By extending our recently proposed magnon-density waves to low dimensions, we investigate, using a microscopic many-body approach, the longitudinal excitations of the quasi-one-dimensional (quasi-1d) and quasi-2d Heisenberg antiferromagnetic systems on a bipartite lattice with a general spin quantum number. We obtain the full energy spectrum of the longitudinal mode as a function of the coupling constants in the original lattice Hamiltonian and find that it always has a nonzero energy gap if the ground state has a long-range order and becomes gapless for the pure isotropic 1d model. The numerical value of the minimum gap in our approximation agrees with that of a longitudinal mode observed in the quasi-1d antiferromagnetic compound KCuF3 at low temperature. It will be interesting to compare values of the energy spectrum at other momenta if their experimental results are available.
By extending our recently proposed magnon-density waves to low dimensions, we investigate, using a microscopic many-body approach, the longitudinal excitations of the quasi-one-dimensional (quasi-1d) and quasi-2d Heisenberg antiferromagnetic systems on a bipartite lattice with a general spin quantum number. We obtain the full energy spectrum of the longitudinal mode as a function of the coupling constants in the original lattice Hamiltonian and find that it always has a nonzero energy gap if the ground state has a long-range order and becomes gapless for the pure isotropic 1d model. The numerical value of the minimum gap in our approximation agrees with that of a longitudinal mode observed in the quasi-1d antiferromagnetic compound KCuF3 at low temperature. It will be interesting to compare values of the energy spectrum at other momenta if their experimental results are available.
Based on our recently proposed magnon-density-waves using the microscopic many- body approach, we investigate the longitudinal excitations in quantum antiferromagnets by including the second order corrections in the large-s expansion. The longitudinal excitation spectra for a general spin quantum number using the antiferromagnetic Heisenberg Hamiltonian are obtained for various spin lattice models. For bipartite lattice models, we find that the numerical results for the energy gaps for the longitudinal modes at q → 0 and the magnetic ordering wavevector Q are reduced by about 40-50 % after including the second order corrections. Thus, our estimate of the energy gaps for the quasi-one-dimensional (quasi- 1D) antiferromagnetic compound KCuF 3 is in better agreement with the experimental result. For the quasi-1D antiferromagnets on hexagonal lattices, the full excitation spectra of both the transverse modes (i.e., magnons) and the longitudinal modes are obtained as functions of the nearest-neighbor coupling and the anisotropy constants. We find two longitudinal modes due to the non-collinear nature of the triangular antiferromagnetic order, similar to that of the phenomenological field theory approach by Affleck. We compare our results for the longitudinal energy gaps at the magnetic wavevectors with the experimental results for several antiferromagnetic compounds with both integer and non-integer spin quantum numbers, and also find good agreement after the higher-order contributions are included in our calculations.
We investigate the quantum dynamics of the spins on different Heisenberg antiferromagnetic spin lattice systems. Firstly, we applied the coupled-cluster method to the spin-1/2 antiferromagnetic \emph{XXZ} model on a square lattice by employing an approximation which contains two-body long-range correlations and high-order four-body local correlations. Improvement is found for the ground-state energy, sublattice magnetization, and the critical anisotropy when comparing with the approximation including the two-body correlations alone. We also obtain the full excitation spectrum which is in good agreement with the quantum Monte Carlo results and the high-order spin-wave theory.Secondly, we study the longitudinal excitations of quantum antiferromagnets on a triangular lattice by a recently proposed microscopic many-body approach based on magnon-density waves. We calculate the full longitudinal excitation spectra of the antiferromagnetic Heisenberg model for a general spin quantum number in the isotropic limit. Similar to the square lattice model, we find that, at the center of the first hexagonal Brillouin zone Γ(q=0) and at the magnetic ordering wavevectors ±[Q=(4π/3,0)], the excitation spectra become gapless in the thermodynamic limit, due to the slow, logarithmic divergence of the structure factor. However, these longitudinal modes on two-dimensional models may be considered as quasi-gapped, as any finite-size effect or small anisotropy will induce a large energy gap, when compared with the counterpart of the transverse spin-wave excitations. We have also investigated the excited states of the quasi-one-dimensional quantum antiferromagnets on hexagonal lattices, including the longitudinal modes based on the magnon-density waves. A model Hamiltonian with a uniaxial single-ion anisotropy is first studied by a spin-wave theory based on the one-boson method; the ground state thus obtained is employed for the study of the longitudinal modes. The full energy spectra of both the transverse modes (i.e., magnons) and the longitudinal modes are obtained as functions of the nearest-neighbor coupling and the anisotropy constants. We have found two longitudinal modes due to the non-collinear nature of the triangular antiferromagnetic order, similar to that of the phenomenological field theory approach by Affleck. The excitation energy gaps due to the anisotropy and the energy gaps of the longitudinal modes without anisotropy are then investigated. We then compares our results for the longitudinal energy gaps at the magnetic wavevectors with the experimental results for several antiferromagnetic compounds with both integer and non-integer spin quantum numbers, and we find good agreements after the higher-order contributions are included in our calculations.
We investigate the excited states of the quasi-one-dimensional quantum antiferromagnets on hexagonal lattices, including the longitudinal modes based on the magnon-density waves. A model Hamiltonian with a uniaxial single-ion anisotropy is first studied by a spin wave theory based on the one-boson method; the ground state thus obtained is employed for the study of the longitudinal modes. The full energy spectra of both the transverse modes (i.e., magnons) and the longitudinal modes are obtained as functions of the nearest-neighbor coupling and the anisotropy constants. We have found two longitudinal modes due to the noncollinear nature of the triangular antiferromagnetic order, similar to that of the phenomenological field theory approach by Affleck. The excitation energy gaps due to the anisotropy and the energy gaps of the longitudinal modes without anisotropy are then investigated. We then compare our results for the longitudinal energy gaps at the magnetic wave vectors with the experimental results for several antiferromagnetic compounds with both integer and noninteger spin quantum numbers, and we find good agreement after the higher-order contributions are included in our calculations.
