (dCu… O = 3.225(6) Å) at an occupancy of 0.72. Both compounds exhibited axial powder EPR spectra, as expected. Variable temperature magnetic measurements are well fit by the uniform chain Heisenberg antiferromagnetic model with J = −10.74(4) K (1) or = −10.64(2) K (2). Comparison with the known 3-halo-4-pyridone compounds suggests an inverse relationship between the Cu-pz-Cu distance and the strength of the magnetic exchange.

General Formula for the Green’s Function Approach to the Spin-1/2 Antiferromagnetic Heisenberg Model

General Formula for the Green’s Function Approach to the Spin-1/2 Antiferromagnetic Heisenberg Model

Quasi-2D spin-Peierls transition through interstitial anionic electrons in K(NH3)2

Electron–phonon interactions and electron–electron correlations represent two crucial facets of condensed matter physics. For instance, in a half-filled spin-1/2 anti-ferromagnetic chain, the lattice dimerization induced by electron-nucleus interaction can be intensified by onsite Coulomb repulsion, resulting in a spin-Peierls state. Through first-principles calculations and crystal structure prediction methods, we have identified that under mild pressures, potassium and ammonia can form stable compounds: R3¯m K(NH3)2, Pm3¯m K(NH3)2, and Cm K2(NH3)3. Our predictions suggest that the R3¯m K(NH3)2 exhibits electride characteristics, marked by the formation of interstitial anionic electrons (IAEs) in the interlayer space. These IAEs are arranged in quasi-two-dimensional triangular arrays. With increasing pressure, the electronic van-Hove singularity shifts toward the Fermi level, resulting in an augmented density of states and the onset of both Peierls and magnetic instabilities. Analyzing these instabilities, we determine that the ground state of the R3¯m K(NH3)2 is the dimerized P21/m phase with zigzag-type anti-ferromagnetic IAEs. This state can be described by the triangular-lattice antiferromagnetic Heisenberg model with modulated magnetic interactions. Furthermore, we unveil the coexistence and positive interplay between magnetic and Peierls instability, constituting a scenario of spin-Peierls instability unprecedented in realistic 2D materials, particularly involving IAEs. This work provides valuable insights into the coupling of IAEs with the adjacent lattice and their spin correlations in quantum materials.

Thermal Hall conductivity on kagome-lattice antiferromagnets

Thermal Hall conductivity κxy and Hall spin conductivity σxy in the nearest-neighbors antiferromagnetic Heisenberg model on kagome lattice with out-of-plane Dzyaloshinskii-Moriya interaction (DMI), which has been an active area of study in condensed matter physics, are studied using the linear spin-wave theory. We analize the effect of this coupling on the behavior of κxy as well as σxy as well. For all cases analyzed, the behavior of κxy and σxy as a function of temperature T is analyzed where the behavior obtained for T finite, being due to the magnons thermally excited. We get a strong effect of temperature and DMI interaction on the behavior of both conductivities.

Towards skyrmion crystal stabilization in the antiferromagnetic triangular lattice at ambient conditions

We explore possibilities of stabilizing a skyrmion lattice (SkX) phase in the frustrated antiferromagnetic (AF) Heisenberg model with the Dzyaloshinskii–Moriya interaction on a triangular lattice at ambient conditions. We show that by stacking multiple AF layers and coupling them with strong ferromagnetic (F) interaction the SkX phase stability temperature window can be extended by several times. The transition temperature increase is supported by the increasing number of layers and interlayer interaction and thus room-temperature SkX phase could be achievable by proper tailoring of the multilayer structure. Further, we demonstrate that in the sandwich heterostructure, obtained by inserting a stiff F layer in between two AF layers, the required external magnetic field can be completely replaced by the effective field imposed by the F layer. Thus, one can design a heterostructure with the SkX phase stabilized at relatively high temperatures and zero field - the environment favorable for technological applications.

