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Progress of Theoretical Physics Supplement

Application of Modified Spin Wave Theory to Ferromagnetic Spin Chain with Arbitrary Range Interactions

Makoto Kaburagi, Takashi Hashimoto, Minkyu Kang, Takashi Tonegawa

Published Jan 1, 2005• 0 citations
Publisher

Abstract

The modified spin-wave (M-SW) theory is generalized to the case of arbitrary range interactions. Applying the results of the theory to the system with up to NNN interactions, we have obtained the analytical expressions of thermodynamic quantities at low temperatures and also analyzed the anomalous behavior near the generalized cross-over point. Numerical calculations of the case S = 1/2 have been performed to compare the results with those obtained by the exact diagonalization method. Our numerical results give a fairly good agreement with those of the exact-diagonalization-method.

DOI
10.1143/ptps.159.163

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The modified spin-wave (M-SW) theory is generalized to the case of arbitrary range interactions. Applying the results of the theory to the system with up to NNN interactions, we have obtained the analytical expressions of thermodynamic quantities at low temperatures and also analyzed the anomalous behavior near the generalized cross-over point. Numerical calculations of the case S = 1/2 have been performed to compare the results with those obtained by the exact diagonalization method. Our numerical results give a fairly good agreement with those of the exact-diagonalization-method.
The Green's function formalism proposed by Kondo and Yamaji for low-dimensional spin systems with S =1/2 has been extended to the cases of S >1/2. We apply this formalism to the study of one- and two-dimensional Heisenberg ferromagnets over the whole temperature range. It is shown that our theory can reproduce the correct results obtained by the high-temperature expansion method. On the other hand, the results at low temperatures are similar to those of the modified spin-wave theory, which is considered to predict the low-temperature properties of such systems rather correctly. The gross behaviors of the calculated thermodynamic quantities of ferromagnetic Heisenberg chains agree with those obtained by the exact diagonalization method.
Abstract In this work, we present a comparative study of thermodynamic quantum equilibrium observables of spin-1 Heisenberg chain. As a theoretical approach, the modified spin-wave theory is chosen. From the numerical side, we consider finite-temperature Lanczos, kernel polynomial, and density matrix renormalization techniques. The results show general consistency of thermodynamic quantities, such as heat capacity and magnetic susceptibility, calculated within the approaches. For the modified spin-wave, the results show some inaccuracy especially at low temperature, failure in capturing the gapped features of spin-1 Heisenberg chain, while the numerical approaches illustrate a good achievement at T→0T\rightarrow 0T→0 T → 0 within the proper parameters chosen.
A modified spin-wave theory is applied to the one-dimensional quantum Heisenberg model with long-range ferromagnetic interactions. ( H =- J ∑ i < j ( r i j ) - p S i · S j ). Low-temperature properties of this model are investigated. The susceptibility and the specific heat are calculated; the relation between their behaviors and strength of the long-range interactions is obtained. This model includes both the Haldane-Shastry model and the nearest-neighbor Heisenberg model; the corresponding results in this paper are in agreement with the solutions of both the models. It is shown that there exists an ordering transition at a finite temperature for 1< p <2 where the model has longer-range interactions than the HS model. The critical temperature is estimated.
We study the thermodynamics of a one-dimensional quantum spin-1/2 Heisenberg ferromagnetic system with random antiferromagnetic impurity bonds. In the dilute impurity limit, we generalize the modified spin-wave theory for random spin chains, where local chemical potentials for spin waves in ferromagnetic spin segments are introduced to ensure zero magnetization at finite temperature. This approach successfully describes the crossover from the behavior of a pure one-dimensional ferromagnet at high temperatures to a distinct Curie behavior due to randomness at low temperatures. We discuss the effects of impurity bond strength and concentration on the crossover and low-temperature behavior.
We have implemented three approaches to describe the thermodynamic properties of ferrimagnetic (S=5∕2S=5∕2S=5∕2, s=2s=2s=2) spin chains. The application of cumulant expansion has been generalized to the ferrimagnetic chain in the presence of an external magnetic field. Using cumulants, we have obtained the field-dependent effective Hamiltonian in terms of the classical variables up to the second order of quantum corrections. Thermodynamic functions, the internal energy, the specific heat, and the magnetic susceptibility are obtained from the effective Hamiltonian. We have also examined the modified spin-wave theory to derive the same physical properties. Finally, we have studied our model using quantum Monte Carlo simulation to obtain accurate results. The comparison of the above results and also the high temperature series expansion shows that cumulant expansion gives good results for moderate and high temperature regions while the modified spin wave theory is good for low temperatures. Moreover, the convergence regions of the cumulant expansion and the modified spin-wave theory overlap each other which propose these two as a set of complement methods to get the thermodynamic properties of spin models.
The low-energy structures of the quantum ferrimagnetic Heisenberg chain consisting of (5/2, 1/2, 1/2) trimers are investigated theoretically. The results of the linear spin-wave theory are compared with those from the numerical exact diagonalization calculation and the matrix product method for the lowest optical mode. The temperature behaviour of thermodynamical properties such as magnetic susceptibility, specific heat and entropy are analysed in the framework of the modified spin-wave theory. The results of the calculations are used to explain the experimental data obtained for the molecule-based heterospin magnets [Mn(hfac) 2 BNO R ] (R = H, F, Cl, Br) with one-dimensional chain structure.