The excitation energies of magnons and solitons as well as the ground-state energy of the spin-1 antiferromagnetic Heisenberg-Ising ring are studied by the numerical method. The method of Vanden Broeck and Schwartz is used to estimate the infinite-lattice limits accurately. The result confirms Haldane's prediction that a novel singlet phase with a nonzero excitation gap appears between the gapless XY phase and the doublet ground-state N\'eel phase. It extends over the range of anisotropy (${\ensuremath{\Delta}}_{l}$\ensuremath{\le}\ensuremath{\Delta}\ensuremath{\le}${\ensuremath{\Delta}}_{u}$) around the isotropic Heisenberg point \ensuremath{\Delta}=0.5. It is ascertained that at the upper transition point ${\ensuremath{\Delta}}_{u}$=0.540\ifmmode\pm\else\textpm\fi{}0.001 (1) the longitudinal magnon gap closes, (2) the soliton existing in the Ising side softens, and (3) the second derivative of the ground-state energy diverges. Around the lower transition point of ${\ensuremath{\Delta}}_{l}$=0.38\ifmmode\pm\else\textpm\fi{}0.02, the transverse magnon gap exhibits an exponential singularity accompanying with the slight anomaly of the second derivative of the ground-state energy.
This thesis investigates exotic phases of matter in magnetic materials that present anisotropic properties in two dimensions. Using the microscopic spin Hamiltonians, the study addresses two problems: (i) the appearance of a novel class of magnetic excitations in the spectra of anisotropic magnets at zero temperature, and (ii) the quantum-to-classical correspondence of spins for the description of magnetic solids in the disordered phase above the critical temperature. Different analytical and numerical means are used to this purpose.In the first part, motivated by experimental observations of multipolar excitations in afamily of strongly-anisotropic van der Waals antiferromagnets, we have developed ageneral theory for these excitations as a distinct type of quasi-particles. We called themlongitudinal magnons. They appear in easy-axis magnetic materials, and are characterized by the quantum number Sz = ±2S. They can exist as coherent long-lived excitations for D ≥ |J|, where D and J are the typical single-ion and exchange coupling constants, respectively. Starting with the strong-coupling limit, this work presented different approaches to compute the dispersion of longitudinal magnons. First, a mapping to an effective spin-1/2 model was performed and illustrated for several lattice spin models: the honeycomb-lattice zigzag antiferromagnet and the square-lattice ferro- and antiferromagnet. The excitation energy was derived for different spin values S = 1, 3/2, 2and 5/2. Second, a thorough study explored the S = 1 anisotropic square-lattice, wherethe analytical results of the effective model are compared to the multi-boson spin-wavetheory, the linked-cluster calculations in antiferromagnetic coupling J > 0, and the exactsolution of the two-magnon problem in ferromagnetic coupling J < 0. In the limit of largeJ/D, the longitudinal magnons start to overlap with the multi-magnon continuum, andtheir finite lifetime can be computed using the multi-boson theory, which is specificallyshown for two-magnon decay processes in S = 1. Moreover, critical values of J/D forthe stability of longitudinal magnons are obtained along high-symmetry lines of the Brillouin zone. Third, we investigated the appearance and condensation of the longitudinal magnons in triangular S = 1 antiferromagnets under high magnetic field. As suggested by recent experiments on a candidate material, a spin nematic phase may appear upon condensation of the multipolar excitations, opening the way for realizations of new phases of matter in classically-ordered magnets.In the second part, the correspondence between quantum and classical spins is investigated for spin Hamiltonians at finite temperature. Given a model of quantum spins, it is useful to determine the classical model that best describes its thermodynamics, which is of interest for semi-classical analyses, e.g. by classical Monte Carlo methods. Based on high-temperature series expansions, we established the scaling laws of the different microscopic constants in a quantum spin model, involving quadratic and biquadratic exchange interactions, single-ion anisotropy and the Zeeman energy. We showed that quantum corrections to the thermodynamic quantities are power series in S(S + 1). Subsequently, the findings were applied to numerically determine the phase transition temperature in several ferro- and antiferromagnetic compounds, using classical Monte Carlo simulations. To this aim, the lattice spin models were constructed with microscopic coupling constants from the literature, and the transition temperatures were compared to the experimental values.This illuminates complex collective magnetic behaviors in different models and materials.
The authors investigate the properties of the two-dimensional quantum S=1/2 Heisenberg antiferromagnetic model on a square lattice by means of a block approach. The lattice is divided into four spin square blocks and the Hamiltonian is expressed in terms of low-energy block states. In the framework of the mean-field theory based on the 'auxiliary-boson' formalism; they show that the spin excitation spectrum contains one singlet mode with the temperature-dependent gap and three degenerate triplet modes. The asymptotic low-temperature spin-spin correlations are proportional to R -3/2 exp(-R(1/ xi 1 +1/ xi 2 )), where xi 1 =exp(A/T), xi 2 =constant and A approximately=0.5J. The uniform susceptibility tends to zero in agreement with numerical results; the energy per site is close to -0.57J. Beyond the meanfield theory the authors find gapless collective excitations analogous to the gapless mode in the neutral Fermi gas with attraction.