Tetrabromidocuprate(II) complexes with diprotonated 1-hydroxy-4methyl-2-(pyridin-2-yl)-5-phenylimidazole and 1-hydroxy-2-(pyridin-2-yl)-4,5,6,7-tetrahydrobenzimidazole ligands: Relationship between the structure and magnetic properties

Two new tetrabromidocuprate(II) complexes with diprotonated 1-hydroxy-2-(pyridin-2-yl)-4,5,6,7-tetrahydrobenzimidazole (1) and 1-hydroxy-4methyl-2-(pyridin-2-yl)-5-phenylimidazole (2) were synthesized and their structure established from single-crystal X-ray data. Compounds crystallized in the monoclinic space groups P21/n and P21/c, respectively, where tetrabromidocuprate anions formed magnetic chains as inferred from the distances between the halide ions of different [CuBr4]2− units. Magnetization measurements showed that both compounds behave as well-isolated uniform S = 1/2 antiferromagnetic chains described by the one-dimensional Heisenberg antiferromagnetic model with intra-chain exchange interaction 2 J = 23 K (1) and 2 J = 33 K (2) (the Hamiltonian Hˆ=2J∑SˆiSˆi+1). Electron paramagnetic resonance, optical absorption, and density functional theory investigations provided complementary results for 1 and 2. A calculation of exchange coupling constants gave values of 2 J = 24 K (1) and 2 J = 39 K (2), in good agreement with the experiment. The quantum theory of atoms in molecules and non-covalent interaction analyses showed that halogen bonding determined the exchange interaction between [CuBr4]2− units in magnetic chains of these cation–anion compounds.

$\Delta$S$^z$=2 quantum magnetization discontinuities proportional in number to the spin s in C$_{60}$: Origin and the role of symmetry

The quantum antiferromagnetic Heisenberg model on the fullerene C_{60}60 in a magnetic field has 4s4s ground-state magnetization discontinuities with \Delta S^z=2ΔSz=2 as a function of the spin quantum number ss that disappear at the classical limit. The molecule can be seen as the fullerene C_{20}20 with interpentagon interactions that generate the discontinuities when sufficiently strong. The discontinuities originate from the antiferromagnetic Ising limit for both molecules. The results show how spatial symmetry dictates the magnetic response of the I_hIh fullerene molecules.

Speeding Up Learning Quantum States Through Group Equivariant Convolutional Quantum Ansätze

We develop a theoretical framework for $S_n$-equivariant quantum convolutional circuits, building on and significantly generalizing Jordan's Permutational Quantum Computing (PQC) formalism. We show that quantum circuits are a natural choice for Fourier space neural architectures affording a super-exponential speedup in computing the matrix elements of $S_n$-Fourier coefficients compared to the best known classical Fast Fourier Transform (FFT) over the symmetric group. In particular, we utilize the Okounkov-Vershik approach to prove Harrow's statement (Ph.D. Thesis 2005 p.160) on the equivalence between $\operatorname{SU}(d)$- and $S_n$-irrep bases and to establish the $S_n$-equivariant Convolutional Quantum Alternating Ans\"atze ($S_n$-CQA) using Young-Jucys-Murphy (YJM) elements. We prove that $S_n$-CQA are dense, thus expressible within each $S_n$-irrep block, which may serve as a universal model for potential future quantum machine learning and optimization applications. Our method provides another way to prove the universality of Quantum Approximate Optimization Algorithm (QAOA), from the representation-theoretical point of view. Our framework can be naturally applied to a wide array of problems with global $\operatorname{SU}(d)$ symmetry. We present numerical simulations to showcase the effectiveness of the ans\"atze to find the sign structure of the ground state of the $J_1$-$J_2$ antiferromagnetic Heisenberg model on the rectangular and Kagome lattices. Our work identifies quantum advantage for a specific machine learning problem, and provides the first application of the celebrated Okounkov-Vershik's representation theory to machine learning and quantum physics.

The \(120^{0}\) ordered phase of the spin-1 \(J_{1} - J_{2}\) antiferromagnetic Heisenbeberg model on a triangular lattice

We study the effect of quantum and thermal fluctuations on the excitation energy spectrum and sublattice magnetization of the 1200 ordered phase of the spin-1 antiferromagnetic Heisenberg model on a triangular lattice with nearest J1 and next-nearest-neighbor J2 exchange interactions. The auxiliary fermionic representation of the spin operators within a functional integral formalism with an imaginary Lagrange multiplier is employed to retain an exact constraint of single particle occupancy. Representing the classical ground state by Luttinger-Tisza ordering vector Q one may consider the fluctuation contributions to the free energy of the system in the entire range of the coupling parameters. We derived the magnon spectrum in one-loop approximation and the magnetization taking into account thermal fluctuations. The obtained results are compared with the result of the linear spin-wave approximation and experimental findings on compound NiGa2S4.

