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3-dimensional Heisenberg antiferromagnet in cubic lattice under time periodic magnetic field

Chi Hung Chan

Published Jan 1, 2009• 0 citations
Publisher

Abstract

Heisenberg model has long been an interesting and intensive research topic owing to its intrinsic theoretical interest and potential application in many areas. Understanding non-equilibrium system of the Heisenberg antiferromagnet might promote our understanding of magnetic system and give us theoretical background on quantum signal manipulation. In this thesis, we consider the Heisenberg antiferromagnet in time periodic magnetic field using the Classical Spin Wave Theory and the Schwinger Boson Theory. The spin-spin response functions for the Heisenberg antiferromagnet in 2 cases of time periodic field were obtained, including case (1) B⃗0(t) = Bo(t)ẑ, where B0(t) is a periodic magnetic field in time, and (2) B⃗0(t) = Bo(cos(Ωt)x̑+sin(Ωt)ŷ). In the Classical Spin Wave Theory, the spin-spin response function and absorption spectrum of spin wave are obtained. In the Schwinger Boson Theory, the spin-spin response calculation gives same result to its classical analog. The 1/S quantum correction factor is shown to be identical to that of case when time dependent magnetic field is absent.

DOI
10.14711/thesis-b1070739

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Heisenberg model has long been an interesting and intensive research topic owing to its intrinsic theoretical interest and potential application in many areas. Understanding non-equilibrium system of the Heisenberg antiferromagnet might promote our understanding of magnetic system and give us theoretical background on quantum signal manipulation. In this thesis, we consider the Heisenberg antiferromagnet in time periodic magnetic field using the Classical Spin Wave Theory and the Schwinger Boson Theory. The spin-spin response functions for the Heisenberg antiferromagnet in 2 cases of time periodic field were obtained, including case (1) B⃗0(t) = Bo(t)ẑ, where B0(t) is a periodic magnetic field in time, and (2) B⃗0(t) = Bo(cos(Ωt)x̑+sin(Ωt)ŷ). In the Classical Spin Wave Theory, the spin-spin response function and absorption spectrum of spin wave are obtained. In the Schwinger Boson Theory, the spin-spin response calculation gives same result to its classical analog. The 1/S quantum correction factor is shown to be identical to that of case when time dependent magnetic field is absent.
The one-dimensional Heisenberg antiferromagnet with 8=1/2 is treated with the use of the Fermi operators and an additional condition that the long-range order is absent.Our spin wave spectrum of a one-dimensional Heisenberg antiferromagnet without longrange order is expressed by andThis is in good agreement with the exact spin wave spectrum role =1!'/2lsin kl which is obtained by des Cloizeaux and Pearson at T=O.Correlation functions <S1S2> and <SlSs> are in good agreement with the exact value at T=O, also.Thermodynamic properties of this system agree with those of Bulaevskii and those of Katsura and Inawashiro. § I. IntroductionThe one-dimensional Heisenberg antiferromagnet has been investigated by many authors.Most of previous theories have been for either zero or infinite temperatures.Recently various experiment on (CD3) 4NMnCl 3 (TMMC)ll requires further theoretical work of a Heisenberg linear-chain magnet for finite temperatures.The experimental results of linear antiferromagnet show that at low temperatures there are long-lived spin waves in spite of the absence of long-range order.At T= 0, the spin wave spectrum, wqoc I sin ql, is gained approximately by Anderson 2 l and exactly by des Cloizeaux and Pearson.8 l Recently Richards, 4 l Scales and Gersh, 5 l Kondo and Yamaji 6 l obtained the spin wave spectrum of linear antiferromagnet at finite temperatures with the use of the second-order Green's function theory.The spin wave spectrum, however, does not show exactly wqoc I sin ql at finite temperatures.
We compute the dynamical structure factor of the spin-½ triangular Heisenberg model using the mean-field Schwinger boson theory. We find that a reconstructed dispersion, resulting from a non-trivial redistribution of the spectral weight, agrees quite well with the spin excitation spectrum recently found with series expansions. In particular, we recover the strong renormalization with respect to linear spin wave theory along with the appearance of roton-like minima. Furthermore, near the roton-like minima the contribution of the two spinon continuum to the static structure factor is about 40% of the total weight. By computing the density-density dynamical structure factor, we identify an unphysical weak signal of the spin excitation spectrum with the relaxation of the local constraint of the Schwinger bosons at the mean-field level. Based on the accurate description obtained for the static and dynamic ground-state properties, we argue that the bosonic spinon theory should be considered seriously as a valid alternative to interpret the physics of the triangular Heisenberg model.
We present the first exact results for the T=0 dynamical structure factor of finite-sized two-dimensional square-lattice spin-(1/2 antiferromagnetic Heisenberg systems with up to 16 spins. Our results are compared to a recently proposed Schwinger boson mean-field theory. We find that the mean-field theory represents an excellent approximation to the exact spin excitation spectra at all allowed wave vectors and for all system sizes studied. We also determine the mean-field value for the T=0 staggered magnetization, mMF=0.306{m}^{\mathrm{MF}=0.306}mMF=0.306, to be in excellent agreement with published Monte Carlo results.
We investigate the spin dynamics of the square-lattice spin- Heisenberg antiferromagnet by means of an improved mean-field Schwinger boson calculation. By identifying both, the long-range Néel and the RVB-like components of the ground state, we propose an educated guess for the mean-field magnetic excitation consisting on a linear combination of local and bond spin flips to compute the dynamical structure factor. Our main result is that when this magnetic excitation is optimized in such a way that the corresponding sum rule is fulfilled, we recover the low- and high-energy spectral weight features of the experimental spectrum. In particular, the anomalous spectral weight depletion at found in recent inelastic neutron scattering experiments can be attributed to the interference of the triplet bond excitations of the RVB component of the ground state. We conclude that the Schwinger boson theory seems to be a good candidate to adequately interpret the dynamic properties of the square-lattice Heisenberg antiferromagnet.
We study the field dependence of the antiferromagnetic spin-12\frac{1}{2}21​ Heisenberg model on the square lattice by means of exact diagonalizations. In the first part, we calculate the spin-wave velocity ccc, the spin stiffness ${\ensuremath{\rho}}_{s}$, and the magnetic susceptibility ${\ensuremath{\chi}}_{\ensuremath{\perp}}$, and thus determine the microscopic parameters of the low-energy long-wavelength description. In the second part, we present a comprehensive study of dynamical spin-correlation functions for magnetic fields ranging from zero up to saturation. We find that, at low fields, magnons are well defined in the whole Brillouin zone but the dispersion is substantially modified by quantum fluctuations compared to the classical spectrum. At higher fields, decay channels open and magnons become unstable with respect to multimagnon scattering. Our results directly apply to inelastic neutron-scattering experiments.
A theoretical study of the low-temperature dynamics of the antiferromagnetic Heisenberg chain in an external field is presented. The time- and frequency-dependent transverse and longitudinal spin fluctuations and energy fluctuations are calculated by means of a continued fraction representation. The frequency moments are evaluated analytically by a computer program. The transfer-operator technique is used to calculate all static correlation functions. For modest magnetic fields, a two-peak structure in the dynamic form factor of the transverse spin fluctuations is observed. Apart from the usual spin-wave excitations, the longitudinal-spin-fluctuation spectra show a broad second resonance for some temperatures and fields. The energy fluctuations display a dominant oscillatory time dependence.