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arXiv:cond-mat/0010446 · Journal of Physics Condensed Matter

Coexistent quantum and classical aspects of magnetization plateaux in alternating-spin chains

Tôru Sakai, Shoji Yamamoto

Published Nov 6, 2000• 11 citations
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Abstract

The processes of magnetization of ferrimagnetic Heisenberg chains of alternating spins are studied theoretically. Size-scaling analysis with the exact diagonalization of finite systems for ( S , s ) = (3/2,1) and (2,1) indicates a multi-plateau structure in the ground-state magnetization curve for S and s >1/2. The first plateau in the spontaneous magnetization can be explained classically: as originating from the Ising gap. In contrast, the second and higher ones must be originating from the quantization of the magnetization. It is also found that all of the 2 s plateaux, both classical and quantum ones, appear even in the isotropic case with no bond alternation.

DOI
10.1088/0953-8984/12/47/306

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The processes of magnetization of ferrimagnetic Heisenberg chains of alternating spins are studied theoretically. Size-scaling analysis with the exact diagonalization of finite systems for ( S , s ) = (3/2,1) and (2,1) indicates a multi-plateau structure in the ground-state magnetization curve for S and s >1/2. The first plateau in the spontaneous magnetization can be explained classically: as originating from the Ising gap. In contrast, the second and higher ones must be originating from the quantization of the magnetization. It is also found that all of the 2 s plateaux, both classical and quantum ones, appear even in the isotropic case with no bond alternation.
The magnetization curve of the (S,s)=(1,1/2)(S,s)=(1,1/2)(S,s)=(1,1/2) ferrimagnetic alternating spin chain with single-ion anisotropy D is investigated with the numerical exact diagonalization of finite clusters and size-scaling analyses. The system has a plateau at (1/3) of the saturation moment, which corresponds to the spontaneous magnetization for D=0.D=0.D=0. Varying D in the 1/3-magnetized ground state under the external field along the axis of D, a quantum phase transition is revealed to occur at the critical value $D/J=1.114\ifmmode\pm\else\textpm\fi{}0.001$ where the plateau vanishes. Except for the critical point, the plateau is always opening, but the mechanism is different between D<DcD<{D}_{c}D<Dc​ and D>Dc.D>{D}_{c}.D>Dc​. The change of mechanisms is an evidence to clarify that the plateau originates from the quantization of magnetization.
Ground-state magnetization curves of ferrimagnetic Heisenberg chains of alternating spins S and s are numerically investigated. Calculating several cases of (S,s),(S,s),(S,s), we conclude that the spin-(S,s)(S,s)(S,s) chain generally exhibits 2s2s2s magnetization plateaus even at the most symmetric point. In the double- or more-plateau structure, the initial plateau is generated on a classical basis, whereas the higher ones are based on a quantum mechanism.
Using mainly numerical methods, we investigate the ground-state magnetization curve of a mixed spin chain with uniaxial single-ion anisotropies, where S = 1 and S = 2 spins are alternating and coupled antiferromagnetically. Special attention is paid to the magnetization plateau, the 1/3-plateau, which appears at one third of the saturation magnetization in the magnetization curve. It is found that there appear three kinds of 1/3-plateaux, one of which has a quantum nature, while the remaining two have a classical (Ising) nature.
The spin-1/2 Ising-Heisenberg branched chain composed of regularly alternating Ising spins and Heisenberg dimers involving an additional side branching is rigorously solved in a magnetic field by the transfer-matrix approach. The ground-state phase diagram, the magnetization process and the concurrence measuring a degree of bipartite entanglement within the Heisenberg dimers are examined in detail. Three different ground states were found depending on a mutual interplay between the magnetic field and two different coupling constants: the modulated quantum antiferromagnetic phase, the quantum ferrimagnetic phase, and the classical ferromagnetic phase. Two former quantum ground states are manifested in zero-temperature magnetization curves as intermediate plateaus at zero and one-half of the saturation magnetization, whereas the one-half plateau disappears at a triple point induced by a strong-enough ferromagnetic Ising coupling. The ground-state phase diagram and zero-temperature magnetization curves of the analogous spin-1/2 Heisenberg branched chain were investigated using density-matrix renormalization group calculations. The latter fully quantum Heisenberg model involves, besides two gapful phases manifested as zero and one-half magnetization plateaus, gapless quantum spin-liquid phase. The intermediate one-half plateau of the spin-1/2 Heisenberg branched chain vanishes at Kosterlitz-Thouless quantum critical point between gapful and gapless quantum ground states unlike the triple point of the spin-1/2 Ising-Heisenberg branched chain.
Employing numerical methods, we study the ground-state magnetization curve of a ( S , S ')=(1,2) spin-alternating chain with uniaxial single-ion anisotropies, where S =1 and S '=2 spins are alternating and coupled antiferromagnetically. Special attention is paid to the magnetization plateau, the one-third plateau, which appears at one third of the saturation magnetization in the ground-state magnetization curve. We find that three kinds of one-third plateaux appear, one of which has a quantum nature, while the remaining two have a classical (Ising) nature. We determine the one-third plateau phase diagram on the D 2 versus D 1 plane, where D 1 ( D 2 ) is the ratio of the single-ion anisotropy constant for the S =1 ( S '=2) spin to the exchange interaction constant. This phase diagram consists of a phase boundary line between the quantum and classical one-third plateau states as well as three phase boundary lines between the one-third plateau and plateauless states. We emphasize that there is no phase transition between two classical one-third plateau states and both states are regarded as a single phase. Furthermore, the region of the one-third plateauless phase is divided into two parts, that is, the region in which the one-third magnetization state is not realized at any magnetic field as the ground state, and the region in which it is realized but no one-third plateau appears in the ground-state magnetization curve.