Unlocking the general relationship between energy and entanglement spectra via the wormhole effect

Based on the path integral formulation of the reduced density matrix, we develop a scheme to overcome the exponential growth of computational complexity in reliably extracting low-lying entanglement spectrum from quantum Monte Carlo simulations. We test the method on the Heisenberg spin ladder with long entangled boundary between two chains and the results support the Li and Haldane’s conjecture on entanglement spectrum of topological phase. We then explain the conjecture via the wormhole effect in the path integral and show that it can be further generalized for systems beyond gapped topological phases. Our further simulation results on the bilayer antiferromagnetic Heisenberg model with 2D entangled boundary across the (2 + 1)D O(3) quantum phase transition clearly demonstrate the correctness of the wormhole picture. Finally, we state that since the wormhole effect amplifies the bulk energy gap by a factor of β, the relative strength of that with respect to the edge energy gap will determine the behavior of low-lying entanglement spectrum of the system.

Gapless Spin Liquid and Nonlocal Corner Excitation in the Spin-1/2 Heisenberg Antiferromagnet on Fractal

Motivated by the mathematical beauty and the recent experimental realizations of fractal systems, we study the spin-1/2 antiferromagnetic Heisenberg model on a Sierpiński gasket. The fractal porous feature generates new kinds of frustration to exhibit exotic quantum states. Using advanced tensor network techniques, we identify a quantum gapless-spin-liquid ground state in fractional spatial dimension. This fractal spin system also demonstrates nontrivial nonlocal properties. While the extremely short-range correlation causes a highly degenerate spin form factor, the entanglement in this fractal system suggests a long-range scaling behavior. We also study the dynamic structure factor and clearly identify the gapless excitation with a stable corner excitation emerged from the ground-state entanglement. Our results unambiguously point out multiple essential properties of this fractal spin system, and open a new route to explore spin liquid and frustrated magnetism.

The Dzyaloshinskii–Moriya interaction effects in antiferromagnetic Heisenberg model

The spin-1/2 antiferromagnetic (AFM) Heisenberg model is considered in the mean-field approximation in terms of the spin operators [Formula: see text] and [Formula: see text] in the matrix forms with the introduction of bilinear exchange interaction ([Formula: see text]), the Dzyaloshinskii–Moriya interaction (DMI) ([Formula: see text]) and external magnetic fields ([Formula: see text]) into the Hamiltonian in three dimensions. The thermal changes of sublattice magnetizations [Formula: see text] and [Formula: see text] are investigated in the isotropic case to identify the critical behaviors displayed by the system. The phase diagrams are illustrated on various planes of system parameters for given coordination numbers [Formula: see text] and 6. In addition, the graphs of the magnetization components in the same directions were drawn against each other and very interesting results were obtained. The model exhibits the ordered phases, i.e., AFM, ferromagnetic (FM), and a phase with random or oscillatory behavior (R). The phase transitions are observed between FM and R phases when for all [Formula: see text], between FM and AFM when [Formula: see text] only and, AFM and R at low temperatures for very small [Formula: see text] and [Formula: see text] values.

Thermodynamic properties of the two-dimensional Heisenberg antiferromagnetic model on kagome lattice

Thermodynamic quantities as entropy and specific heat that are of evident interest, are obtained for the nearest-neighbor antiferromagnetic Heisenberg model on kagome lattice using the linear spin-wave approach. The results are obtained for different extensions of the model with single-ion anisotropy and out-of-plane Dzyaloshinskii–Moriya (DMI) interaction. We obtain the entropy as a function of the DMI interaction, single-ion anisotropy strength and anisotropy with aim to verify the effect of these corrections that occurs in real magnetic materials on entropy and specific heat. Furthermore, we obtain the specific heat as a function of temperature T and found a discontinuity in the range of large T indicating so, a phase transition in this range of temperature.

Coordination chemistry and magnetic properties of copper(II) halide complexes of quinoline

Complexes Cu(quin)2X2 [quin = quinoline, X = Cl (1), Br (2)] have been prepared and characterized via single-crystal X-ray diffraction and variable temperature magnetization measurements. The compounds are isomorphous in the monoclinic space group C2/c and crystallize as square planar complexes linked into chains via short X…X contacts. Magnetic susceptibility data were collected over the temperature range 1.8–300 K and were fitted to the one-dimensional Heisenberg antiferromagnetic model yielding J/kB = −33.7(5) K (1) and −145(4) K (2) with the larger exchange in the bromide complex a result of greater overlap due to the larger van der Waals contribution. Low temperature data indicate the presence of some short chains in the sample which provide for a paramagnetic contribution (odd length chains) or diamagnetic contribution (even length chains) at the lowest temperatures.

