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arXiv:cond-mat/9810112 · Physical review. B, Condensed matter

Magnetic properties of quantum ferrimagnetic spin chains

Shoji Yamamoto

Published Jan 1, 1999• 57 citations
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Abstract

Magnetic susceptibilities of spin-$(S,s)$ ferrimagnetic Heisenberg chains are numerically investigated. It is argued how the ferromagnetic and antiferromagnetic features of quantum ferrimagnets are exhibited as functions of $(S,s).$ Spin-$(S,s)$ ferrimagnetic chains behave similar to combinations of spin-$(S\ensuremath{-}s)$ ferromagnetic and spin-$(2s)$ antiferromagnetic chains provided $S=2s.$

DOI
10.1103/physrevb.59.1024

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Magnetic susceptibilities of spin-(S,s)(S,s)(S,s) ferrimagnetic Heisenberg chains are numerically investigated. It is argued how the ferromagnetic and antiferromagnetic features of quantum ferrimagnets are exhibited as functions of (S,s).(S,s).(S,s). Spin-(S,s)(S,s)(S,s) ferrimagnetic chains behave similar to combinations of spin-(S\ensuremath−s)(S\ensuremath{-}s)(S\ensuremath−s) ferromagnetic and spin-(2s)(2s)(2s) antiferromagnetic chains provided S=2s.S=2s.S=2s.
Energy spectra and thermodynamic quantities (partition function, entropy, specific heat, susceptibility) of ferrimagnetic Heisenberg chains, made up of two spin sublattices [(1/2-S], are discussed from the exact results computed for finite rings. Extrapolation of the theoretical data versus the length of finite rings N is discussed for S ranging from 1 to (5/2 and compared with previous reported findings for the [(1/2-\ensuremath{\infty}] spin chain. In the low-temperature region, similarities between the ferrimagnetic chains [(1/2-S] and the regular ferromagnetic ones (with spin S-(1/2) are used for the determination of the limiting curves.
We investigate the thermodynamic properties of Heisenberg ferrimagnetic mixed-spin chains both numerically and analytically with particular emphasis on the combination of ferromagnetic and antiferromagnetic features. Employing a new density-matrix renormalization-group technique as well as a quantum Monte Carlo method, we reveal the overall thermal behaviour: at very low temperatures, the specific heat and the magnetic susceptibility multiplied by the temperature behave like and , respectively, whereas at intermediate temperatures, they exhibit a Schottky-like peak and a minimum, respectively. Developing the modified spin-wave theory, we complement the numerical findings and give precise estimates for the low-temperature behaviour.
Static and dynamic structure factors of Heisenberg ferrimagnetic spin chains are numerically investigated. There exist two distinct branches of elementary excitations, which exhibit ferromagnetic and antiferromagnetic aspects. The ferromagnetic feature is smeared out with the increase of temperature, whereas the antiferromagnetic one persists up to higher temperatures. The scattering intensity is remarkably large at lower boundaries of the ferromagnetic and antiferromagnetic spectra. All these observations are consistent with the ferromagnetic-to-antiferromagnetic crossover in the thermal behavior which has recently been reported.
By means of the density matrix renormalization group (DMRG) method, the magnetic properties of the J-J-J′^{\prime}′ quantum Heisenberg chains with spin S=1/2S=1/2S=1/2, 1, 3/2 and 2 in the ground states are investigated in the presence of a magnetic field. Two different cases are considered: (a) when JJJ is antiferromagnetic and J′J^{\prime}J′ is ferromagnetic (i.e. the AF-AF-F chain), the system is a ferrimagnet. The plateaus of the magnetization are observed. It is found that the width of the plateaus decreases with increasing the ferromagnetic coupling, and disappears when % J^{\prime}/J passes over a critical value. The saturated field is observed to be independent of the ferromagnetic coupling; (b) when JJJ is ferromagnetic and J′J^{\prime}J′ is antiferromagnetic (i.e. the F-F-AF chain), the system becomes an antiferromagnet. The plateaus of the magnetization are also seen. The width of the plateaus decreases with decreasing the antiferromagnetic coupling, and disappears when $J^{\prime}/J $ passes over a critical value. Though the ground state properties are quite different, the magnetization plateaus in both cases tend to disappear when the ferromagnetic coupling becomes more dominant. Besides, no fundamental difference between the systems with spin half-integer and integer has been found.
We study quantum ferrimagnets in one, two, and three dimensions by using a variety of methods and approximations. These include: (i) a treatment based on the spin coherent state path-integral formulation of quantum ferrimagnets by taking into account the leading order quantum and thermal fluctuations (ii) a field-theoretical (non-linear σσσ-model type) formulation of the special case of one-dimensional quantum ferrimagnets at zero temperature (iii) an effective description in terms of dimers and quantum rotors, and (iv) a quantum renormalization group study of ferrimagnetic Heisenberg chains. Some of the formalism discussed here can be used for a unified treatment of both ferromagnets and antiferromagnets in the semiclassical limit. We show that the low (high) energy effective Hamiltonian of a (S_1, S_2) Heisenberg ferrimagnet is a ferromagnetic (antiferromagnetic) Heisenberg model. We also study the phase diagram of quantum ferrimagnets in the presence of an external magnetic field h (hc1<h<hc2h_{c1} < h < h_{c2}hc1​<h<hc2​) and show that the low- and the high-field phases correspond respectively to the classical Néel and the fully polarized ferromagnetic states. We also calculate the transition temperature for the Berezinskii-Kosterlitz-Thouless phase transition in the special case of two-dimensional quantum ferrimagnets.
This thesis is divided into 4 chapters. The first chapter gives a brief discussion on the need for the study of Quantum spin systems, and an introduction to Heisenberg Model. In the second chapter, we start the discussion with Quantum entanglement and then go on to show the importance of anti ferromagnetic ground state from the view of entanglement. In the third chapter, we discuss the ways to obtain the ground states of Heisenberg model, both ferromagnet and antiferromagnet. Then we discuss the effect of magnetic field on the antiferromagnetic ground states, for a good understanding of magnetic properties in Chapter(4). In the fourth and the final chapter, we discuss how Bonner Fisher model uses the Bethe ansatz to obtain all the properties of finite Heisenberg chains. Then we analyze the magnetic properties, like Magnetic moment and Susceptibility, of Heisenberg antiferromagnets for finite as well as infinite chains.