Competing quantum spin liquids, gauge fluctuations, and anisotropic interactions in a breathing pyrochlore lattice

We use the projective symmetry group analysis to classify the quantum spin liquids on the $S=1/2$ pyrochlore magnet with a breathing anisotropy. We find 40 $\mathbb{Z}_2$ spin liquids and 16 $U(1)$ spin liquids that respect the $F\bar{4}3m$ space group and the time reversal symmetry. As an application, we consider the antiferromagnetic Heisenberg model, which is proposed to be the dominant interaction in the candidate material Ba$_3$Yb$_2$Zn$_5$O$_{11}$. Focusing on the $U(1)$ spin liquid ansatze, we find that only two of them are physical when restricted to this model. We present an analytical solution to the parton mean field theory for each of these two $U(1)$ spin liquids. It is revealed that one of them has gapless, while the other one has gapped, spinon excitations. The two $U(1)$ spin liquids are equal in energy regardless of the degree of breathing anisotropy, and they can be differentiated by the low-temperature heat capacity contribution from the quadratically-dispersing gapless spinons. We further show that the latter is unaffected by fluctuations of the $U(1)$ gauge field within the random phase approximation. Finally, we demonstrate that a small Dzyaloshinskii-Moriya interaction lifts the degeneracy between the two $U(1)$ spin liquids, and it eventually causes the lattice to decouple into independent tetrahedra at strong coupling. While current model parameters for Ba$_3$Yb$_2$Zn$_5$O$_{11}$ place it indeed in the decoupled regime, other candidate materials may be synthesised in the near future that realize the spin liquid states discussed in our work.

Ground states and dynamical properties of the S>1/2 quantum Heisenberg model on the 1/5-depleted square lattice

We study the $S>1/2$ antiferromagnetic Heisenberg model on the 1/5-depleted square lattice as a function of the ratio of the intraplaquette coupling to the interplaquette coupling. Using stochastic series expansion quantum Monte Carlo simulations, we numerically identify three quantum phases, including the dimer phase, N\'eel phase, and plaquette valence-bond-solid phase. We also obtain the accurate quantum critical points that belong to the $O$(3) universality class using the large-scale finite-size scaling. Most importantly, we study the dynamic spin structure factors of different phases, which can be measured by inelastic neutron scattering experiments. The low-energy excitations can be explained as triplons in the dimer phase and plaquette valence-bond-solid phase, while in the N\'eel phase, the more prominent magnon mode can be found as the spin magnitude increases. Furthermore, we find a broader continuum at smaller $S$, which may be the dynamical signature of nearly deconfined spinon excitations.

Spin transport in the two-dimensional antiferromagnet on kagome lattice

Spin transport in the antiferromagnetic Heisenberg model of nearest-neighbors on kagome lattice, with single-ion planar anisotropy D and out-of-plane Dzyaloshinskii–Moriya interaction (DMI) is studied using the spin-wave approach. We obtain the effect of the DMI interaction and single-ion anisotropy strength on longitudinal and transversal spin conductivities with aim to analyze the influence of these coupling parameters on spin transport. Since we found a finite spin stiffness (Drude’s weight) as a function of T, we have an ideal spin transport for the system in spite of it to be an insulator of electric current.

Competing emergent Potts orders and possible nematic spin liquids in the kagome J1−J3 Heisenberg model

The extreme frustration in the kagome antiferromagnet makes it possible to realize a large number of closely competing magnetic phases either at the classical or the quantum level. Motivated by recent neutron scattering study on the kagome antiferromagnet vesignieite ${\mathrm{BaCu}}_{3}{\mathrm{V}}_{2}{\mathrm{O}}_{8}{(\mathrm{OH})}_{2}$, we have made systematic investigation of the phase diagram of the classical and quantum ${J}_{1}\ensuremath{-}{J}_{3}$ antiferromagnetic Heisenberg model defined on the kagome lattice (KAFHM). While it is shown previously that a large antiferromagnetic exchange between the third-neighboring spins can drive an emergent $q=4$ Potts order through the order-by-disorder mechanism, it is elusive what will happen in the region where the Luttinger-Tisza criteria fails to predict the classical ordering pattern. Through extensive Monte Carlo simulation, we find that such a region is characterized by competing emergent $q=3$ and $q=4$ Potts order, whose emergence are beyond the description of the conventional order-by-disorder mechanism. Our Schwinger boson mean-field calculation suggests the existence of the Potts-3 order in the ground state of quantum ${J}_{1}\ensuremath{-}{J}_{3}$ KAFHM in such an extremely frustrated region. The predicted Potts-3 state is found to take two different forms distinguished by their projective symmetry group character (PSG or quantum order), although they have exactly the same symmetry. The transition between these two quantum orders is found to occur at a ${J}_{3}$ value intriguingly close to the tricritical point in the Potts-3 phase of the classical phase diagram of the model. A comparison with the exact diagonalization result on a 36-site cluster shows that the intermediate region may indeed host a nematic spin liquid ground state featuring an anisotropic ring structure around the $\mathbf{q}=0$ point in its spinon dispersion relation. We find that such an extremely frustrated region should better be taken as the playground to study the rich competition between exotic emergent phases, rather than a burden on their theoretical analysis.

Excited-state exchange interaction in NiO determined by high-resolution resonant inelastic x-ray scattering at the Ni M2,3 edges

The electronic and magnetic excitations of bulk NiO have been determined using the ${}^{3}{A}_{2g}$ to ${}^{3}{T}_{2g}$ crystal-field transition at the Ni ${M}_{2,3}$ edges with resonant inelastic x-ray scattering at 66.3- and 67.9-eV photon energies and 33-meV spectral resolution. Unambiguous assignment of the high-energy side of this state to a spin-flip satellite is achieved. We extract an effective exchange field of $89\ifmmode\pm\else\textpm\fi{}4$ meV in the ${}^{3}{T}_{2g}$ excited final state from empirical two-peak spin-flip model. The experimental data is found consistent with crystal-field model calculations using exchange fields of 60--100 meV. Full agreement with crystal-field multiplet calculations is achieved for the incident photon energy dependence of line shapes. The lower exchange parameter in the excited state as compared to the ground-state value of 120 meV is discussed in terms of the modification of the orbital occupancy (electronic effects) and of the structural dynamics: (A) With pure electronic effects, the lower exchange energy is attributed to the reduction in effective hopping integral. (B) With no electronic effects, we use the $S=1$ Heisenberg model of antiferromagnetism to derive a second-nearest-neighbor exchange constant ${J}_{2}$ = $14.8\ifmmode\pm\else\textpm\fi{}0.6$ meV. Based on the linear correlation between ${J}_{2}$ and the lattice parameter from pressure-dependent experiments, an upper limit of 2% local Ni-O bond elongation during the femtosecond scattering duration is derived.

Elastically induced magnetization at ultrafast time scales in a chiral helimagnet

The extreme frustration in the Kagome antiferromagnet makes it possible to realize a large number of closely competing magnetic phases either at the classical or the quantum level. Motivated by recent neutron scattering study on the Kagome antiferromagnet vesignieite BaCu$_{3}$V$_{2}$O$_{8}$(OH)$_{2}$, we have made systematic investigation of the phase diagram of the classical and quantum $J_{1}-J_{3}$ antiferromagnetic Heisenberg model defined on the Kagome lattice(KAFHM). While it is shown previously that a large antiferromagnetic exchange between the third-neighboring spins can drive an emergent $q=4$ Potts order through the order-by-disorder mechanism, it is elusive what will happen in the so called "grey region" where the Luttinger-Tisza criteria fails to predict the classical ordering pattern. Through extensive Monte Carlo simulation, we find that the "grey region" is characterized by competing emergent $q=3$ and $q=4$ Potts order, whose emergence are beyond the description of the conventional order-by-disorder mechanism. Our Schwinger Boson mean field calculation in the "grey region" confirms the existence of the Potts-3 order in the ground state of quantum $J_{1}-J_{3}$ KAFHM. The predicted Potts-3 state is found to take two different forms distinguished by their projective symmetry group character(PSG or quantum order), although they have exactly the same symmetry. A comparison with the exact diagonalization result on a 36-site cluster shows that the "grey region" may indeed host a nematic spin liquid ground state featuring an anisotropic ring structure around the $\mathbf{q}=0$ point in its spinon dispersion relation. We find that such "grey region" of extremely frustrated magnets should better be taken as the playground to study the rich competition between exotic emergent phases, rather than a burden on their theoretical analysis.